X-Git-Url: http://git.liburcu.org/?a=blobdiff_plain;f=lttv%2Flttv%2Fsync%2Fevent_analysis_chull.c;h=154258e00effc5af9369dc13c1c036e2d999125a;hb=ab6edc6a1a55aefe52cfd9e610b5f21ee2029544;hp=1dc995b17da63a406b850cb317ce06d034837dac;hpb=8d7d16dd4f5f6ae09f556a9b0b477baaa93d468c;p=lttv.git

diff --git a/lttv/lttv/sync/event_analysis_chull.c b/lttv/lttv/sync/event_analysis_chull.c
index 1dc995b1..154258e0 100644
--- a/lttv/lttv/sync/event_analysis_chull.c
+++ b/lttv/lttv/sync/event_analysis_chull.c
@@ -1,19 +1,18 @@
 /* This file is part of the Linux Trace Toolkit viewer
- * Copyright (C) 2009 Benjamin Poirier <benjamin.poirier@polymtl.ca>
+ * Copyright (C) 2009, 2010 Benjamin Poirier <benjamin.poirier@polymtl.ca>
  *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License Version 2 as
- * published by the Free Software Foundation;
+ * This program is free software: you can redistribute it and/or modify it
+ * under the terms of the GNU Lesser General Public License as published by
+ * the Free Software Foundation, either version 2.1 of the License, or (at
+ * your option) any later version.
  *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
+ * This program is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+ * License for more details.
  *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
  */
 #define _ISOC99_SOURCE
 
@@ -22,10 +21,12 @@
 #endif
 
 #include <errno.h>
+#include <inttypes.h>
 #include <math.h>
 #include <float.h>
 #include <stdlib.h>
 #include <stdio.h>
+#include <string.h>
 #include <unistd.h>
 
 #include "sync_chain.h"
@@ -33,24 +34,27 @@
 #include "event_analysis_chull.h"
 
 
-#ifndef g_info
-#define g_info(format...) g_log (G_LOG_DOMAIN, G_LOG_LEVEL_INFO, format)
-#endif
-
-
 typedef enum
 {
 	LOWER,
 	UPPER
 } HullType;
 
-
 typedef enum
 {
 	MINIMUM,
 	MAXIMUM
 } LineType;
 
+#ifdef HAVE_LIBGLPK
+struct LPAddRowInfo
+{
+	glp_prob* lp;
+	int boundType;
+	GArray* iArray, * jArray, * aArray;
+};
+#endif
+
 
 // Functions common to all analysis modules
 static void initAnalysisCHull(SyncState* const syncState);
@@ -58,69 +62,91 @@ static void destroyAnalysisCHull(SyncState* const syncState);
 
 static void analyzeMessageCHull(SyncState* const syncState, Message* const
 	message);
-static GArray* finalizeAnalysisCHull(SyncState* const syncState);
+static AllFactors* finalizeAnalysisCHull(SyncState* const syncState);
 static void printAnalysisStatsCHull(SyncState* const syncState);
-static void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const
-	unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceForePlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j);
 
 // Functions specific to this module
-static void registerAnalysisCHull() __attribute__((constructor (101)));
-
 static void openGraphFiles(SyncState* const syncState);
 static void closeGraphFiles(SyncState* const syncState);
 static void writeGraphFiles(SyncState* const syncState);
 static void gfDumpHullToFile(gpointer data, gpointer userData);
 
+AllFactors* calculateAllFactors(struct _SyncState* const syncState);
+void calculateFactorsMiddle(PairFactors* const factors);
+static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
+	LineType lineType) __attribute__((pure));
+static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
+	PairFactors* const result);
 static void grahamScan(GQueue* const hull, Point* const newPoint, const
 	HullType type);
 static int jointCmp(const Point* const p1, const Point* const p2, const Point*
 	const p3) __attribute__((pure));
 static double crossProductK(const Point const* p1, const Point const* p2,
 	const Point const* p3, const Point const* p4) __attribute__((pure));
-static FactorsCHull** calculateAllFactors(SyncState* const syncState);
-static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
-	LineType lineType) __attribute__((pure));
-static void calculateFactorsMiddle(FactorsCHull* factors);
-static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
-	FactorsCHull* const result);
 static double slope(const Point* const p1, const Point* const p2)
 	__attribute__((pure));
 static double intercept(const Point* const p1, const Point* const p2)
 	__attribute__((pure));
-static GArray* reduceFactors(SyncState* const syncState, FactorsCHull**
-	allFactors);
-static void freeAllFactors(const SyncState* const syncState, FactorsCHull**
-	const allFactors);
 static double verticalDistance(Point* p1, Point* p2, Point* const point)
 	__attribute__((pure));
-static void floydWarshall(SyncState* const syncState, FactorsCHull** const
-	allFactors, double*** const distances, unsigned int*** const
-	predecessors);
-static void getFactors(FactorsCHull** const allFactors, unsigned int** const
-	predecessors, unsigned int* const references, const unsigned int traceNum,
-	Factors* const factors);
 
 static void gfPointDestroy(gpointer data, gpointer userData);
 
+// The next group of functions is only needed when computing synchronization
+// accuracy.
+#ifdef HAVE_LIBGLPK
+static AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState);
+static void writeAnalysisTraceTimeBackPlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTimeForePlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceBackPlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j);
+
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+	upperHull);
+static void gfLPAddRow(gpointer data, gpointer user_data);
+static Factors* calculateFactorsLP(glp_prob* const lp, const int direction);
+static void calculateCompleteFactorsLP(glp_prob* const lp, PairFactors*
+	factors);
+void timeCorrectionLP(glp_prob* const lp, const PairFactors* const lpFactors,
+	const uint64_t time, CorrectedTime* const correctedTime);
+
+static void gfAddAbsiscaToArray(gpointer data, gpointer user_data);
+static gint gcfCompareUint64(gconstpointer a, gconstpointer b);
+#else
+static inline AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState)
+{
+	return NULL;
+}
+#endif
+
+
 
 static AnalysisModule analysisModuleCHull= {
 	.name= "chull",
 	.initAnalysis= &initAnalysisCHull,
 	.destroyAnalysis= &destroyAnalysisCHull,
 	.analyzeMessage= &analyzeMessageCHull,
-	.analyzeExchange= NULL,
-	.analyzeBroadcast= NULL,
 	.finalizeAnalysis= &finalizeAnalysisCHull,
 	.printAnalysisStats= &printAnalysisStatsCHull,
-	.writeAnalysisGraphsPlots= &writeAnalysisGraphsPlotsCHull,
-	.writeAnalysisGraphsOptions= NULL,
+	.graphFunctions= {
+#ifdef HAVE_LIBGLPK
+		.writeTraceTimeBackPlots= &writeAnalysisTraceTimeBackPlotsCHull,
+		.writeTraceTimeForePlots= &writeAnalysisTraceTimeForePlotsCHull,
+		.writeTraceTraceBackPlots= &writeAnalysisTraceTraceBackPlotsCHull,
+#endif
+		.writeTraceTraceForePlots= &writeAnalysisTraceTraceForePlotsCHull,
+	}
 };
 
 
 /*
  * Analysis module registering function
  */
-static void registerAnalysisCHull()
+void registerAnalysisCHull()
 {
 	g_queue_push_tail(&analysisModules, &analysisModuleCHull);
 }
@@ -159,19 +185,19 @@ static void initAnalysisCHull(SyncState* const syncState)
 			analysisData->hullArray[i][j]= g_queue_new();
 		}
 	}
+#ifdef HAVE_LIBGLPK
+	analysisData->lps= NULL;
+#endif
 
 	if (syncState->stats)
 	{
-		analysisData->stats= malloc(sizeof(AnalysisStatsCHull));
-		analysisData->stats->dropped= 0;
-		analysisData->stats->allFactors= NULL;
+		analysisData->stats= calloc(1, sizeof(AnalysisStatsCHull));
 	}
 
 	if (syncState->graphsStream)
 	{
-		analysisData->graphsData= malloc(sizeof(AnalysisGraphsDataCHull));
+		analysisData->graphsData= calloc(1, sizeof(AnalysisGraphsDataCHull));
 		openGraphFiles(syncState);
-		analysisData->graphsData->allFactors= NULL;
 	}
 }
 
@@ -193,7 +219,7 @@ static void openGraphFiles(SyncState* const syncState)
 
 	analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
-	cwd= changeToGraphDir(syncState->graphsDir);
+	cwd= changeToGraphsDir(syncState->graphsDir);
 
 	analysisData->graphsData->hullPoints= malloc(syncState->traceNb *
 		sizeof(FILE**));
@@ -270,7 +296,7 @@ static void gfDumpHullToFile(gpointer data, gpointer userData)
 	Point* point;
 
 	point= (Point*) data;
-	fprintf((FILE*) userData, "%20llu %20llu\n", point->x, point->y);
+	fprintf((FILE*) userData, "%20" PRIu64 " %20" PRIu64 "\n", point->x, point->y);
 }
 
 
@@ -341,33 +367,59 @@ static void destroyAnalysisCHull(SyncState* const syncState)
 	{
 		for (j= 0; j < syncState->traceNb; j++)
 		{
-			g_queue_foreach(analysisData->hullArray[i][j], gfPointDestroy, NULL);
+			g_queue_foreach(analysisData->hullArray[i][j], gfPointDestroy,
+				NULL);
+			g_queue_free(analysisData->hullArray[i][j]);
 		}
 		free(analysisData->hullArray[i]);
 	}
 	free(analysisData->hullArray);
 
-	if (syncState->stats)
+#ifdef HAVE_LIBGLPK
+	if (analysisData->lps != NULL)
 	{
-		if (analysisData->stats->allFactors != NULL)
+		for (i= 0; i < syncState->traceNb; i++)
 		{
-			freeAllFactors(syncState, analysisData->stats->allFactors);
+			unsigned int j;
+
+			for (j= 0; j < i; j++)
+			{
+				// There seems to be a memory leak in glpk, valgrind reports a
+				// loss (reachable) even if the problem is deleted
+				glp_delete_prob(analysisData->lps[i][j]);
+			}
+			free(analysisData->lps[i]);
 		}
+		free(analysisData->lps);
+	}
+#endif
+
+	if (syncState->stats)
+	{
+		freeAllFactors(analysisData->stats->allFactors, syncState->traceNb);
+		freeAllFactors(analysisData->stats->geoFactors, syncState->traceNb);
+
+#ifdef HAVE_LIBGLPK
+		freeAllFactors(analysisData->stats->lpFactors, syncState->traceNb);
+#endif
 
 		free(analysisData->stats);
 	}
 
 	if (syncState->graphsStream)
 	{
-		if (analysisData->graphsData->hullPoints != NULL)
+		AnalysisGraphsDataCHull* graphs= analysisData->graphsData;
+
+		if (graphs->hullPoints != NULL)
 		{
 			closeGraphFiles(syncState);
 		}
 
-		if (!syncState->stats && analysisData->graphsData->allFactors != NULL)
-		{
-			freeAllFactors(syncState, analysisData->graphsData->allFactors);
-		}
+		freeAllFactors(graphs->allFactors, syncState->traceNb);
+
+#ifdef HAVE_LIBGLPK
+		freeAllFactors(graphs->lpFactors, syncState->traceNb);
+#endif
 
 		free(analysisData->graphsData);
 	}
@@ -400,7 +452,8 @@ static void analyzeMessageCHull(SyncState* const syncState, Message* const messa
 		newPoint->x= message->inE->cpuTime;
 		newPoint->y= message->outE->cpuTime;
 		hullType= UPPER;
-		g_debug("Reception point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
+		g_debug("Reception point hullArray[%lu][%lu] "
+			"x= inE->time= %" PRIu64 " y= outE->time= %" PRIu64,
 			message->inE->traceNum, message->outE->traceNum, newPoint->x,
 			newPoint->y);
 	}
@@ -410,7 +463,8 @@ static void analyzeMessageCHull(SyncState* const syncState, Message* const messa
 		newPoint->x= message->outE->cpuTime;
 		newPoint->y= message->inE->cpuTime;
 		hullType= LOWER;
-		g_debug("Send point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
+		g_debug("Send point hullArray[%lu][%lu] "
+			"x= inE->time= %" PRIu64 " y= outE->time= %" PRIu64,
 			message->inE->traceNum, message->outE->traceNum, newPoint->x,
 			newPoint->y);
 	}
@@ -500,13 +554,13 @@ static void grahamScan(GQueue* const hull, Point* const newPoint, const
  *   syncState     container for synchronization data.
  *
  * Returns:
- *   Factors[traceNb] synchronization factors for each trace
+ *   AllFactors*   synchronization factors for each trace pair, the caller is
+ *   responsible for freeing the structure
  */
-static GArray* finalizeAnalysisCHull(SyncState* const syncState)
+static AllFactors* finalizeAnalysisCHull(SyncState* const syncState)
 {
 	AnalysisDataCHull* analysisData;
-	GArray* factors;
-	FactorsCHull** allFactors;
+	AllFactors* geoFactors, * lpFactors;
 
 	analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
@@ -516,28 +570,50 @@ static GArray* finalizeAnalysisCHull(SyncState* const syncState)
 		closeGraphFiles(syncState);
 	}
 
-	allFactors= calculateAllFactors(syncState);
+	geoFactors= calculateAllFactors(syncState);
+	lpFactors= finalizeAnalysisCHullLP(syncState);
 
-	factors= reduceFactors(syncState, allFactors);
-
-	if (syncState->stats || syncState->graphsStream)
+	if (syncState->stats)
 	{
-		if (syncState->stats)
+		geoFactors->refCount++;
+		analysisData->stats->geoFactors= geoFactors;
+
+		if (lpFactors != NULL)
 		{
-			analysisData->stats->allFactors= allFactors;
+			lpFactors->refCount++;
+			analysisData->stats->allFactors= lpFactors;
 		}
+		else
+		{
+			geoFactors->refCount++;
+			analysisData->stats->allFactors= geoFactors;
+		}
+	}
 
-		if (syncState->graphsStream)
+	if (syncState->graphsStream)
+	{
+		if (lpFactors != NULL)
+		{
+			lpFactors->refCount++;
+			analysisData->graphsData->allFactors= lpFactors;
+		}
+		else
 		{
-			analysisData->graphsData->allFactors= allFactors;
+			geoFactors->refCount++;
+			analysisData->graphsData->allFactors= geoFactors;
 		}
 	}
+
+	if (lpFactors != NULL)
+	{
+		freeAllFactors(geoFactors, syncState->traceNb);
+		return lpFactors;
+	}
 	else
 	{
-		freeAllFactors(syncState, allFactors);
+		freeAllFactors(lpFactors, syncState->traceNb);
+		return geoFactors;
 	}
-
-	return factors;
 }
 
 
@@ -582,41 +658,38 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
 	{
 		for (j= i + 1; j < syncState->traceNb; j++)
 		{
-			FactorsCHull* factorsCHull;
+			PairFactors* factorsCHull;
 
-			factorsCHull= &analysisData->stats->allFactors[j][i];
-			printf("\t\t%3d - %-3d: ", i, j);
+			factorsCHull= &analysisData->stats->allFactors->pairFactors[j][i];
+			printf("\t\t%3d - %-3d: %s", i, j,
+				approxNames[factorsCHull->type]);
 
 			if (factorsCHull->type == EXACT)
 			{
-				printf("Exact      a0= % 7g a1= 1 %c %7g\n",
+				printf("      a0= % 7g a1= 1 %c %7g\n",
 					factorsCHull->approx->offset,
 					factorsCHull->approx->drift < 0. ? '-' : '+',
 					fabs(factorsCHull->approx->drift));
 			}
-			else if (factorsCHull->type == MIDDLE)
+			else if (factorsCHull->type == ACCURATE)
 			{
-				printf("Middle     a0= % 7g a1= 1 %c %7g accuracy %7g\n",
-					factorsCHull->approx->offset, factorsCHull->approx->drift
-					- 1. < 0. ? '-' : '+', fabs(factorsCHull->approx->drift -
-						1.), factorsCHull->accuracy);
-				printf("\t\t                      a0: % 7g to % 7g (delta= %7g)\n",
+				printf("\n\t\t                      a0: % 7g to % 7g (delta= %7g)\n",
 					factorsCHull->max->offset, factorsCHull->min->offset,
 					factorsCHull->min->offset - factorsCHull->max->offset);
 				printf("\t\t                      a1: 1 %+7g to %+7g (delta= %7g)\n",
 					factorsCHull->min->drift - 1., factorsCHull->max->drift -
 					1., factorsCHull->max->drift - factorsCHull->min->drift);
 			}
-			else if (factorsCHull->type == FALLBACK)
+			else if (factorsCHull->type == APPROXIMATE)
 			{
-				printf("Fallback   a0= % 7g a1= 1 %c %7g error= %7g\n",
+				printf("   a0= % 7g a1= 1 %c %7g error= %7g\n",
 					factorsCHull->approx->offset, factorsCHull->approx->drift
 					- 1. < 0. ? '-' : '+', fabs(factorsCHull->approx->drift -
 						1.), factorsCHull->accuracy);
 			}
 			else if (factorsCHull->type == INCOMPLETE)
 			{
-				printf("Incomplete\n");
+				printf("\n");
 
 				if (factorsCHull->min->drift != -INFINITY)
 				{
@@ -633,9 +706,9 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
 							1.));
 				}
 			}
-			else if (factorsCHull->type == SCREWED)
+			else if (factorsCHull->type == FAIL)
 			{
-				printf("Screwed\n");
+				printf("\n");
 
 				if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY)
 				{
@@ -654,7 +727,7 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
 			}
 			else if (factorsCHull->type == ABSENT)
 			{
-				printf("Absent\n");
+				printf("\n");
 			}
 			else
 			{
@@ -662,6 +735,47 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
 			}
 		}
 	}
+
+#ifdef HAVE_LIBGLPK
+	printf("\tFactor comparison:\n"
+		"\t\tTrace pair  Factors type  Differences (lp - chull)\n"
+		"\t\t                          a0                    a1\n"
+		"\t\t                          Min        Max        Min        Max\n");
+
+	for (i= 0; i < syncState->traceNb; i++)
+	{
+		for (j= 0; j < i; j++)
+		{
+			PairFactors* geoFactors=
+				&analysisData->stats->geoFactors->pairFactors[i][j];
+			PairFactors* lpFactors=
+				&analysisData->stats->lpFactors->pairFactors[i][j];
+
+			printf("\t\t%3d - %-3d   ", i, j);
+			if (lpFactors->type == geoFactors->type)
+			{
+				if (lpFactors->type == ACCURATE)
+				{
+					printf("%-13s %-10.4g %-10.4g %-10.4g %.4g\n",
+						approxNames[lpFactors->type],
+						lpFactors->min->offset - geoFactors->min->offset,
+						lpFactors->max->offset - geoFactors->max->offset,
+						lpFactors->min->drift - geoFactors->min->drift,
+						lpFactors->max->drift - geoFactors->max->drift);
+				}
+				else if (lpFactors->type == ABSENT)
+				{
+					printf("%s\n", approxNames[lpFactors->type]);
+				}
+			}
+			else
+			{
+				printf("Different! %s and %s\n", approxNames[lpFactors->type],
+					approxNames[geoFactors->type]);
+			}
+		}
+	}
+#endif
 }
 
 
@@ -701,7 +815,9 @@ static int jointCmp(const Point const* p1, const Point const* p2, const
 	const double fuzzFactor= 0.;
 
 	result= crossProductK(p1, p2, p1, p3);
-	g_debug("crossProductK(p1= (%llu, %llu), p2= (%llu, %llu), p1= (%llu, %llu), p3= (%llu, %llu))= %g",
+	g_debug("crossProductK(p1= (%" PRIu64 ", %" PRIu64 "), "
+		"p2= (%" PRIu64 ", %" PRIu64 "), p1= (%" PRIu64 ", %" PRIu64 "), "
+		"p3= (%" PRIu64 ", %" PRIu64 "))= %g",
 		p1->x, p1->y, p2->x, p2->y, p1->x, p1->y, p3->x, p3->y, result);
 	if (result < fuzzFactor)
 	{
@@ -738,55 +854,6 @@ static double crossProductK(const Point const* p1, const Point const* p2,
 }
 
 
-/*
- * Free a container of FactorsCHull
- *
- * Args:
- *   syncState:     container for synchronization data.
- *   allFactors:   container of Factors
- */
-static void freeAllFactors(const SyncState* const syncState, FactorsCHull**
-	const allFactors)
-{
-	unsigned int i, j;
-
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		for (j= 0; j <= i; j++)
-		{
-			FactorsCHull* factorsCHull;
-
-			factorsCHull= &allFactors[i][j];
-			if (factorsCHull->type == MIDDLE || factorsCHull->type ==
-				INCOMPLETE || factorsCHull->type == ABSENT)
-			{
-				free(factorsCHull->min);
-				free(factorsCHull->max);
-			}
-			else if (factorsCHull->type == SCREWED)
-			{
-				if (factorsCHull->min != NULL)
-				{
-					free(factorsCHull->min);
-				}
-				if (factorsCHull->max != NULL)
-				{
-					free(factorsCHull->max);
-				}
-			}
-
-			if (factorsCHull->type == EXACT || factorsCHull->type == MIDDLE ||
-				factorsCHull->type == FALLBACK)
-			{
-				free(factorsCHull->approx);
-			}
-		}
-		free(allFactors[i]);
-	}
-	free(allFactors);
-}
-
-
 /*
  * Analyze the convex hulls to determine the synchronization factors between
  * each pair of trace.
@@ -795,28 +862,21 @@ static void freeAllFactors(const SyncState* const syncState, FactorsCHull**
  *   syncState     container for synchronization data.
  *
  * Returns:
- *   FactorsCHull*[TraceNum][TraceNum] array. See the documentation for the
- *   member allFactors of AnalysisStatsCHull.
+ *   AllFactors*, see the documentation for the member geoFactors of
+ *   AnalysisStatsCHull.
  */
-static FactorsCHull** calculateAllFactors(SyncState* const syncState)
+AllFactors* calculateAllFactors(SyncState* const syncState)
 {
 	unsigned int traceNumA, traceNumB;
-	FactorsCHull** allFactors;
+	AllFactors* geoFactors;
 	AnalysisDataCHull* analysisData;
 
 	analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
-	// Allocate allFactors and calculate min and max
-	allFactors= malloc(syncState->traceNb * sizeof(FactorsCHull*));
+	// Allocate geoFactors and calculate min and max
+	geoFactors= createAllFactors(syncState->traceNb);
 	for (traceNumA= 0; traceNumA < syncState->traceNb; traceNumA++)
 	{
-		allFactors[traceNumA]= malloc((traceNumA + 1) * sizeof(FactorsCHull));
-
-		allFactors[traceNumA][traceNumA].type= EXACT;
-		allFactors[traceNumA][traceNumA].approx= malloc(sizeof(Factors));
-		allFactors[traceNumA][traceNumA].approx->drift= 1.;
-		allFactors[traceNumA][traceNumA].approx->offset= 0.;
-
 		for (traceNumB= 0; traceNumB < traceNumA; traceNumB++)
 		{
 			unsigned int i;
@@ -826,8 +886,8 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
 				LineType lineType;
 				size_t factorsOffset;
 			} loopValues[]= {
-				{MINIMUM, offsetof(FactorsCHull, min)},
-				{MAXIMUM, offsetof(FactorsCHull, max)}
+				{MINIMUM, offsetof(PairFactors, min)},
+				{MAXIMUM, offsetof(PairFactors, max)}
 			};
 
 			cr= analysisData->hullArray[traceNumB][traceNumA];
@@ -835,12 +895,14 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
 
 			for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
 			{
-				g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
+				g_debug("geoFactors[%u][%u].%s = calculateFactorsExact(cr= "
+					"hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
 					traceNumA, traceNumB, loopValues[i].factorsOffset ==
-					offsetof(FactorsCHull, min) ? "min" : "max", traceNumB,
+					offsetof(PairFactors, min) ? "min" : "max", traceNumB,
 					traceNumA, traceNumA, traceNumB, loopValues[i].lineType ==
 					MINIMUM ? "MINIMUM" : "MAXIMUM");
-				*((Factors**) ((void*) &allFactors[traceNumA][traceNumB] +
+				*((Factors**) ((void*)
+						&geoFactors->pairFactors[traceNumA][traceNumB] +
 						loopValues[i].factorsOffset))=
 					calculateFactorsExact(cr, cs, loopValues[i].lineType);
 			}
@@ -852,22 +914,22 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
 	{
 		for (traceNumB= 0; traceNumB < traceNumA; traceNumB++)
 		{
-			FactorsCHull* factorsCHull;
+			PairFactors* factorsCHull;
 
-			factorsCHull= &allFactors[traceNumA][traceNumB];
+			factorsCHull= &geoFactors->pairFactors[traceNumA][traceNumB];
 			if (factorsCHull->min == NULL && factorsCHull->max == NULL)
 			{
-				factorsCHull->type= FALLBACK;
+				factorsCHull->type= APPROXIMATE;
 				calculateFactorsFallback(analysisData->hullArray[traceNumB][traceNumA],
 					analysisData->hullArray[traceNumA][traceNumB],
-					&allFactors[traceNumA][traceNumB]);
+					&geoFactors->pairFactors[traceNumA][traceNumB]);
 			}
 			else if (factorsCHull->min != NULL && factorsCHull->max != NULL)
 			{
 				if (factorsCHull->min->drift != -INFINITY &&
 					factorsCHull->max->drift != INFINITY)
 				{
-					factorsCHull->type= MIDDLE;
+					factorsCHull->type= ACCURATE;
 					calculateFactorsMiddle(factorsCHull);
 				}
 				else if (factorsCHull->min->drift != -INFINITY ||
@@ -883,12 +945,12 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
 			else
 			{
 				//g_assert_not_reached();
-				factorsCHull->type= SCREWED;
+				factorsCHull->type= FAIL;
 			}
 		}
 	}
 
-	return allFactors;
+	return geoFactors;
 }
 
 
@@ -908,7 +970,7 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
  * Args:
  *   factors:      contains the min and max limits, used to store the result
  */
-static void calculateFactorsMiddle(FactorsCHull* factors)
+void calculateFactorsMiddle(PairFactors* const factors)
 {
 	double amin, amax, bmin, bmax, bhat;
 
@@ -917,7 +979,7 @@ static void calculateFactorsMiddle(FactorsCHull* factors)
 	bmin= factors->min->drift;
 	bmax= factors->max->drift;
 
-	g_assert_cmpfloat(bmax, >, bmin);
+	g_assert_cmpfloat(bmax, >=, bmin);
 
 	factors->approx= malloc(sizeof(Factors));
 	bhat= (bmax * bmin - 1. + sqrt(1. + pow(bmax, 2.) * pow(bmin, 2.) +
@@ -1064,14 +1126,15 @@ static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
 	p1= g_queue_peek_nth(c1, i1);
 	p2= g_queue_peek_nth(c2, i2);
 
-	g_debug("Resulting points are: c1[i1]: x= %llu y= %llu c2[i2]: x= %llu y= %llu",
-		p1->x, p1->y, p2->x, p2->y);
+	g_debug("Resulting points are: c1[i1]: x= %" PRIu64 " y= %" PRIu64
+		" c2[i2]: x= %" PRIu64 " y= %" PRIu64 "", p1->x, p1->y, p2->x, p2->y);
 
 	result= malloc(sizeof(Factors));
 	result->drift= slope(p1, p2);
 	result->offset= intercept(p1, p2);
 
-	g_debug("Resulting factors are: drift= %g offset= %g", result->drift, result->offset);
+	g_debug("Resulting factors are: drift= %g offset= %g", result->drift,
+		result->offset);
 
 	return result;
 }
@@ -1103,7 +1166,7 @@ static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
  *                 will be stored
  */
 static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
-	FactorsCHull* const result)
+	PairFactors* const result)
 {
 	unsigned int i, j, k;
 	double errorMin;
@@ -1210,314 +1273,6 @@ static double intercept(const Point* const p1, const Point* const p2)
 }
 
 
-/*
- * Calculate a resulting offset and drift for each trace.
- *
- * Traces are assembled in groups. A group is an "island" of nodes/traces that
- * exchanged messages. A reference is determined for each group by using a
- * shortest path search based on the accuracy of the approximation. This also
- * forms a tree of the best way to relate each node's clock to the reference's
- * based on the accuracy. Sometimes it may be necessary or advantageous to
- * propagate the factors through intermediary clocks. Resulting factors for
- * each trace are determined based on this tree.
- *
- * This part was not the focus of my research. The algorithm used here is
- * inexact in some ways:
- * 1) The reference used may not actually be the best one to use. This is
- *    because the accuracy is not corrected based on the drift during the
- *    shortest path search.
- * 2) The min and max factors are not propagated and are no longer valid.
- * 3) Approximations of different types (MIDDLE and FALLBACK) are compared
- *    together. The "accuracy" parameters of these have different meanings and
- *    are not readily comparable.
- *
- * Nevertheless, the result is satisfactory. You just can't tell "how much" it
- * is.
- *
- * Two alternative (and subtly different) ways of propagating factors to
- * preserve min and max bondaries have been proposed, see:
- * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time
- * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing
- * Systems, Berlin, volume 18, 1987] p.304
- *
- * [Jezequel, J.M., and Jard, C.: Building a global clock for observing
- * computations in distributed memory parallel computers, Concurrency:
- * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester,
- * 1996, 32] Section 5; which is mostly the same as
- * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings
- * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume
- * 392, 136–147, 1989] Section 5
- *
- * Args:
- *   syncState:    container for synchronization data.
- *   allFactors:   offset and drift between each pair of traces
- *
- * Returns:
- *   Factors[traceNb] synchronization factors for each trace
- */
-static GArray* reduceFactors(SyncState* const syncState, FactorsCHull** const
-	allFactors)
-{
-	GArray* factors;
-	double** distances;
-	unsigned int** predecessors;
-	double* distanceSums;
-	unsigned int* references;
-	unsigned int i, j;
-
-	// Solve the all-pairs shortest path problem using the Floyd-Warshall
-	// algorithm
-	floydWarshall(syncState, allFactors, &distances, &predecessors);
-
-	/* Find the reference for each node
-	 *
-	 * First calculate, for each node, the sum of the distances to each other
-	 * node it can reach.
-	 *
-	 * Then, go through each "island" of traces to find the trace that has the
-	 * lowest distance sum. Assign this trace as the reference to each trace
-	 * of the island.
-	 */
-	distanceSums= malloc(syncState->traceNb * sizeof(double));
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		distanceSums[i]= 0.;
-		for (j= 0; j < syncState->traceNb; j++)
-		{
-			distanceSums[i]+= distances[i][j];
-		}
-	}
-
-	references= malloc(syncState->traceNb * sizeof(unsigned int));
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		references[i]= UINT_MAX;
-	}
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		if (references[i] == UINT_MAX)
-		{
-			unsigned int reference;
-			double distanceSumMin;
-
-			// A node is its own reference by default
-			reference= i;
-			distanceSumMin= INFINITY;
-			for (j= 0; j < syncState->traceNb; j++)
-			{
-				if (distances[i][j] != INFINITY && distanceSums[j] <
-					distanceSumMin)
-				{
-					reference= j;
-					distanceSumMin= distanceSums[j];
-				}
-			}
-			for (j= 0; j < syncState->traceNb; j++)
-			{
-				if (distances[i][j] != INFINITY)
-				{
-					references[j]= reference;
-				}
-			}
-		}
-	}
-
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		free(distances[i]);
-	}
-	free(distances);
-	free(distanceSums);
-
-	/* For each trace, calculate the factors based on their corresponding
-	 * tree. The tree is rooted at the reference and the shortest path to each
-	 * other nodes are the branches.
-	 */
-	factors= g_array_sized_new(FALSE, FALSE, sizeof(Factors),
-		syncState->traceNb);
-	g_array_set_size(factors, syncState->traceNb);
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		getFactors(allFactors, predecessors, references, i, &g_array_index(factors,
-				Factors, i));
-	}
-
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		free(predecessors[i]);
-	}
-	free(predecessors);
-	free(references);
-
-	return factors;
-}
-
-
-/*
- * Perform an all-source shortest path search using the Floyd-Warshall
- * algorithm.
- *
- * The algorithm is implemented accoding to the description here:
- * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html
- *
- * Args:
- *   syncState:    container for synchronization data.
- *   allFactors:   offset and drift between each pair of traces
- *   distances:    resulting matrix of the length of the shortest path between
- *                 two nodes. If there is no path between two nodes, the
- *                 length is INFINITY
- *   predecessors: resulting matrix of each node's predecessor on the shortest
- *                 path between two nodes
- */
-static void floydWarshall(SyncState* const syncState, FactorsCHull** const
-	allFactors, double*** const distances, unsigned int*** const
-	predecessors)
-{
-	unsigned int i, j, k;
-
-	// Setup initial conditions
-	*distances= malloc(syncState->traceNb * sizeof(double*));
-	*predecessors= malloc(syncState->traceNb * sizeof(unsigned int*));
-	for (i= 0; i < syncState->traceNb; i++)
-	{
-		(*distances)[i]= malloc(syncState->traceNb * sizeof(double));
-		for (j= 0; j < syncState->traceNb; j++)
-		{
-			if (i == j)
-			{
-				g_assert(allFactors[i][j].type == EXACT);
-
-				(*distances)[i][j]= 0.;
-			}
-			else
-			{
-				unsigned int row, col;
-
-				if (i > j)
-				{
-					row= i;
-					col= j;
-				}
-				else if (i < j)
-				{
-					row= j;
-					col= i;
-				}
-
-				if (allFactors[row][col].type == MIDDLE ||
-					allFactors[row][col].type == FALLBACK)
-				{
-					(*distances)[i][j]= allFactors[row][col].accuracy;
-				}
-				else if (allFactors[row][col].type == INCOMPLETE ||
-					allFactors[row][col].type == SCREWED ||
-					allFactors[row][col].type == ABSENT)
-				{
-					(*distances)[i][j]= INFINITY;
-				}
-				else
-				{
-					g_assert_not_reached();
-				}
-			}
-		}
-
-		(*predecessors)[i]= malloc(syncState->traceNb * sizeof(unsigned int));
-		for (j= 0; j < syncState->traceNb; j++)
-		{
-			if (i != j)
-			{
-				(*predecessors)[i][j]= i;
-			}
-			else
-			{
-				(*predecessors)[i][j]= UINT_MAX;
-			}
-		}
-	}
-
-	// Run the iterations
-	for (k= 0; k < syncState->traceNb; k++)
-	{
-		for (i= 0; i < syncState->traceNb; i++)
-		{
-			for (j= 0; j < syncState->traceNb; j++)
-			{
-				double distanceMin;
-
-				distanceMin= MIN((*distances)[i][j], (*distances)[i][k] +
-					(*distances)[k][j]);
-
-				if (distanceMin != (*distances)[i][j])
-				{
-					(*predecessors)[i][j]= (*predecessors)[k][j];
-				}
-
-				(*distances)[i][j]= distanceMin;
-			}
-		}
-	}
-}
-
-
-/*
- * Cummulate the time correction factors to convert a node's time to its
- * reference's time.
- * This function recursively calls itself until it reaches the reference node.
- *
- * Args:
- *   allFactors:   offset and drift between each pair of traces
- *   predecessors: matrix of each node's predecessor on the shortest
- *                 path between two nodes
- *   references:   reference node for each node
- *   traceNum:     node for which to find the factors
- *   factors:      resulting factors
- */
-static void getFactors(FactorsCHull** const allFactors, unsigned int** const
-	predecessors, unsigned int* const references, const unsigned int traceNum,
-	Factors* const factors)
-{
-	unsigned int reference;
-
-	reference= references[traceNum];
-
-	if (reference == traceNum)
-	{
-		factors->offset= 0.;
-		factors->drift= 1.;
-	}
-	else
-	{
-		Factors previousVertexFactors;
-
-		getFactors(allFactors, predecessors, references,
-			predecessors[reference][traceNum], &previousVertexFactors);
-
-		// convertir de traceNum à reference
-
-		// allFactors convertit de col à row
-
-		if (reference > traceNum)
-		{
-			factors->offset= previousVertexFactors.drift *
-				allFactors[reference][traceNum].approx->offset +
-				previousVertexFactors.offset;
-			factors->drift= previousVertexFactors.drift *
-				allFactors[reference][traceNum].approx->drift;
-		}
-		else
-		{
-			factors->offset= previousVertexFactors.drift * (-1. *
-				allFactors[traceNum][reference].approx->offset /
-				allFactors[traceNum][reference].approx->drift) +
-				previousVertexFactors.offset;
-			factors->drift= previousVertexFactors.drift * (1. /
-				allFactors[traceNum][reference].approx->drift);
-		}
-	}
-}
-
-
 /*
  * Write the analysis-specific graph lines in the gnuplot script.
  *
@@ -1526,11 +1281,11 @@ static void getFactors(FactorsCHull** const allFactors, unsigned int** const
  *   i:            first trace number
  *   j:            second trace number, garanteed to be larger than i
  */
-void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
+void writeAnalysisTraceTraceForePlotsCHull(SyncState* const syncState, const unsigned
 	int i, const unsigned int j)
 {
 	AnalysisDataCHull* analysisData;
-	FactorsCHull* factorsCHull;
+	PairFactors* factorsCHull;
 
 	analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
@@ -1543,7 +1298,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
 			"linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n",
 		i, j);
 
-	factorsCHull= &analysisData->graphsData->allFactors[j][i];
+	factorsCHull= &analysisData->graphsData->allFactors->pairFactors[j][i];
 	if (factorsCHull->type == EXACT)
 	{
 		fprintf(syncState->graphsStream,
@@ -1552,7 +1307,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
 				"linecolor rgb \"black\" linetype 1, \\\n",
 				factorsCHull->approx->offset, factorsCHull->approx->drift);
 	}
-	else if (factorsCHull->type == MIDDLE)
+	else if (factorsCHull->type == ACCURATE)
 	{
 		fprintf(syncState->graphsStream,
 			"\t%.2f + %.10f * x "
@@ -1567,10 +1322,10 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
 		fprintf(syncState->graphsStream,
 			"\t%.2f + %.10f * x "
 				"title \"Middle conversion\" with lines "
-				"linecolor rgb \"gray60\" linetype 1, \\\n",
+				"linecolor rgb \"black\" linetype 1, \\\n",
 				factorsCHull->approx->offset, factorsCHull->approx->drift);
 	}
-	else if (factorsCHull->type == FALLBACK)
+	else if (factorsCHull->type == APPROXIMATE)
 	{
 		fprintf(syncState->graphsStream,
 			"\t%.2f + %.10f * x "
@@ -1598,7 +1353,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
 					factorsCHull->max->offset, factorsCHull->max->drift);
 		}
 	}
-	else if (factorsCHull->type == SCREWED)
+	else if (factorsCHull->type == FAIL)
 	{
 		if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY)
 		{
@@ -1626,3 +1381,480 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
 		g_assert_not_reached();
 	}
 }
+
+
+#ifdef HAVE_LIBGLPK
+/*
+ * Create the linear programming problem containing the constraints defined by
+ * two half-hulls. The objective function and optimization directions are not
+ * written.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ * Returns:
+ *   A new glp_prob*, this problem must be freed by the caller with
+ *   glp_delete_prob()
+ */
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+	upperHull)
+{
+	unsigned int it;
+	const int zero= 0;
+	const double zeroD= 0.;
+	glp_prob* lp= glp_create_prob();
+	unsigned int hullPointNb= g_queue_get_length(lowerHull) +
+		g_queue_get_length(upperHull);
+	GArray* iArray= g_array_sized_new(FALSE, FALSE, sizeof(int), hullPointNb +
+		1);
+	GArray* jArray= g_array_sized_new(FALSE, FALSE, sizeof(int), hullPointNb +
+		1);
+	GArray* aArray= g_array_sized_new(FALSE, FALSE, sizeof(double),
+		hullPointNb + 1);
+	struct {
+		GQueue* hull;
+		struct LPAddRowInfo rowInfo;
+	} loopValues[2]= {
+		{lowerHull, {lp, GLP_UP, iArray, jArray, aArray}},
+		{upperHull, {lp, GLP_LO, iArray, jArray, aArray}},
+	};
+
+	// Create the LP problem
+	glp_term_out(GLP_OFF);
+	if (hullPointNb > 0)
+	{
+		glp_add_rows(lp, hullPointNb);
+	}
+	glp_add_cols(lp, 2);
+
+	glp_set_col_name(lp, 1, "a0");
+	glp_set_col_bnds(lp, 1, GLP_FR, 0., 0.);
+	glp_set_col_name(lp, 2, "a1");
+	glp_set_col_bnds(lp, 2, GLP_LO, 0., 0.);
+
+	// Add row constraints
+	g_array_append_val(iArray, zero);
+	g_array_append_val(jArray, zero);
+	g_array_append_val(aArray, zeroD);
+
+	for (it= 0; it < sizeof(loopValues) / sizeof(*loopValues); it++)
+	{
+		g_queue_foreach(loopValues[it].hull, &gfLPAddRow,
+			&loopValues[it].rowInfo);
+	}
+
+	g_assert_cmpuint(iArray->len, ==, jArray->len);
+	g_assert_cmpuint(jArray->len, ==, aArray->len);
+	g_assert_cmpuint(aArray->len - 1, ==, hullPointNb * 2);
+
+	glp_load_matrix(lp, aArray->len - 1, &g_array_index(iArray, int, 0),
+		&g_array_index(jArray, int, 0), &g_array_index(aArray, double, 0));
+
+	glp_scale_prob(lp, GLP_SF_AUTO);
+
+	g_array_free(iArray, TRUE);
+	g_array_free(jArray, TRUE);
+	g_array_free(aArray, TRUE);
+
+	return lp;
+}
+
+
+/*
+ * A GFunc for g_queue_foreach(). Add constraints and bounds for one row.
+ *
+ * Args:
+ *   data          Point*, synchronization point for which to add an LP row
+ *                 (a constraint)
+ *   user_data     LPAddRowInfo*
+ */
+static void gfLPAddRow(gpointer data, gpointer user_data)
+{
+	Point* p= data;
+	struct LPAddRowInfo* rowInfo= user_data;
+	int indexes[2];
+	double constraints[2];
+
+	indexes[0]= g_array_index(rowInfo->iArray, int, rowInfo->iArray->len - 1) + 1;
+	indexes[1]= indexes[0];
+
+	if (rowInfo->boundType == GLP_UP)
+	{
+		glp_set_row_bnds(rowInfo->lp, indexes[0], GLP_UP, 0., p->y);
+	}
+	else if (rowInfo->boundType == GLP_LO)
+	{
+		glp_set_row_bnds(rowInfo->lp, indexes[0], GLP_LO, p->y, 0.);
+	}
+	else
+	{
+		g_assert_not_reached();
+	}
+
+	g_array_append_vals(rowInfo->iArray, indexes, 2);
+	indexes[0]= 1;
+	indexes[1]= 2;
+	g_array_append_vals(rowInfo->jArray, indexes, 2);
+	constraints[0]= 1.;
+	constraints[1]= p->x;
+	g_array_append_vals(rowInfo->aArray, constraints, 2);
+}
+
+
+/*
+ * Calculate min or max correction factors (as possible) using an LP problem.
+ *
+ * Args:
+ *   lp:           A linear programming problem with constraints and bounds
+ *                 initialized.
+ *   direction:    The type of factors desired. Use GLP_MAX for max
+ *                 approximation factors (a1, the drift or slope is the
+ *                 largest) and GLP_MIN in the other case.
+ *
+ * Returns:
+ *   If the calculation was successful, a new Factors struct. Otherwise, NULL.
+ *   The calculation will fail if the hull assumptions are not respected.
+ */
+static Factors* calculateFactorsLP(glp_prob* const lp, const int direction)
+{
+	int retval, status;
+	Factors* factors;
+
+	glp_set_obj_coef(lp, 1, 0.);
+	glp_set_obj_coef(lp, 2, 1.);
+
+	glp_set_obj_dir(lp, direction);
+	retval= glp_simplex(lp, NULL);
+	status= glp_get_status(lp);
+
+	if (retval == 0 && status == GLP_OPT)
+	{
+		factors= malloc(sizeof(Factors));
+		factors->offset= glp_get_col_prim(lp, 1);
+		factors->drift= glp_get_col_prim(lp, 2);
+	}
+	else
+	{
+		factors= NULL;
+	}
+
+	return factors;
+}
+
+
+/*
+ * Calculate min, max and approx correction factors (as possible) using an LP
+ * problem.
+ *
+ * Args:
+ *   lp            A linear programming problem with constraints and bounds
+ *                 initialized.
+ *   factors       Resulting factors, must be preallocated
+ */
+static void calculateCompleteFactorsLP(glp_prob* const lp, PairFactors* factors)
+{
+	factors->min= calculateFactorsLP(lp, GLP_MIN);
+	factors->max= calculateFactorsLP(lp, GLP_MAX);
+
+	if (factors->min && factors->max)
+	{
+		factors->type= ACCURATE;
+		calculateFactorsMiddle(factors);
+	}
+	else if (factors->min || factors->max)
+	{
+		factors->type= INCOMPLETE;
+	}
+	else
+	{
+		factors->type= ABSENT;
+	}
+}
+
+
+/*
+ * A GFunc for g_queue_foreach()
+ *
+ * Args:
+ *   data          Point*, a convex hull point
+ *   user_data     GArray*, an array of convex hull point absisca values, as
+ *                 uint64_t
+ */
+static void gfAddAbsiscaToArray(gpointer data, gpointer user_data)
+{
+	Point* p= data;
+	GArray* a= user_data;
+	uint64_t v= p->x;
+
+	g_array_append_val(a, v);
+}
+
+
+/*
+ * A GCompareFunc for g_array_sort()
+ *
+ * Args:
+ *   a, b          uint64_t*, absisca values
+ *
+ * Returns:
+ *   "returns less than zero for first arg is less than second arg, zero for
+ *   equal, greater zero if first arg is greater than second arg"
+ *   - the great glib documentation
+ */
+static gint gcfCompareUint64(gconstpointer a, gconstpointer b)
+{
+	if (*(uint64_t*) a < *(uint64_t*) b)
+	{
+		return -1;
+	}
+	else if (*(uint64_t*) a > *(uint64_t*) b)
+	{
+		return 1;
+	}
+	else
+	{
+		return 0;
+	}
+}
+
+
+/*
+ * Compute synchronization factors using a linear programming approach.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ */
+static AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState)
+{
+	AnalysisDataCHull* analysisData= syncState->analysisData;
+	unsigned int i, j;
+	AllFactors* lpFactorsArray;
+
+	lpFactorsArray= createAllFactors(syncState->traceNb);
+	
+	analysisData->lps= malloc(syncState->traceNb * sizeof(glp_prob**));
+	for (i= 0; i < syncState->traceNb; i++)
+	{
+		analysisData->lps[i]= malloc(i * sizeof(glp_prob*));
+	}
+
+	for (i= 0; i < syncState->traceNb; i++)
+	{
+		for (j= 0; j < i; j++)
+		{
+			glp_prob* lp;
+			unsigned int it;
+			GQueue*** hullArray= analysisData->hullArray;
+			PairFactors* lpFactors= &lpFactorsArray->pairFactors[i][j];
+
+			// Create the LP problem
+			lp= lpCreateProblem(hullArray[i][j], hullArray[j][i]);
+			analysisData->lps[i][j]= lp;
+
+			// Use the LP problem to find the correction factors for this pair of
+			// traces
+			calculateCompleteFactorsLP(lp, lpFactors);
+
+			// If possible, compute synchronization accuracy information for
+			// graphs
+			if (syncState->graphsStream && lpFactors->type == ACCURATE)
+			{
+				int retval;
+				char* cwd;
+				char fileName[43];
+				FILE* fp;
+				GArray* xValues;
+
+				// Open the data file
+				snprintf(fileName, sizeof(fileName),
+					"analysis_chull_accuracy-%03u_and_%03u.data", j, i);
+				fileName[sizeof(fileName) - 1]= '\0';
+
+				cwd= changeToGraphsDir(syncState->graphsDir);
+
+				if ((fp= fopen(fileName, "w")) == NULL)
+				{
+					g_error(strerror(errno));
+				}
+				fprintf(fp, "#%-24s %-25s %-25s %-25s\n", "x", "middle", "min", "max");
+
+				retval= chdir(cwd);
+				if (retval == -1)
+				{
+					g_error(strerror(errno));
+				}
+				free(cwd);
+
+				// Build the list of absisca values for the points in the accuracy graph
+				xValues= g_array_sized_new(FALSE, FALSE, sizeof(uint64_t),
+					g_queue_get_length(hullArray[i][j]) +
+					g_queue_get_length(hullArray[j][i]));
+
+				g_queue_foreach(hullArray[i][j], &gfAddAbsiscaToArray, xValues);
+				g_queue_foreach(hullArray[j][i], &gfAddAbsiscaToArray, xValues);
+
+				g_array_sort(xValues, &gcfCompareUint64);
+
+				/* For each absisca value and each optimisation direction, solve the LP
+				 * and write a line in the data file */
+				for (it= 0; it < xValues->len; it++)
+				{
+					uint64_t time;
+					CorrectedTime correctedTime;
+
+					time= g_array_index(xValues, uint64_t, it);
+					timeCorrectionLP(lp, lpFactors, time, &correctedTime);
+					fprintf(fp, "%24" PRIu64 " %24" PRIu64 " %24" PRIu64
+						"%24" PRIu64 "\n", time, correctedTime.time,
+						correctedTime.min, correctedTime.max);
+				}
+
+				g_array_free(xValues, TRUE);
+				fclose(fp);
+			}
+		}
+	}
+
+	if (syncState->stats)
+	{
+		lpFactorsArray->refCount++;
+		analysisData->stats->lpFactors= lpFactorsArray;
+	}
+
+	if (syncState->graphsStream)
+	{
+		lpFactorsArray->refCount++;
+		analysisData->graphsData->lpFactors= lpFactorsArray;
+	}
+
+	return lpFactorsArray;
+}
+
+
+/*
+ * Perform correction on one time value and calculate accuracy bounds.
+ *
+ * Args:
+ *   lp:           Linear Programming problem containing the coefficients for
+ *                 the trace pair between which to perform time correction.
+ *   lpFactors:    Correction factors for this trace pair, the factors must be
+ *                 of type ACCURATE.
+ *   time:         Time value to correct.
+ *   correctedTime: Result of the time correction, preallocated.
+ */
+void timeCorrectionLP(glp_prob* const lp, const PairFactors* const lpFactors,
+	const uint64_t time, CorrectedTime* const correctedTime)
+{
+	unsigned int it;
+	const struct
+	{
+		int direction;
+		size_t offset;
+	} loopValues[]= {
+		{GLP_MIN, offsetof(CorrectedTime, min)},
+		{GLP_MAX, offsetof(CorrectedTime, max)}
+	};
+
+	glp_set_obj_coef(lp, 1, 1.);
+	glp_set_obj_coef(lp, 2, time);
+
+	g_assert(lpFactors->type == ACCURATE);
+
+	correctedTime->time= lpFactors->approx->offset + lpFactors->approx->drift
+		* time;
+
+	for (it= 0; it < ARRAY_SIZE(loopValues); it++)
+	{
+		int status;
+		int retval;
+
+		glp_set_obj_dir(lp, loopValues[it].direction);
+		retval= glp_simplex(lp, NULL);
+		status= glp_get_status(lp);
+
+		g_assert(retval == 0 && status == GLP_OPT);
+		*(uint64_t*) ((void*) correctedTime + loopValues[it].offset)=
+			round(glp_get_obj_val(lp));
+	}
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeBackPlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j)
+{
+	if (((AnalysisDataCHull*)
+			syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+		== ACCURATE)
+	{
+		fprintf(syncState->graphsStream,
+			"\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+				"using 1:(($3 - $2) / clock_freq_%2$u):(($4 - $2) / clock_freq_%2$u) "
+				"title \"Synchronization accuracy\" "
+				"with filledcurves linewidth 2 linetype 1 "
+				"linecolor rgb \"black\" fill solid 0.25 noborder, \\\n", i,
+				j);
+	}
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeForePlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j)
+{
+	if (((AnalysisDataCHull*)
+			syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+		== ACCURATE)
+	{
+		fprintf(syncState->graphsStream,
+			"\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+				"using 1:(($3 - $2) / clock_freq_%2$u) notitle "
+				"with lines linewidth 2 linetype 1 "
+				"linecolor rgb \"gray60\", \\\n"
+			"\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+				"using 1:(($4 - $2) / clock_freq_%2$u) notitle "
+				"with lines linewidth 2 linetype 1 "
+				"linecolor rgb \"gray60\", \\\n", i, j);
+	}
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTraceBackPlotsCHull(SyncState* const syncState,
+	const unsigned int i, const unsigned int j)
+{
+	if (((AnalysisDataCHull*)
+			syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+		== ACCURATE)
+	{
+		fprintf(syncState->graphsStream,
+			"\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+			"using 1:3:4 "
+			"title \"Synchronization accuracy\" "
+			"with filledcurves linewidth 2 linetype 1 "
+			"linecolor rgb \"black\" fill solid 0.25 noborder, \\\n", i, j);
+	}
+}
+#endif