From eb15bbac5bfc67702e3a9fb8b497389c7430dd23 Mon Sep 17 00:00:00 2001
From: Apostolof <apotwohd@gmail.com>
Date: Thu, 20 Sep 2018 14:15:59 +0300
Subject: [PATCH] Change transition sparse matrix to coordinates wise
 representation, Add comments, Improve code readability

---
 serial/Makefile                       |   8 +-
 serial/coo_sparse_matrix.c            | 117 ++++++++++++
 serial/coo_sparse_matrix.h            |  31 ++++
 serial/lil_sparse_matrix.c            |  76 ++++++++
 serial/lil_sparse_matrix.h            |  29 +++
 serial/serial_gs_pagerank.c           |   9 +-
 serial/serial_gs_pagerank_functions.c | 251 +++++++++++++++-----------
 serial/serial_gs_pagerank_functions.h |  67 ++++---
 serial/sparse_matrix.c                | 130 -------------
 serial/sparse_matrix.h                |  30 ---
 10 files changed, 446 insertions(+), 302 deletions(-)
 create mode 100644 serial/coo_sparse_matrix.c
 create mode 100644 serial/coo_sparse_matrix.h
 create mode 100644 serial/lil_sparse_matrix.c
 create mode 100644 serial/lil_sparse_matrix.h
 delete mode 100644 serial/sparse_matrix.c
 delete mode 100644 serial/sparse_matrix.h

diff --git a/serial/Makefile b/serial/Makefile
index a6ed4bc..9c4e0e6 100644
--- a/serial/Makefile
+++ b/serial/Makefile
@@ -5,10 +5,10 @@ SHELL := /bin/bash
 
 CC = gcc
 RM = rm -f
-CFLAGS_DEBUG=-O0 -g -I.
-CFLAGS=-O3 -I.
-OBJ=serial_gs_pagerank.o serial_gs_pagerank_functions.o sparse_matrix.o
-DEPS=serial_gs_pagerank_functions.h sparse_matrix.h
+CFLAGS_DEBUG=-O0 -ggdb3 -Wall -I.
+CFLAGS=-O3 -Wall -I.
+OBJ=serial_gs_pagerank.o serial_gs_pagerank_functions.o coo_sparse_matrix.o lil_sparse_matrix.o
+DEPS=serial_gs_pagerank_functions.h coo_sparse_matrix.h lil_sparse_matrix.h
 
 # ==========================================
 # TARGETS
diff --git a/serial/coo_sparse_matrix.c b/serial/coo_sparse_matrix.c
new file mode 100644
index 0000000..42fc7f1
--- /dev/null
+++ b/serial/coo_sparse_matrix.c
@@ -0,0 +1,117 @@
+#include "coo_sparse_matrix.h"
+
+CooSparseMatrix initCooSparseMatrix() {
+	CooSparseMatrix sparseMatrix;
+	sparseMatrix.size = 0;
+	sparseMatrix.elements = NULL;
+	return sparseMatrix;
+}
+
+void allocMemoryForElements (CooSparseMatrix *sparseMatrix, int elements) {
+	sparseMatrix->elements = (CooSparseMatrixElement **) malloc(
+		elements * sizeof(CooSparseMatrixElement *));
+}
+
+void addElement(CooSparseMatrix *sparseMatrix, double value, int row, int column) {
+	// Creates the new element
+	CooSparseMatrixElement *newElement = (CooSparseMatrixElement *) malloc(
+		sizeof(CooSparseMatrixElement));
+	newElement->value = value;
+	newElement->rowIndex = row;
+	newElement->columnIndex = column;
+
+	sparseMatrix->elements[sparseMatrix->size] = newElement;
+	sparseMatrix->size = sparseMatrix->size + 1;
+}
+
+void zeroOutRow(CooSparseMatrix *sparseMatrix, int row) {
+	for (int i=0; i<sparseMatrix->size; ++i) {
+		CooSparseMatrixElement *element = sparseMatrix->elements[i];
+		if (element->rowIndex == row) {
+			element->value = 0;
+		}
+	}
+}
+void zeroOutColumn(CooSparseMatrix *sparseMatrix, int column) {
+	for (int i=0; i<sparseMatrix->size; ++i) {
+		CooSparseMatrixElement *element = sparseMatrix->elements[i];
+		if (element->columnIndex == column) {
+			element->value = 0;
+		}
+	}
+}
+
+int *getRowIndexes(CooSparseMatrix sparseMatrix, int row, int *rowSize) {
+	*rowSize = 0;
+	for (int i=0; i<sparseMatrix.size; ++i) {
+		if (sparseMatrix.elements[i]->rowIndex == row) {
+			++(*rowSize);
+		}
+	}
+
+	if (!(*rowSize)) {
+		return NULL;
+	}
+
+	int *indexes = (int *) malloc((*rowSize) * sizeof(int));
+	int rowElementIndex = 0;
+	for (int i=0; i<sparseMatrix.size; ++i) {
+		if (sparseMatrix.elements[i]->rowIndex == row) {
+			indexes[rowElementIndex] = i;
+			++rowElementIndex;
+		}
+	}
+
+	return indexes;
+}
+
+void transposeSparseMatrix(CooSparseMatrix *sparseMatrix) {
+	for (int i=0; i<sparseMatrix->size; ++i) {
+		CooSparseMatrixElement *element = sparseMatrix->elements[i];
+		int tempRow = element->rowIndex;
+		element->rowIndex = element->columnIndex;
+		element->columnIndex = tempRow;
+	}
+}
+
+void cooSparseMatrixVectorMultiplication(CooSparseMatrix sparseMatrix,
+	double *vector, double **product, int vectorSize) {
+	// Initializes the elements of the product vector to zero
+	for (int i=0; i<vectorSize; ++i) {
+		(*product)[i] = 0;
+	}
+
+	CooSparseMatrixElement *element;
+	for (int i=0; i<sparseMatrix.size; ++i) {
+		element = sparseMatrix.elements[i];
+		int row = element->rowIndex, column = element->columnIndex;
+
+		if (row >= vectorSize) {
+			printf("Error at sparseMatrixVectorMultiplication. Matrix has more rows than vector!\n");
+			printf("row = %d\n", row);
+			exit(EXIT_FAILURE);
+		}
+
+		(*product)[row] = (*product)[row] + element->value * vector[column];
+	}
+}
+
+void destroyCooSparseMatrix(CooSparseMatrix *sparseMatrix) {
+	for (int i=0; i<sparseMatrix->size; ++i) {
+		free(sparseMatrix->elements[i]);
+	}
+	free(sparseMatrix->elements);
+}
+
+void printCooSparseMatrix(CooSparseMatrix sparseMatrix) {
+	if (sparseMatrix.size == 0) {
+		return;
+	}
+
+	CooSparseMatrixElement *element;
+	for (int i=0; i<sparseMatrix.size; ++i) {
+		element = sparseMatrix.elements[i];
+		printf("[%d,%d] = %f\n", element->rowIndex, element->columnIndex,
+			element->value);
+	}
+}
\ No newline at end of file
diff --git a/serial/coo_sparse_matrix.h b/serial/coo_sparse_matrix.h
new file mode 100644
index 0000000..66f538b
--- /dev/null
+++ b/serial/coo_sparse_matrix.h
@@ -0,0 +1,31 @@
+#ifndef COO_SPARSE_MATRIX_H	/* Include guard */
+#define COO_SPARSE_MATRIX_H
+
+#include <stdbool.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+typedef struct cooSparseMatrixElement {
+	double value;
+	int rowIndex, columnIndex;
+} CooSparseMatrixElement;
+
+typedef struct cooSparseMatrix {
+	int size;
+	CooSparseMatrixElement **elements;
+} CooSparseMatrix;
+
+CooSparseMatrix initCooSparseMatrix();
+void allocMemoryForElements (CooSparseMatrix *sparseMatrix, int elements);
+void addElement(CooSparseMatrix *sparseMatrix, double value, int row, int column);
+void zeroOutRow(CooSparseMatrix *sparseMatrix, int row);
+void zeroOutColumn(CooSparseMatrix *sparseMatrix, int column);
+int *getRowIndexes(CooSparseMatrix sparseMatrix, int row, int *rowSize);
+void transposeSparseMatrix(CooSparseMatrix *sparseMatrix);
+void cooSparseMatrixVectorMultiplication(CooSparseMatrix sparseMatrix, double *vector,
+	double **product, int vectorSize);
+void destroyCooSparseMatrix(CooSparseMatrix *sparseMatrix);
+void printCooSparseMatrix(CooSparseMatrix sparseMatrix);
+
+#endif	// COO_SPARSE_MATRIX_H
\ No newline at end of file
diff --git a/serial/lil_sparse_matrix.c b/serial/lil_sparse_matrix.c
new file mode 100644
index 0000000..61777ea
--- /dev/null
+++ b/serial/lil_sparse_matrix.c
@@ -0,0 +1,76 @@
+#include "lil_sparse_matrix.h"
+
+LilSparseMatrix createLilSparseMatrix() {
+	LilSparseMatrix sparseMatrix;
+	sparseMatrix.elements = 0;
+	sparseMatrix.firstElement = NULL;
+	sparseMatrix.lastElement = NULL;
+	return sparseMatrix;
+}
+
+void apendElement(LilSparseMatrix *sparseMatrix, double value, int row, int column) {
+	// Creates the new element
+	LilSparseMatrixElement *newElement = (LilSparseMatrixElement *) malloc(sizeof(LilSparseMatrixElement));
+	newElement->value = value;
+	newElement->rowIndex = row;
+	newElement->columnIndex = column;
+	newElement->nextElement = NULL;
+
+	if (sparseMatrix->firstElement == NULL) {
+		// Sparse matrix is empty, this is the first element
+		sparseMatrix->firstElement = newElement;
+		sparseMatrix->lastElement = newElement;
+	} else {
+		//Gets last element of the matrix
+		LilSparseMatrixElement *lastElement = sparseMatrix->lastElement;
+
+		lastElement->nextElement = newElement;
+		sparseMatrix->lastElement = newElement;
+	}
+
+	sparseMatrix->elements = sparseMatrix->elements + 1;
+}
+
+void lilSparseMatrixVectorMultiplication(LilSparseMatrix sparseMatrix,
+	double *vector, double **product, int vectorSize) {
+	// Initializes the elements of the product vector to zero
+	for (int i=0; i<vectorSize; ++i) {
+		(*product)[i] = 0;
+	}
+
+	LilSparseMatrixElement *element = sparseMatrix.firstElement;
+	for (int i=0; i<sparseMatrix.elements; ++i) {
+		int row = element->rowIndex, column = element->columnIndex;
+
+		if (row >= vectorSize) {
+			printf("Error at sparseMatrixVectorMultiplication. Matrix has more rows than vector!\n");
+			printf("row = %d\n", row);
+			exit(EXIT_FAILURE);
+		}
+
+		(*product)[row] = (*product)[row] + element->value * vector[column];
+		element = element->nextElement;
+	}
+}
+
+void destroyLilSparseMatrix(LilSparseMatrix *sparseMatrix) {
+	LilSparseMatrixElement *currentElement = sparseMatrix->firstElement;
+	while (currentElement != NULL) {
+		LilSparseMatrixElement *toDelete = currentElement;
+		currentElement = currentElement->nextElement;
+		free(toDelete);
+	}
+}
+
+void printLilSparseMatrix(LilSparseMatrix sparseMatrix) {
+	if (sparseMatrix.elements == 0) {
+		return;
+	}
+
+	LilSparseMatrixElement *currentElement = sparseMatrix.firstElement;
+	for (int i=0; i<sparseMatrix.elements; ++i) {
+		printf("[%d,%d] = %f\n", currentElement->rowIndex,
+			currentElement->columnIndex, currentElement->value);
+		currentElement = currentElement->nextElement;
+	}
+}
\ No newline at end of file
diff --git a/serial/lil_sparse_matrix.h b/serial/lil_sparse_matrix.h
new file mode 100644
index 0000000..599cdae
--- /dev/null
+++ b/serial/lil_sparse_matrix.h
@@ -0,0 +1,29 @@
+#ifndef LIL_SPARSE_MATRIX_H	/* Include guard */
+#define LIL_SPARSE_MATRIX_H
+
+#include <stdbool.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+typedef struct lilSparseMatrixElement {
+	double value;
+	int rowIndex, columnIndex;
+	struct lilSparseMatrixElement *nextElement;
+} LilSparseMatrixElement;
+
+typedef struct lilSparseMatrix {
+	int elements;
+	LilSparseMatrixElement *firstElement;
+	LilSparseMatrixElement *lastElement;
+} LilSparseMatrix;
+
+LilSparseMatrix createLilSparseMatrix();
+void apendElement(LilSparseMatrix *sparseMatrix, double value, int row,
+	int column);
+void lilSparseMatrixVectorMultiplication(LilSparseMatrix sparseMatrix,
+	double *vector, double **product, int vectorSize);
+void destroyLilSparseMatrix(LilSparseMatrix *sparseMatrix);
+void printLilSparseMatrix(LilSparseMatrix sparseMatrix);
+
+#endif	// LIL_SPARSE_MATRIX_H
\ No newline at end of file
diff --git a/serial/serial_gs_pagerank.c b/serial/serial_gs_pagerank.c
index fdb7031..9a4cf6f 100644
--- a/serial/serial_gs_pagerank.c
+++ b/serial/serial_gs_pagerank.c
@@ -1,19 +1,17 @@
 #include <sys/time.h>
 
 #include "serial_gs_pagerank_functions.h"
-#include "sparse_matrix.h"
+//#include "coo_sparse_matrix.h"
 
 struct timeval startwtime, endwtime;
 double seq_time;
 
 int main(int argc, char **argv) {
-	SparseMatrix transitionMatrix;
+	CooSparseMatrix transitionMatrix = initCooSparseMatrix();
 	double *pagerankVector;
 	bool convergenceStatus;
 	Parameters parameters;
 
-	transitionMatrix = createSparseMatrix();
-
 	parseArguments(argc, argv, &parameters);
 
 	initialize(&transitionMatrix, &pagerankVector, &parameters);
@@ -40,4 +38,7 @@ int main(int argc, char **argv) {
 		endwtime.tv_sec - startwtime.tv_sec);
 	printf("%s wall clock time = %f\n","Pagerank (Gauss-Seidel method), serial implementation",
 		seq_time);
+
+	free(pagerankVector);
+	destroyCooSparseMatrix(&transitionMatrix);
 }
diff --git a/serial/serial_gs_pagerank_functions.c b/serial/serial_gs_pagerank_functions.c
index d3ec921..b8b9e9e 100644
--- a/serial/serial_gs_pagerank_functions.c
+++ b/serial/serial_gs_pagerank_functions.c
@@ -1,5 +1,9 @@
+/* ===== INCLUDES ===== */
+
 #include "serial_gs_pagerank_functions.h"
 
+/* ===== CONSTANTS ===== */
+
 const char *ARGUMENT_CONVERGENCE_TOLERANCE = "-c";
 const char *ARGUMENT_MAX_ITERATIONS = "-m";
 const char *ARGUMENT_DAMPING_FACTOR = "-a";
@@ -11,24 +15,43 @@ const int NUMERICAL_BASE = 10;
 char *DEFAULT_OUTPUT_FILENAME = "pagerank_output";
 const int FILE_READ_BUFFER_SIZE = 4096;
 
-// ==================== PAGERANK ====================
+const int CONVERGENCE_CHECK_ITERATION_PERIOD = 3;
+const int SPARSITY_INCREASE_ITERATION_PERIOD = 9;
 
-int pagerank(SparseMatrix *transitionMatrix, double **pagerankVector,
+/* ===== FUNCTIONS ===== */
+
+int pagerank(CooSparseMatrix *transitionMatrix, double **pagerankVector,
 	bool *convergenceStatus, Parameters parameters) {
-	int iterations = 0;
-	double delta,
-	*vectorDifference = (double *) malloc(parameters.numberOfPages * sizeof(double)),
-	*previousPagerankVector = (double *) malloc(parameters.numberOfPages * sizeof(double)),
-	*convergedPagerankVector = (double *) malloc(parameters.numberOfPages * sizeof(double)),
-	*linksFromConvergedPagesPagerankVector = (double *) malloc(parameters.numberOfPages * sizeof(double));
-	SparseMatrix linksFromConvergedPages = createSparseMatrix();
-	bool *converganceMatrix = (bool *) malloc(parameters.numberOfPages * sizeof(bool));
-	*convergenceStatus = false;
-
-	for (int i=0; i<parameters.numberOfPages; ++i) {
-		convergedPagerankVector[i] = 0;
-		converganceMatrix[i] = false;
-		linksFromConvergedPagesPagerankVector[i] = 0;
+	// Variables declaration
+	int iterations = 0, numberOfPages = parameters.numberOfPages;
+	double delta, *pagerankDifference, *previousPagerankVector,
+	*convergedPagerankVector, *linksFromConvergedPagesPagerankVector;
+	LilSparseMatrix linksFromConvergedPages = createLilSparseMatrix();
+	bool *convergenceMatrix;
+
+	// Space allocation
+	{
+		size_t sizeofDouble = sizeof(double);
+		// pagerankDifference used to calculate delta
+		pagerankDifference = (double *) malloc(numberOfPages * sizeofDouble);
+		// previousPagerankVector holds last iteration's pagerank vector
+		previousPagerankVector = (double *) malloc(numberOfPages * sizeofDouble);
+		// convergedPagerankVector is the pagerank vector of converged pages only
+		convergedPagerankVector = (double *) malloc(numberOfPages * sizeofDouble);
+		// linksFromConvergedPagesPagerankVector holds the partial sum of the
+		// pagerank vector, that describes effect of the links from converged
+		// pages to non converged pages
+		linksFromConvergedPagesPagerankVector = (double *) malloc(numberOfPages * sizeofDouble);
+		// convergenceMatrix indicates which pages have converged
+		convergenceMatrix = (bool *) malloc(numberOfPages * sizeof(bool));
+		*convergenceStatus = false;
+
+		// Initialization
+		for (int i=0; i<numberOfPages; ++i) {
+			convergedPagerankVector[i] = 0;
+			convergenceMatrix[i] = false;
+			linksFromConvergedPagesPagerankVector[i] = 0;
+		}
 	}
 
 	if (parameters.verbose) {
@@ -36,81 +59,115 @@ int pagerank(SparseMatrix *transitionMatrix, double **pagerankVector,
 	}
 
 	do {
-		memcpy(previousPagerankVector, *pagerankVector, parameters.numberOfPages * sizeof(double));
-
-		matrixVectorMultiplication(transitionMatrix, previousPagerankVector,
-			pagerankVector, parameters.numberOfPages, parameters.dampingFactor);
+		// Stores previous pagerank vector
+		memcpy(previousPagerankVector, *pagerankVector, numberOfPages * sizeof(double));
 
-		for (int i=0; i<parameters.numberOfPages; ++i) {
-			(*pagerankVector)[i] += linksFromConvergedPagesPagerankVector[i] + convergedPagerankVector[i];
-		}
+		// Calculates new pagerank vector
+		calculateNextPagerank(transitionMatrix, previousPagerankVector,
+			pagerankVector, linksFromConvergedPagesPagerankVector,
+			convergedPagerankVector, numberOfPages,
+			parameters.dampingFactor);
 
 		if (parameters.history) {
+			// Outputs pagerank vector to file
 			savePagerankToFile(parameters.outputFilename, iterations != 0,
-				*pagerankVector, parameters.numberOfPages);
+				*pagerankVector, numberOfPages);
 		}
 
-		for (int i=0; i<parameters.numberOfPages; ++i) {
-			vectorDifference[i] = (*pagerankVector)[i] - previousPagerankVector[i];
-		}
-		delta = vectorNorm(vectorDifference, parameters.numberOfPages);
-		if (delta < parameters.convergenceCriterion) {
-			*convergenceStatus = true;
+		// Periodically checks for convergence
+		if (!(iterations % CONVERGENCE_CHECK_ITERATION_PERIOD)) {
+			// Builds pagerank vectors difference
+			for (int i=0; i<numberOfPages; ++i) {
+				pagerankDifference[i] = (*pagerankVector)[i] - previousPagerankVector[i];
+			}
+			// Calculates convergence
+			delta = vectorNorm(pagerankDifference, numberOfPages);
+
+			if (delta < parameters.convergenceCriterion) {
+				// Converged
+				*convergenceStatus = true;
+			}
 		}
 
-		if (iterations && (!iterations % 10)) {
-			for (int i=0; i<parameters.numberOfPages; ++i) {
-				double temp = fabs((*pagerankVector)[i] - previousPagerankVector[i]) / fabs(previousPagerankVector[i]);
-				if (temp < parameters.convergenceCriterion){
-					converganceMatrix[i] = true;
+		// Periodically increases sparsity
+		if (iterations && !(iterations % SPARSITY_INCREASE_ITERATION_PERIOD)) {
+			bool *newlyConvergedPages = (bool *) malloc(numberOfPages * sizeof(bool));
+			// Checks each individual page for convergence
+			for (int i=0; i<numberOfPages; ++i) {
+				double difference = fabs((*pagerankVector)[i] -
+					previousPagerankVector[i]) / fabs(previousPagerankVector[i]);
+
+				newlyConvergedPages[i] = false;
+				if (!convergenceMatrix[i] && difference < parameters.convergenceCriterion){
+					// Page converged
+					newlyConvergedPages[i] = true;
+					convergenceMatrix[i] = true;
 					convergedPagerankVector[i] = (*pagerankVector)[i];
 				}
 			}
 
-			for (int i=0; i<parameters.numberOfPages; ++i) {
-				if (converganceMatrix[i] == true) {
-					for (int j=0; j<parameters.numberOfPages; ++j){
-						if (converganceMatrix[j] == false){
-							SparseMatrixElement *element = getElement(*transitionMatrix, i, j);
-							if (element != NULL) {
-								apendElement(&linksFromConvergedPages, element->value, i, j);
-							}
+			for (int i=0; i<numberOfPages; ++i) {
+				if (newlyConvergedPages[i] == true) {
+					int rowSize;
+					int *rowIndexes = getRowIndexes(*transitionMatrix, i, &rowSize);
+					for (int j=0; j<rowSize; ++j){
+						CooSparseMatrixElement *element = transitionMatrix->elements[rowIndexes[j]];
+						// Checks for links from converged pages to non converged
+						int pageLinksTo = element->columnIndex;
+						if (convergenceMatrix[pageLinksTo] == false){
+							// Link exists, adds element to the vector
+							apendElement(&linksFromConvergedPages,
+								element->value, i, pageLinksTo);
 						}
-						deleteElement(transitionMatrix, i, j);
-						deleteElement(transitionMatrix, j, i);
 					}
 
-					sparseMatrixVectorMultiplication(linksFromConvergedPages, *pagerankVector,
-						&linksFromConvergedPagesPagerankVector, parameters.numberOfPages);
+					// Increases sparsity of the transition matrix by
+					// deleting elements that correspond to converged pages
+					zeroOutRow(transitionMatrix, i);
+					zeroOutColumn(transitionMatrix, i);
+
+					// Builds the new linksFromConvergedPagesPagerankVector
+					lilSparseMatrixVectorMultiplication(linksFromConvergedPages,
+						*pagerankVector, &linksFromConvergedPagesPagerankVector,
+						numberOfPages);
 				}
 			}
+			free(newlyConvergedPages);
 		}
 
 		++iterations;
+		// Outputs information about this iteration
 		if (iterations%2) {
 			printf(ANSI_COLOR_BLUE "Iteration %d: delta = %f\n" ANSI_COLOR_RESET, iterations, delta);
 		} else {
 			printf(ANSI_COLOR_CYAN "Iteration %d: delta = %f\n" ANSI_COLOR_RESET, iterations, delta);
 		}
-	} while (!*convergenceStatus &&
-		(parameters.maxIterations == 0 || iterations < parameters.maxIterations));
+	} while (!*convergenceStatus && (parameters.maxIterations == 0 ||
+		iterations < parameters.maxIterations));
 
 	if (!parameters.history) {
+		// Outputs last pagerank vector to file
 		savePagerankToFile(parameters.outputFilename, false, *pagerankVector,
-			parameters.numberOfPages);
+			numberOfPages);
 	}
 
+	// Frees memory
+	free(pagerankDifference);
+	free(previousPagerankVector);
+	free(convergedPagerankVector);
+	free(linksFromConvergedPagesPagerankVector);
+	free(convergenceMatrix);
+	destroyLilSparseMatrix(&linksFromConvergedPages);
+
 	return iterations;
 }
 
-// ==================== INITIALIZATION ====================
-
 /*
  * initialize allocates required memory for arrays, reads the web graph from the
  * from the file and creates the initial transition probability distribution
  * matrix.
 */
-void initialize(SparseMatrix *transitionMatrix,
+void initialize(CooSparseMatrix *transitionMatrix,
 	double **pagerankVector, Parameters *parameters) {
 
 	// Reads web graph from file
@@ -148,14 +205,17 @@ void initialize(SparseMatrix *transitionMatrix,
 // ==================== MATH UTILS ====================
 
 /*
- * matrixVectorMultiplication calculates the product of the multiplication
+ * calculateNextPagerank calculates the product of the multiplication
  * between a matrix and the a vector in a cheap way.
 */
-void matrixVectorMultiplication(SparseMatrix *transitionMatrix, double *previousPagerankVector,
-	double **pagerankVector, int vectorSize, double dampingFactor) {
+void calculateNextPagerank(CooSparseMatrix *transitionMatrix,
+	double *previousPagerankVector, double **pagerankVector,
+	double *linksFromConvergedPagesPagerankVector,
+	double *convergedPagerankVector, int vectorSize, double dampingFactor) {
+	// Calculates the web uniform probability once.
 	double webUniformProbability = 1. / vectorSize;
 
-	sparseMatrixVectorMultiplication(*transitionMatrix, previousPagerankVector,
+	cooSparseMatrixVectorMultiplication(*transitionMatrix, previousPagerankVector,
 		pagerankVector, vectorSize);
 
 	for (int i=0; i<vectorSize; ++i) {
@@ -166,7 +226,8 @@ void matrixVectorMultiplication(SparseMatrix *transitionMatrix, double *previous
 	vectorNorm(*pagerankVector, vectorSize);
 
 	for (int i=0; i<vectorSize; ++i) {
-		(*pagerankVector)[i] += normDifference * webUniformProbability;
+		(*pagerankVector)[i] += normDifference * webUniformProbability +
+		linksFromConvergedPagesPagerankVector[i] + convergedPagerankVector[i];
 	}
 }
 
@@ -258,7 +319,7 @@ void parseArguments(int argumentCount, char **argumentVector, Parameters *parame
  * readGraphFromFile loads the file supplied in the command line arguments to an
  * array (directedWebGraph) that represents the graph.
 */
-void generateNormalizedTransitionMatrixFromFile(SparseMatrix *transitionMatrix,
+void generateNormalizedTransitionMatrixFromFile(CooSparseMatrix *transitionMatrix,
 	Parameters *parameters){
 	FILE *graphFile;
 
@@ -280,7 +341,7 @@ void generateNormalizedTransitionMatrixFromFile(SparseMatrix *transitionMatrix,
 	}
 
 	// Third line contains the numbers of nodes and edges
-	int numberOfNodes = 0, numberOfEdges;
+	int numberOfNodes = 0, numberOfEdges = 0;
 
 	readResult = fgets(buffer, FILE_READ_BUFFER_SIZE, graphFile);
 	if (readResult == NULL) {
@@ -324,21 +385,14 @@ void generateNormalizedTransitionMatrixFromFile(SparseMatrix *transitionMatrix,
 		exit(EXIT_FAILURE);
 	}
 
-	printf("SIZE OF STRUCT = %lu Bytes\n", sizeof(SparseMatrixElement));
-
-	int fivePercentIncrements = (int) numberOfEdges/20;
+	int tenPercentIncrements = (int) numberOfEdges/10;
 	int maxPageIndex = 0;
-	fivePercentIncrements = fivePercentIncrements != 0 ? fivePercentIncrements : 1;
+	allocMemoryForElements(transitionMatrix, numberOfEdges);
 
 	for (int i=0; i<numberOfEdges; i++) {
-		if (((*parameters).verbose) && ((i % fivePercentIncrements) == 0)) {
-			int percentage = (i/fivePercentIncrements)*5;
-			printf("%d%% done", percentage);
-			if (percentage%20 == 0) {
-				printf("\n");
-			} else {
-				printf(" •••• ");
-			}
+		if (((*parameters).verbose) && (tenPercentIncrements != 0) && ((i % tenPercentIncrements) == 0)) {
+			int percentage = (i/tenPercentIncrements)*10;
+			printf("%d%% • ", percentage);
 		}
 
 		int fileFrom = 0, fileTo = 0;
@@ -349,8 +403,12 @@ void generateNormalizedTransitionMatrixFromFile(SparseMatrix *transitionMatrix,
 		if (fileFrom > maxPageIndex) {
 			maxPageIndex = fileFrom;
 		}
-		apendElement(transitionMatrix, 1, fileFrom, fileTo);
+		if (fileTo > maxPageIndex) {
+			maxPageIndex = fileTo;
+		}
+		addElement(transitionMatrix, 1, fileFrom, fileTo);
 	}
+	printf("\n");
 
 	if ((*parameters).verbose) {
 		printf("Max page index found is: %d\n", maxPageIndex);
@@ -359,41 +417,26 @@ void generateNormalizedTransitionMatrixFromFile(SparseMatrix *transitionMatrix,
 
 	// Calculates the outdegree of each page and assigns the uniform probability
 	// of transition to the elements of the corresponding row
-	int currentRow = transitionMatrix->firstElement->rowIndex;
-	SparseMatrixElement *startElement = transitionMatrix->firstElement;
-	while(true) {
-		int pageOutdegree = 1;
-		SparseMatrixElement *currentElement = startElement->nextElement;
-
-		// Calculates current page's outdegree
-		while (currentElement != NULL) {
-			if (currentElement->rowIndex == currentRow) {
-				++pageOutdegree;
-				currentElement = currentElement->nextElement;
-			} else {
-				break;
-			}
-		}
-
-		// Assigns the value 1/outdegree to current page's columns
-		currentElement = startElement;
-		double pageUniformProbability = 1. / pageOutdegree;
-		for (int i=0; i<pageOutdegree; ++i) {
-			if (currentElement->rowIndex == currentRow) {
-				currentElement->value = pageUniformProbability;
-				currentElement = currentElement->nextElement;
-			} else {
-				break;
+	int currentRow = transitionMatrix->elements[0]->rowIndex, pageOutdegree = 1;
+	for (int i=1; i<transitionMatrix->size; ++i) {
+		CooSparseMatrixElement *currentElement = transitionMatrix->elements[i];
+		if (currentElement->rowIndex == currentRow) {
+			++pageOutdegree;
+		} else {
+			double pageUniformProbability = 1. / pageOutdegree;
+			for (int j=i-pageOutdegree; j<i; ++j) {
+				transitionMatrix->elements[j]->value = pageUniformProbability;
 			}
-		}
 
-		// Reached the last element;
-		if (currentElement == NULL) {
-			break;
+			currentRow = currentElement->rowIndex;
+			pageOutdegree = 1;
 		}
+	}
 
-		startElement = currentElement;
-		currentRow = startElement->rowIndex;
+	// Does the last row
+	double pageUniformProbability = 1. / pageOutdegree;
+	for (int j=transitionMatrix->size-pageOutdegree; j<transitionMatrix->size; ++j) {
+		transitionMatrix->elements[j]->value = pageUniformProbability;
 	}
 
 	fclose(graphFile);
diff --git a/serial/serial_gs_pagerank_functions.h b/serial/serial_gs_pagerank_functions.h
index 9e5267c..40ed518 100644
--- a/serial/serial_gs_pagerank_functions.h
+++ b/serial/serial_gs_pagerank_functions.h
@@ -1,14 +1,20 @@
 #ifndef SERIAL_GS_PAGERANK_FUNCTIONS_H	/* Include guard */
 #define SERIAL_GS_PAGERANK_FUNCTIONS_H
 
+/* ===== INCLUDES ===== */
+
 #include <stdbool.h>
 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>
 #include <math.h>
 
-#include "sparse_matrix.h"
+#include "coo_sparse_matrix.h"
+#include "lil_sparse_matrix.h"
+
+/* ===== DEFINITIONS ===== */
 
+//Colors used for better console output formating.
 #define ANSI_COLOR_RED     "\x1B[31m"
 #define ANSI_COLOR_GREEN   "\x1B[32m"
 #define ANSI_COLOR_YELLOW  "\x1B[33m"
@@ -16,25 +22,25 @@
 #define ANSI_COLOR_CYAN    "\x1B[36m"
 #define ANSI_COLOR_RESET   "\x1B[0m"
 
-/*
- * Constant strings that store the command line options available.
-*/
+/* ===== CONSTANTS DEFINITION ===== */
+
+// Constant strings that store the command line options available.
 extern const char *ARGUMENT_CONVERGENCE_TOLERANCE;
 extern const char *ARGUMENT_MAX_ITERATIONS;
 extern const char *ARGUMENT_DAMPING_FACTOR;
 extern const char *ARGUMENT_VERBAL_OUTPUT;
 extern const char *ARGUMENT_OUTPUT_HISTORY;
 extern const char *ARGUMENT_OUTPUT_FILENAME;
-
-// This is the numerical base used when parsing the numerical command line
-// arguments.
+// The numerical base used when parsing numerical command line arguments.
 extern const int NUMERICAL_BASE;
 // Default filename used for the output.
 extern char *DEFAULT_OUTPUT_FILENAME;
+// The size of the buffer used for reading the graph input file.
+extern const int FILE_READ_BUFFER_SIZE;
 
-extern const int MAX_PAGE_LINKS_TEXT_SIZE;
+/* ===== STRUCTURES ===== */
 
-// Declares a data structure to conveniently hold the algorithm's parameters.
+// A data structure to conveniently hold the algorithm's parameters.
 typedef struct parameters {
 	int numberOfPages, maxIterations;
 	double convergenceCriterion, dampingFactor;
@@ -42,8 +48,7 @@ typedef struct parameters {
 	char *outputFilename, *graphFilename;
 } Parameters;
 
-//extern typedef SparseMatrixElement;
-//extern typedef SparseMatrix;
+/* ===== FUNCTION DEFINITIONS ===== */
 
 // Function validUsage outputs the correct way to use the program with command
 // line arguments.
@@ -54,39 +59,41 @@ void validUsage(char *programName);
 int checkIncrement(int previousIndex, int maxIndex, char *programName);
 
 // Function parseArguments parses command line arguments.
-void parseArguments(int argumentCount, char **argumentVector, Parameters *parameters);
+void parseArguments(int argumentCount, char **argumentVector,
+	Parameters *parameters);
 
-// Function readGraphFromFile loads adjacency matrix, that represents the web
-// graph, stored in the file provided in the command line arguments to the array
-// directedWebGraph.
-void generateNormalizedTransitionMatrixFromFile(SparseMatrix *transitionMatrix, Parameters *parameters);
+// Function generateNormalizedTransitionMatrixFromFile reads through the entries
+// of the file specified in the arguments (parameters->graphFilename), using
+// them to populate the sparse array (transitionMatrix). The entries of the file
+// represent the edges of the web transition graph. The entries are then
+// modified to become the rows of the transition matrix.
+void generateNormalizedTransitionMatrixFromFile(CooSparseMatrix *transitionMatrix,
+	Parameters *parameters);
 
 // Function savePagerankToFile appends or overwrites the pagerank vector
-// "pagerankVector" to the file with the filename supplied in the arguments 
+// "pagerankVector" to the file with the filename supplied in the arguments.
 void savePagerankToFile(char *filename, bool append, double *pagerankVector,
 	int vectorSize);
 
-// Function initialize allocates required memory for arrays, reads the dataset
-// from the file and creates the transition probability distribution matrix.
-void initialize(
-	SparseMatrix *transitionMatrix, /*This is matrix A (transition probability distribution matrix)*/
-	double **pagerankVector, /*This is the resulting pagerank vector*/
-	Parameters *parameters
-	);
+// Function initialize allocates memory for the pagerank vector, reads the
+// dataset from the file and creates the transition probability distribution
+// matrix.
+void initialize(CooSparseMatrix *transitionMatrix, double **pagerankVector,
+	Parameters *parameters);
 
 // Function vectorNorm calculates the first norm of a vector.
 double vectorNorm(double *vector, int vectorSize);
 
-// Function matrixVectorMultiplication calculates the product of the
-// multiplication between a matrix and the a vector.
-void matrixVectorMultiplication(SparseMatrix *transitionMatrix,
-	double *previousPagerankVector, double **pagerankVector, int vectorSize,
-	double dampingFactor);
+// Function calculateNextPagerank calculates the next pagerank vector.
+void calculateNextPagerank(CooSparseMatrix *transitionMatrix,
+	double *previousPagerankVector, double **pagerankVector,
+	double *linksFromConvergedPagesPagerankVector,
+	double *convergedPagerankVector, int vectorSize, double dampingFactor);
 
 // Function pagerank iteratively calculates the pagerank of each page until
 // either the convergence criterion is met or the maximum number of iterations
 // is reached.
-int pagerank(SparseMatrix *transitionMatrix, double **pagerankVector,
+int pagerank(CooSparseMatrix *transitionMatrix, double **pagerankVector,
 	bool *convergenceStatus, Parameters parameters);
 
 #endif	// SERIAL_GS_PAGERANK_FUNCTIONS_H
\ No newline at end of file
diff --git a/serial/sparse_matrix.c b/serial/sparse_matrix.c
deleted file mode 100644
index 2df1b0d..0000000
--- a/serial/sparse_matrix.c
+++ /dev/null
@@ -1,130 +0,0 @@
-#include "sparse_matrix.h"
-
-SparseMatrix createSparseMatrix() {
-	SparseMatrix sparseMatrix;
-	sparseMatrix.elements = 0;
-	sparseMatrix.firstElement = NULL;
-	sparseMatrix.lastElement = NULL;
-	return sparseMatrix;
-}
-
-void apendElement(SparseMatrix *sparseMatrix, double value, int row, int column) {
-	// Creates the new element
-	SparseMatrixElement *newElement = (SparseMatrixElement *) malloc(sizeof(SparseMatrixElement));
-	newElement->value = value;
-	newElement->rowIndex = row;
-	newElement->columnIndex = column;
-	newElement->nextElement = NULL;
-
-	if (sparseMatrix->firstElement == NULL) {
-		// Sparse matrix is empty, this is the first element
-		sparseMatrix->firstElement = newElement;
-		sparseMatrix->lastElement = newElement;
-	} else {
-		//Gets last element of the matrix
-		SparseMatrixElement *lastElement = sparseMatrix->lastElement;
-
-		lastElement->nextElement = newElement;
-		sparseMatrix->lastElement = newElement;
-	}
-
-	sparseMatrix->elements = sparseMatrix->elements + 1;
-}
-
-bool deleteElement(SparseMatrix *sparseMatrix, int row, int column) {
-	if (sparseMatrix->elements == 0) {
-		// Matrix is empty, nothing can be deleted
-		return false;
-	} else if (sparseMatrix->elements == 1) {
-		// Matrix has one element. Deletes it.
-		free(sparseMatrix->firstElement);
-		sparseMatrix->firstElement = NULL;
-		sparseMatrix->lastElement = NULL;
-		sparseMatrix->elements = sparseMatrix->elements - 1;
-		return true;
-	}
-
-	SparseMatrixElement *currentElement = sparseMatrix->firstElement;
-
-	if (currentElement->rowIndex == row && currentElement->columnIndex == column) {
-		sparseMatrix->firstElement = currentElement->nextElement;
-		free(currentElement);
-		sparseMatrix->elements = sparseMatrix->elements - 1;
-		return true;
-	}
-
-	// Matrix has multiple elements. Finds the first element that has the coordinates
-	// (row,column) and deletes it.
-	for (int i=0; i<sparseMatrix->elements - 1; ++i) {
-		SparseMatrixElement *nextElement = currentElement->nextElement;
-		if (nextElement->rowIndex == row && nextElement->columnIndex == column) {
-			currentElement->nextElement = nextElement->nextElement;
-			if (currentElement->nextElement == NULL) {
-				sparseMatrix->lastElement = currentElement;
-			}
-			free(nextElement);
-			sparseMatrix->elements = sparseMatrix->elements - 1;
-			return true;
-		} else {
-			currentElement = currentElement->nextElement;
-		}
-	}
-}
-
-SparseMatrixElement *getElement(SparseMatrix sparseMatrix, int row, int column) {
-	SparseMatrixElement *currentElement = sparseMatrix.firstElement;
-	do {
-		if (currentElement->rowIndex == row && currentElement->columnIndex == column) {
-			return currentElement;
-		}
-		currentElement = currentElement->nextElement;
-	} while (currentElement != NULL);
-
-	return NULL;
-}
-
-void transposeSparseMatrix(SparseMatrix *sparseMatrix) {
-	SparseMatrixElement *currentElement = sparseMatrix->firstElement;
-	for (int i=0; i<sparseMatrix->elements; ++i) {
-		int temp = currentElement->rowIndex;
-		currentElement->rowIndex = currentElement->columnIndex;
-		currentElement->columnIndex = temp;
-
-		currentElement = currentElement->nextElement;
-	}
-}
-
-void sparseMatrixVectorMultiplication(SparseMatrix sparseMatrix,
-	double *vector, double **product, int vectorSize) {
-	// Initializes the elements of the product vector to zero
-	for (int i=0; i<vectorSize; ++i) {
-		(*product)[i] = 0;
-	}
-
-	SparseMatrixElement *element = sparseMatrix.firstElement;
-	for (int i=0; i<sparseMatrix.elements; ++i) {
-		int row = element->rowIndex, column = element->columnIndex;
-
-		if (row >= vectorSize) {
-			printf("Error at sparseMatrixVectorMultiplication. Matrix has more rows than vector!\n");
-			printf("row = %d\n", row);
-			exit(EXIT_FAILURE);
-		}
-
-		(*product)[row] = (*product)[row] + element->value * vector[column];
-		element = element->nextElement;
-	}
-}
-
-void printSparseMatrix(SparseMatrix sparseMatrix) {
-	if (sparseMatrix.elements == 0) {
-		return;
-	}
-
-	SparseMatrixElement *currentElement = sparseMatrix.firstElement;
-	for (int i=0; i<sparseMatrix.elements; ++i) {
-		printf("[%d,%d] = %f\n", currentElement->rowIndex,
-			currentElement->columnIndex, currentElement->value);
-		currentElement = currentElement->nextElement;
-	}
-}
\ No newline at end of file
diff --git a/serial/sparse_matrix.h b/serial/sparse_matrix.h
deleted file mode 100644
index 7a977d2..0000000
--- a/serial/sparse_matrix.h
+++ /dev/null
@@ -1,30 +0,0 @@
-#ifndef SPARSE_MATRIX_H	/* Include guard */
-#define SPARSE_MATRIX_H
-
-#include <stdbool.h>
-#include <stdlib.h>
-#include <stdio.h>
-#include <stdlib.h>
-
-typedef struct sparseMatrixElement {
-	double value;
-	int rowIndex, columnIndex;
-	struct sparseMatrixElement *nextElement;
-} SparseMatrixElement;
-
-typedef struct sparseMatrix {
-	int elements;
-	SparseMatrixElement *firstElement;
-	SparseMatrixElement *lastElement;
-} SparseMatrix;
-
-SparseMatrix createSparseMatrix();
-void apendElement(SparseMatrix *sparseMatrix, double value, int row, int column);
-bool deleteElement(SparseMatrix *sparseMatrix, int row, int column);
-SparseMatrixElement *getElement(SparseMatrix sparseMatrix, int row, int column);
-void transposeSparseMatrix(SparseMatrix *sparseMatrix);
-void sparseMatrixVectorMultiplication(SparseMatrix sparseMatrix, double *vector,
-	double **product, int vectorSize);
-void printSparseMatrix(SparseMatrix sparseMatrix);
-
-#endif	// SPARSE_MATRIX_H
\ No newline at end of file