root / latex / report_feb_16.tex @ 4ca27bae
History | View | Annotate | Download (5.61 KB)
1 |
\documentclass[12pt]{article} |
---|---|
2 |
% This first part of the file is called the PREAMBLE. It includes |
3 |
% customizations and command definitions. The preamble is everything |
4 |
% between \documentclass and \begin{document}. |
5 |
|
6 |
\usepackage[margin=1in]{geometry} % set the margins to 1in on all sides |
7 |
\usepackage{graphicx} % to include figures |
8 |
\graphicspath{ {report_images/} } % '/' is needed |
9 |
\usepackage{epstopdf} % for the .ps image |
10 |
\epstopdfsetup{update} |
11 |
\DeclareGraphicsExtensions{.eps} |
12 |
\epstopdfDeclareGraphicsRule{.eps}{pdf}{.pdf}{ps2pdf -dEPSCrop -dNOSAFER #1 \OutputFile} |
13 |
\usepackage[noabbrev,capitalise]{cleveref} |
14 |
\usepackage{amsmath} % great math stuff |
15 |
\usepackage{amsfonts} % for blackboard bold, etc |
16 |
\usepackage{amsthm} % better theorem environments |
17 |
\usepackage{listings} % to add code |
18 |
\lstset{language=Java} |
19 |
\renewcommand{\lstlistingname}{Code} % change "Listing 1.1" to "Code 1.1" |
20 |
|
21 |
\usepackage[utf8]{inputenc} |
22 |
\usepackage{color} |
23 |
|
24 |
\usepackage{cite} |
25 |
|
26 |
\usepackage[colorlinks]{hyperref} % from http://tex.stackexchange.com/questions/3568/how-does-one-typeset-a-url |
27 |
\hypersetup{citecolor=green} |
28 |
\hypersetup{linkcolor=red} |
29 |
\hypersetup{urlcolor=blue} |
30 |
\usepackage{cleveref} |
31 |
|
32 |
\definecolor{codegreen}{rgb}{0,0.6,0} |
33 |
\definecolor{codegray}{rgb}{0.5,0.5,0.5} |
34 |
\definecolor{codepurple}{rgb}{0.58,0,0.82} |
35 |
\definecolor{backcolour}{rgb}{0.95,0.95,0.92} |
36 |
|
37 |
\lstdefinestyle{mystyle}{ |
38 |
backgroundcolor=\color{backcolour}, |
39 |
commentstyle=\color{codegreen}, |
40 |
keywordstyle=\color{magenta}, |
41 |
numberstyle=\tiny\color{codegray}, |
42 |
stringstyle=\color{codepurple}, |
43 |
basicstyle=\footnotesize, |
44 |
breakatwhitespace=false, |
45 |
breaklines=true, |
46 |
captionpos=b, |
47 |
keepspaces=true, |
48 |
numbers=left, |
49 |
numbersep=5pt, |
50 |
showspaces=false, |
51 |
showstringspaces=false, |
52 |
showtabs=false, |
53 |
tabsize=2 |
54 |
} |
55 |
|
56 |
\lstset{style=mystyle} |
57 |
\DeclareMathOperator{\id}{id} |
58 |
|
59 |
\newcommand{\bd}[1]{\mathbf{#1}} % for bolding symbols |
60 |
\newcommand{\RR}{\mathbb{R}} % for Real numbers |
61 |
\newcommand{\ZZ}{\mathbb{Z}} % for Integers |
62 |
\newcommand{\col}[1]{\left[\begin{matrix} #1 \end{matrix} \right]} |
63 |
\newcommand{\comb}[2]{\binom{#1^2 + #2^2}{#1+#2}} |
64 |
|
65 |
\usepackage[T1]{fontenc} |
66 |
\AtBeginDocument{% |
67 |
\begingroup\lccode`~=`_% |
68 |
\lowercase{\endgroup\let~}_% |
69 |
\catcode`_=12 |
70 |
} |
71 |
|
72 |
\usepackage{booktabs} % To thicken table lines |
73 |
|
74 |
\usepackage{algorithm} |
75 |
\usepackage[noend]{algpseudocode} % For pseudocode |
76 |
|
77 |
\begin{document} |
78 |
|
79 |
\title{Thesis - Report Feb 10 - Heuristic Betweenness Centrality for Weighted Graph} |
80 |
|
81 |
\author{Quynh Nguyen - DISI - University of Trento} |
82 |
|
83 |
\maketitle |
84 |
\clearpage |
85 |
|
86 |
\section{Introduction} |
87 |
\subsection{Notation} |
88 |
\textbf{BBC}: the score obtained by Brandes Betweenness Centrality |
89 |
|
90 |
\textbf{BBCT}: the score obtained by Brandes BC with the inclusion of targets |
91 |
|
92 |
\textbf{HBCU}: the heuristic way to obtain BC score, for unweighted graph |
93 |
|
94 |
\textbf{HBCW}: the heuristic way to obtain BC score, for weighted graph |
95 |
|
96 |
\subsection{Dataset} |
97 |
There are 5 datasets in total: |
98 |
|
99 |
\begin{itemize} |
100 |
\item Unweighted graphs |
101 |
\begin{itemize} |
102 |
\item \emph{simple}: this is the graph getting from paper \cite{PuzisZEDB12} |
103 |
\item \emph{ninux_unweighted_connected}: all the vertices and edges are the same as \emph{ninux_30_1}, but the costs for all edges are 1. It's |
104 |
\end{itemize} |
105 |
\item Weighted graphs |
106 |
\begin{itemize} |
107 |
\item \emph{ninux_30_1} |
108 |
\item \emph{olsr-netjson} |
109 |
\item \emph{jsoninfo_topo} |
110 |
\end{itemize} |
111 |
\end{itemize} |
112 |
|
113 |
\subsection{Comparison between BBC, BBCT, HBCU} |
114 |
We have BBC $\sim$ HBCU, there are constant difference between the scores obtained by these 2 methods. |
115 |
|
116 |
And we have BBCT = HBCU. See \ref{fig:feb16_jsoninfo_topo_unweighted} |
117 |
|
118 |
\begin{figure}[h] |
119 |
\caption{BBCT \& HBCU for jsoninfo_topo. Their results are the same} |
120 |
\label{fig:feb16_jsoninfo_topo_unweighted} |
121 |
\includegraphics[]{feb16_jsoninfo_topo_unweighted.eps} |
122 |
\end{figure} |
123 |
|
124 |
\subsection{Purpose} |
125 |
This report will |
126 |
\begin{itemize} |
127 |
\item Show how HBCW is obtained |
128 |
\item Comparing HBCU and HBCW |
129 |
\end{itemize} |
130 |
|
131 |
\section{HBC for weighted graph} |
132 |
\subsection{Method} |
133 |
When calculating the BC for each bi-connected component, \emph{weight_map} is included. As a result, HBCW will take into account the weight of each edge when calculating the number of shortest paths $\sigma$. And the $\sigma$ will affect the final BC score. |
134 |
|
135 |
\subsection{Result} |
136 |
For \textbf{unweighted graph}, BBCT = HBCW. |
137 |
|
138 |
For \textbf{weighted graph}, BBCT = HBCW with these dataset: |
139 |
\begin{itemize} |
140 |
\item \emph{ninux_30_1}. See \ref{fig:feb16_ninux_30_1_weighted} |
141 |
\item \emph{olsr-netjson} |
142 |
\end{itemize} |
143 |
|
144 |
And BBCT != HBCW in the dataset \emph{jsoninfo_topo}. See \ref{fig:feb16_jsoninfo_topo_weighted}. Compare to the result obtained by HBCU in \ref{fig:feb16_jsoninfo_topo_unweighted} |
145 |
|
146 |
\begin{figure}[h] |
147 |
\caption{BBCT \& HBCW for ninux_30_1} |
148 |
\label{fig:feb16_ninux_30_1_weighted} |
149 |
\includegraphics[]{feb16_ninux_30_1_weighted.eps} |
150 |
\end{figure} |
151 |
\begin{figure}[h] |
152 |
\caption{BBCT \& HBCW for jsoninfo_topo. Their results are different} |
153 |
\label{fig:feb16_jsoninfo_topo_weighted} |
154 |
\includegraphics[]{feb16_jsoninfo_topo_weighted.eps} |
155 |
\end{figure} |
156 |
|
157 |
\clearpage |
158 |
\bibliography{references}{} |
159 |
\bibliographystyle{plain} |
160 |
|
161 |
\end{document} |