KCCA

This repository contains C++ codes for the paper:

A Counting-based Approach for Efficient 𝑘-Clique Densest Subgraph Discovery

Introduction

In this paper, we study the problem of k-clique densest subgraph (CDS). k-clique densest subgraph (CDS) problem aims to detect a subgraph from a graph, such that the ratio of the number of k-cliques over its vertices is maximized. This problem has received plenty of attention in the literature, and is widely used in identifying larger ``near-cliques''. We develop an efficient approximation algorithm, by employing the state-of-the-art k-clique counting algorithm and proposing some optimization techniques. We have performed extensive experimental evaluation on 14 real-world large graphs and the results demonstrate the high efficiency of our algorithms.

Environment

The codes of KCCA are implemented and tested under the following development environment:

Hardware : Intel(R) Xeon(R) Gold 6338R 2.0GHz CPU and 512GB of memory
Operation System : Ubuntu 20.04.4 LTS (GNU/Linux 5.13.0-40-generic x86_64)
C++ Version: 14

Datasets

We use 14 real-world datasets from different domains, which are downloaded from the Stanford Network Analysis Platform, Laboratory of Web Algorithmics, Network Repository, and Networks.

The statistical information is as follows, and you can click on the Name to navigate to the download link.

Name	\|V\|	\|E\|
bio-SC-GT	1,716	31,564
econ-beacxc	507	42,176
WikiTalk	120,834	237,551
Slashdot	77,360	469,180
loc-gowalla	196,591	950,327
DBLP	317,080	1,049,866
web-Stanford	281,903	1,992,636
web-Google	916,428	4,322,051
as-skitter	1,696,415	11,095,298
Wikipedia-link	3,033,374	43,845,958
zhishi-baidu	7,827,193	62,246,014
ew-2013	4,206,785	101,355,853
Orkut	3,072,627	117,185,083
Friendster	124,836,180	1,806,067,135

How to Run the Codes

The implementations of both KCCA-basic and KCCA algorithms are included in the kcca.cpp, you can use arguments to switch these two algorithms.

You can compile kcca.cpp in KCCA/:

g++ kcca.cpp graph.cpp sct.cpp pava.cpp -O3 -o kcca

and run this file by :

./kcca <graph-path> <k> <max_iter> <output_path> <KCCA-basic/KCCA> <update roder> <approximation rate>

The application of these arguments is as follows.

graph-path is the path to the file that contains the graph data. The graph file should be in txt format and organized as follows:

The first line of this file should contain two integers $n$ (the number of vertices) and $m$ (the number of edges) separated by a space. The index of vertices should be ranged from $0$ to $n - 1$. Each of the following $m$ lines contains one edge by two integers separated by a space. There should be no multiple edges and self-loops in this file.

For example, here is a correct graph file with 4 vertices and 5 edges

k is the k selected for k-cliques.

max_iter is a number of iterations the program takes. If you want the program to stop by a given approximation rate, please set this as 0.

output_path is the path to the file where the program will save its result.

KCCA-basic/KCCA is the option to switch algorithms, 0 stands for KCCA-basic, and 1 stands for KCCA.

update order is the option to switch the update order. Here are three options which are the same as the order given in Figure 6 in our paper.

1 stands for degeneracy order
2 stands for depth order
3 stands for random order

For best performance, simply set this as 1. Note that this option does not work for the KCCA-basic algorithm.

approximation rate is the threshold for approximation rate. The program will terminate itself once it reaches the given approximation rate. This should be set as a float number greater than 1. To use this argument, please set max iter as zero.

For example, if we want to run the KCCA-basic algorithm to approximate 5-cliques densest subgraph from the graph in test.txt taking 10 iterations and output the result to result.txt. The command should be:

./kcca test.txt 5 10 result.txt 0 0 0

If we want to run the KCCA algorithm to approximate 7-cliques densest subgraph from the graph in test.txt by an approximation rate of 1.01 using depth order and output the result to result.txt. The command should be:

./kcca test.txt 7 0 result.txt 1 2 1.01

Contact

If you have any questions about the code or find any errors, please list them in the issue or contact us directly by email:

qingshuoguo@link.cuhk.edu.cn

yinglizhou@link.cuhk.edu.cn

forxenn / KCCA