**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**8

# Search results for: Bipartite graph

##### 8 Web Proxy Detection via Bipartite Graphs and One-Mode Projections

**Authors:**
Zhipeng Chen,
Peng Zhang,
Qingyun Liu,
Li Guo

**Abstract:**

With the Internet becoming the dominant channel for business and life, many IPs are increasingly masked using web proxies for illegal purposes such as propagating malware, impersonate phishing pages to steal sensitive data or redirect victims to other malicious targets. Moreover, as Internet traffic continues to grow in size and complexity, it has become an increasingly challenging task to detect the proxy service due to their dynamic update and high anonymity. In this paper, we present an approach based on behavioral graph analysis to study the behavior similarity of web proxy users. Specifically, we use bipartite graphs to model host communications from network traffic and build one-mode projections of bipartite graphs for discovering social-behavior similarity of web proxy users. Based on the similarity matrices of end-users from the derived one-mode projection graphs, we apply a simple yet effective spectral clustering algorithm to discover the inherent web proxy users behavior clusters. The web proxy URL may vary from time to time. Still, the inherent interest would not. So, based on the intuition, by dint of our private tools implemented by WebDriver, we examine whether the top URLs visited by the web proxy users are web proxies. Our experiment results based on real datasets show that the behavior clusters not only reduce the number of URLs analysis but also provide an effective way to detect the web proxies, especially for the unknown web proxies.

**Keywords:**
Bipartite graph,
clustering,
one-mode projection,
web proxy detection.

##### 7 A New Bound on the Average Information Ratio of Perfect Secret-Sharing Schemes for Access Structures Based On Bipartite Graphs of Larger Girth

**Authors:**
Hui-Chuan Lu

**Abstract:**

In a perfect secret-sharing scheme, a dealer distributes a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of the participants in any unqualified subset is statistically independent of the secret. The access structure of the scheme refers to the collection of all qualified subsets. In a graph-based access structures, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing a given access structure is the ratio of the average length of the shares given to the participants to the length of the secret. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing an access structure is called the optimal average information ratio of that access structure. We study the optimal average information ratio of the access structures based on bipartite graphs. Based on some previous results, we give a bound on the optimal average information ratio for all bipartite graphs of girth at least six. This bound is the best possible for some classes of bipartite graphs using our approach.

**Keywords:**
Secret-sharing scheme,
average information ratio,
star
covering,
deduction,
core cluster.

##### 6 Enhancing the Error-Correcting Performance of LDPC Codes through an Efficient Use of Decoding Iterations

**Authors:**
Insah Bhurtah,
P. Clarel Catherine,
K. M. Sunjiv Soyjaudah

**Abstract:**

The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed conventional LDPC Codes. In this work, the use of the recovery algorithm is further explored to test the performance of LDPC codes while the number of iterations is progressively increased. For experiments conducted with small blocklengths of up to 800 bits and number of iterations of up to 2000, the results interestingly demonstrate that contrary to conventional wisdom, the error-correcting performance keeps increasing with increasing number of iterations.

**Keywords:**
Error-correcting codes,
information theory,
low-density parity-check codes,
sum-product algorithm.

##### 5 The Bipartite Ramsey Numbers b(C2m; C2n)

**Authors:**
Rui Zhang,
Yongqi Sun,
and Yali Wu

**Abstract:**

Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b such that any subgraph G of the complete bipartite graph Kb,b, either G contains a copy of H1 or its complement relative to Kb,b contains a copy of H2. It is known that b(K2,2;K2,2) = 5, b(K2,3;K2,3) = 9, b(K2,4;K2,4) = 14 and b(K3,3;K3,3) = 17. In this paper we study the case that both H1 and H2 are even cycles, prove that b(C2m;C2n) ≥ m + n - 1 for m = n, and b(C2m;C6) = m + 2 for m ≥ 4.

**Keywords:**
bipartite graph,
Ramsey number,
even cycle

##### 4 A Study on the Average Information Ratio of Perfect Secret-Sharing Schemes for Access Structures Based On Bipartite Graphs

**Authors:**
Hui-Chuan Lu

**Abstract:**

A perfect secret-sharing scheme is a method to distribute a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of participants in any unqualified subset is statistically independent of the secret. The collection of all qualified subsets is called the access structure of the perfect secret-sharing scheme. In a graph-based access structure, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing the access structure based on G is defined as AR = (Pv2V (G) H(v))/(|V (G)|H(s)), where s is the secret and v is the share of v, both are random variables from and H is the Shannon entropy. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing a given access structure is called the optimal average information ratio of that access structure. Most known results about the optimal average information ratio give upper bounds or lower bounds on it. In this present structures based on bipartite graphs and determine the exact values of the optimal average information ratio of some infinite classes of them.

**Keywords:**
secret-sharing scheme,
average information ratio,
star covering,
core sequence.

##### 3 The Spanning Laceability of k-ary n-cubes when k is Even

**Authors:**
Yuan-Kang Shih,
Shu-Li Chang,
Shin-Shin Kao

**Abstract:**

**Keywords:**
container,
Hamiltonian,
k-ary n-cube,
m*-connected.

##### 2 N-Sun Decomposition of Complete, Complete Bipartite and Some Harary Graphs

**Authors:**
R. Anitha,
R. S. Lekshmi

**Abstract:**

**Keywords:**
Decomposition,
Hamilton cycle,
n-sun graph,
perfect matching,
spanning tree.

##### 1 N-Sun Decomposition of Complete Graphs and Complete Bipartite Graphs

**Authors:**
R. Anitha,
R. S. Lekshmi

**Abstract:**

**Keywords:**
Hamilton cycle,
n-sun decomposition,
perfectmatching,
spanning tree.