Maximal Total Length Of k Disjoint Cycles In Bipartite Graphs
Let k, s and n be three integers with s≥k≥2, n≥2k+1. Let G=(V1,V2;E) be a bipartite graph with |V1|=|V2|=n. If the minimum degree of G is at least s+1, then G contains k vertex-disjoint cycles covering at least min(2n,4s) vertices of G.

title: On Independent Cycles in a Bipartite Graph
abstract: Let G=(V1,V2;E) be a bipartite graph with 2k≤m=|V1|≤|V2|=n, where k is a positive integer. We show that if the number of edges of G is at least (2k−1)(n−1)+m, then G contains k vertex-disjoint cycles, unless e(G)=(2k−1)(n−1)+m and G belongs to a known class of graphs.

title: Packing Three Copies of a Tree into a Complete Graph
abstract: A three T of order n is said to be 3-placeable if there are three edge-disjoint copies of T in Kn. In this paper we characterize all the trees T such that T is 3-placeable.

title: On Quadrilaterals and Cycle Covers in a Bipartite Graph

title: On Covering a Bipartite Graph with Cycles
abstract: We conjectured in [H. Wang,  (1999), pp. 115--121] that, for each integer $k\geq 2$, there exists N(k) such that if G=(V1,V2;E) is a bipartite graph with $|V_1|=|V_2|=n\geq N(k)$ and d(x)+d(y)\geq n+k$ for each pair of nonadjacent vertices x and y of G with $x\in V_1$ and $y\in V_2$, then for any k independent edges e1, . . ., ek of G, there exist k vertex-disjoint cycles C1, . . . ,Ck in G such that $e_i\in E(C_i)$ for all $i\in\{1,\ldots ,k\}$ and $V(C_1\cup\cdots \cup C_k)=V(G)$. This conjecture is also verified for k=2 in [H. Wang,  (1999), pp. 115--121]. We prove this conjecture for k=3 in this paper.

title: Vertex-Disjoint Triangles in Claw-Free Graphs with Minimum Degree at Least Three
abstract: . Our main result is as follows: For any integer , if G is a claw-free graph of order at least and with minimum degree at least 3, then G contains k vertex-disjoint triangles unless G is of order and G belongs to a known class of graphs. We also construct a claw-free graph with minimum degree 3 on n vertices for each such that it does not contain k vertex-disjoint triangles. We put forward a conjecture on vertex-disjoint triangles in -free graphs.

title: Prime Cube Graph Approach for Processor Allocation in Hypercube Multiprocessors

title: How to fool an unbounded adversary with a short key
abstract: The symmetric encryption problem which manifests itself when two parties must securely transmit a message m with a short shared secret key is considered in conjunction with a computationally unbounded adversary. As the adversary is unbounded, any encryption scheme must leak information about m; in particular, the mutual information between m and its ciphertext cannot be zero. Despite this, a family of encryption schemes is presented that guarantee that for any message space in {0,1}n with minimum entropy n-lscr and for any Boolean function h:{0,1}n rarr {0,1}, no adversary can predict h(m) from the ciphertext of m with more than 1/nomega(1)  advantage; this is achieved with keys of length lscr+omega(logn). In general, keys of length lscr+s yield a bound of 2-Theta(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently. Applications of this to cryptosystems based on complexity-theoretic assumptions are discussed and, in addition, a simplified proof of a fundamental "elision lemma" of Goldwasser and Micali is provided

title: A Performance Study of Secure Data Mining on the Cell Processor
abstract: This paper examines the potential of the Cell processor as a platform for secure data mining on the future volunteer computing systems. Volunteer computing platforms have the potential to provide massive computing power. However, privacy and security concerns prevent using volunteer computing for data mining of sensitive data. The Cell processor comes with a hardware security feature. The secure volunteer data mining can be achieved by using this hardware security feature. In this paper, we present a general security scheme for the volunteer computing, and a secure parallelized K-Means clustering algorithm for the Cell processor. We also evaluate the performance of the algorithm on the Cell secure system simulator. Evaluation results indicate that the proposed secure data clustering outperforms a non-secure clustering algorithm on the general purpose CPU, but incurs a huge performance overhead introduced by the decryption process of the Cell security features.

title: How to fool an unbounded adversary with a short key
abstract: The symmetric encryption problem which manifests itself when two parties must securely transmit a message m with a short shared secret key is considered in conjunction with a computationally unbounded adversary. As the adversary is unbounded, any encryption scheme must leak information about m; in particular, the mutual information between m and its ciphertext cannot be zero. Despite this, a family of encryption schemes is presented that guarantee that for any message space in {0,1}n with minimum entropy n-lscr and for any Boolean function h:{0,1}n rarr {0,1}, no adversary can predict h(m) from the ciphertext of m with more than 1/nomega(1) advantage; this is achieved with keys of length lscr+omega(logn). In general, keys of length lscr+s yield a bound of 2-Theta(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently. Applications of this to cryptosystems based on complexity-theoretic assumptions are discussed and, in addition, a simplified proof of a fundamental "elision lemma" of Goldwasser and Micali is provided

title: A Scalable Pipelined Associative SIMD Array with Reconfigurable PE Interconnection Network for Embedded Applications
abstract: This paper describes the FPGA implementation of a specialized SIMD processor array for embedded applications. An alternative to traditional SoC or MPSoC architectures, this array combines the massive parallelism inherent in SIMD architectures with the search capabilities of associative computing, producing a SIMD Processor Array System on a Chip (PASoC) well suited for applications such as data mining and bioinformatics. This paper first describes the architecture of the system, and then the pipelining of the processing elements and the addition of a reconfigurable interconnection network. Finally, the paper concludes with a brief description of a string-matching algorithm that can be used for the applications cited above.