11189498
On the spanning connectivity of graphs
Abstract A k-container C ( u , v ) of G between u and v is a set of k internally disjoint paths between u and v . A k -container C ( u , v ) of G is a k * - container if it contains all vertices of G . A graph G is k * - connected if there exists a k * -container between any two distinct vertices. The spanning connectivity of G , κ * ( G ) , is defined to be the largest integer k such that G is w * -connected for all 1 ⩽ w ⩽ k if G is a 1 * -connected graph. In this paper, we prove that κ * ( G ) ⩾ 2 δ ( G ) - n ( G ) + 2 if ( n ( G ) / 2 ) + 1 ⩽ δ ( G ) ⩽ n ( G ) - 2 . Furthermore, we prove that κ * ( G - T ) ⩾ 2 δ ( G ) - n ( G ) + 2 - | T | if T is a vertex subset with | T | ⩽ 2 δ ( G ) - n ( G ) - 1 .
12579085
The super laceability of the hypercubes
A k-container C(u,v) of a graph G is a set of k disjoint paths joining u to v. A k-container C(u, v) is a k*-container if every vertex of G is incident with a path in C(u,v). A bipartite graph G is k*-laceable if there exists a k*-container between any two vertices u, v from different partite set of G. A bipartite graph G with connectivity k is super laceable if it is i*-laceable for all i ≤ k. A bipartite graph G with connectivity k is f-edge fault-tolerant super laceable if G - F is i*-laceable for any 1 ≤ i ≤ k-f and for any edge subset F with |F|=f r is super laceable. Moreover, Q r is f-edge fault-tolerant super laceable for any f ≤ r - 2.
3010311
On the spanning w-wide diameter of the star graph
Let u and v be any two distinct nodes of an undirected graph G, which is k -connected. A container C(u, v ) between u and v is a set of internally disjoint paths {P1, P2, . . . , Pw } between u and v where 1 ≤ w ≤ k . The width of C(u, v ) is w and the length of C(u, v ) {written as l [C(u, v )]} is max{l (Pi ) | 1 ≤ i ≤ w }. A w -container C(u, v ) is a container with width w . The w -wide distance between u and v , dw (u, v ), is min{l (C(u, v )) | C(u, v ) is a w -container}. A w -container C(u, v ) of the graph G is a w ∗-container if every node of G is incident with a path in C(u, v ). That means that the w -container C(u, v ) spans the whole graph. Let Sn be the n-dimensional star graph with n ≥ 5. It is known that Sn is bipartite. In this article, we show that, for any pair of distinct nodes u and v in different partite sets of Sn , there exists an (n − 1)∗-container C(u, v ) and the (n − 1)-wide distance d(n−1)(u, v ) is less than or equal to n! n−2 + 1. In addition, we also show the existence of a 2∗-container C(u, v ) and the 2-wide distance d2(u, v ) is bounded above by n! 2 + 1. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(4), 235–249 2006
40521773
Cycle decompositions of crowns
Abstract For an integer n ⩾3, the crown S n 0 is defined to be the graph with vertex set { x 0 , x 1 ,…, x n −1 , y 0 , y 1 ,…, y n −1 } and edge set {x i y j : 0⩽i,j⩽n−1, i≠j} . In this paper we give some sufficient conditions for the edge decomposition of the crown into isomorphic cycles.
1057171
ZPL's WYSIWYG performance model
ZPL is a parallel array language designed for high performance scientific and engineering computations. Unlike other parallel languages, ZPL is founded on a machine model (the CTA) that accurately abstracts contemporary MIMD parallel computers. This makes it possible to correlate ZPL programs with machine behavior. As a result, programmers can reason about how code will perform on a typical parallel machine and thereby make informed decisions between alternative programming solutions. The paper describes ZPL's performance model and its syntactic cues for conveying operation cost. The what you see is what you get (WYSIWYG) nature of ZPL operations is demonstrated on the IBM SP-2, Intel Paragon, SGI Power Challenge, and Cray T3E. Additionally, the model is used to evaluate two algorithms for matrix multiplication. Experiments show that the performance model correctly predicts the faster solution on all four platforms for a range of problem sizes.
37848261
A New Force-Directed Graph Drawing Method Based on Edge-Edge Repulsion
The conventional force-directed methods for drawing undirected graphs are based on either vertex-vertex repulsion or vertex-edge repulsion. In this paper, we propose a new force-directed method based on edge-edge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and a final drawing can be generated by adjusting positions of vertices according to spring forces and the repulsive forces, derived from potential fields, among edges. Different from the previous methods, our new framework has the advantage of overcoming the problem of zero angular resolution, guaranteeing the absence of any overlapping of edges incident to the common vertex. Given graph layouts probably generated by classical algorithms as the inputs to our algorithm, experimental results reveal that our approach produces promising drawings (especially for trees and hypercubes) not only preserving the original properties of a high degree of symmetry and uniform edge length, but also preventing zero angular resolution. By allowing vertex-vertex overlapping, our algorithm also results in more symmetrical drawings.
9253913
BEARR: Batch Extraction and Analysis of cis-Regulatory Regions
Transcription factors play important roles in regulating biological and disease processes. Microarray technology has enabled researchers to simultaneously monitor changes in the expression of thousands of transcripts. By identifying specific transcription factor binding sites in the cis-regulatory regions of differentially expressed genes, it is then possible to identify direct targets of transcription factors, model transcriptional regulatory networks and mine the dataset for relevant targets for experimental and clinical manipulation. We have developed web-based software to assist biologists in efficiently carrying out the analysis of microarray data from studies of specific transcription factors. Batch Extraction and Analysis of cis-Regulatory Regions, or BEARR, accepts gene identifier lists from microarray data analysis tools and facilitates identification, extraction and analysis of regulatory regions from the large amount of data that is typically generated in these types of studies. The software is publicly available at http://giscompute.gis.a-star.edu.sg/~vega/BEARR1.0/.
5604476
A robust image authentication method distinguishing JPEG compression from malicious manipulation
Image authentication verifies the originality of an image by detecting malicious manipulations. Its goal is different from that of image watermarking, which embeds into the image a signature surviving most manipulations. Most existing methods for image authentication treat all types of manipulation equally (i.e., as unacceptable). However, some practical applications demand techniques that can distinguish acceptable manipulations (e.g., compression) from malicious ones. In this paper, we present an effective technique for image authentication which can prevent malicious manipulations but allow JPEG lossy compression. The authentication signature is based on the invariance of the relationships between discrete cosine transform (DCT) coefficients at the same position in separate blocks of an image. These relationships are preserved when DCT coefficients are quantized in JPEG compression. Our proposed method can distinguish malicious manipulations from JPEG lossy compression regardless of the compression ratio or the number of compression iterations. We describe adaptive methods with probabilistic guarantee to handle distortions introduced by various acceptable manipulations such as integer rounding, image filtering, image enhancement, or scaling-recaling. We also present theoretical and experimental results to demonstrate the effectiveness of the technique.