40411122
Super Restricted Edge Connectivity of Regular Graphs
An edge cut of a connected graph is called restricted if it separates this graph into components each having order at least 2; a graph G is super restricted edge connected if G−S contains an isolated edge for every minimum restricted edge cut S of G. It is proved in this paper that k-regular connected graph G is super restricted edge connected if k > |V(G)|/2+1. The lower bound on k is exemplified to be sharp to some extent. With this observation, we determined the number of edge cuts of size at most 2k−2 of these graphs.
205056734
Hamiltonicity of a Type of Interchange Graphs
Abstract Let R(r1,…, rm) and S(s1,…, sn) be two nonnegative integral vectors, and let U (R,S) denote the class of all m×n matrices of 0's and 1's having row sum vector R and column sum vector S. We prove that if s1s2⋯sn1, the interchange graph G(R,S) of U (R,S) is hamiltonian.
46002685
3-Restricted Edge Connectivity Of Vertex Transitive Graphs
32475390
k-Cycle resonant graphs
Abstract A connected graph G is said to be k -cycle resonant if, for 1 ⩽ t ⩽ k , any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M -alternating cycle. In this paper, we at the first time introduce the concept of k -cycle resonant graphs, and investigate some properties of k -cycle resonant graphs. Some simple necessary and sufficient conditions for a graph to be k -cycle resonant are given. The construction of k -cycle resonant hexagonal systems are also characterized.
5788058
Heredity of the index of convergence of the line digraph
Let D be a digraph, and let Ln(D) and k(D) denote the nth iterated line digraph of D and the index of convergence of D, respectively. We prove that if D contains neither sources nor sinks, then: (1) k(Ln(D))=k(D)=0 if every connected component of D is a directed cycle. (2) k(Ln(D))=k(D)+n if there exists at least one connected component of D that is not a directed cycle. Finally, we prove that if D has no sources or no sinks then k(D) ≤ k(L(D)) ≤ k(D)+1.
16653289
Reducible chains of planar 1-cycle resonant graphs
A connected graph G is said to be k-cycle resonant if, for 1≤t≤k, any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M-alternating cycle. The concept of k-cycle resonant graphs was introduced by the present authors in 1994. Some necessary and sufficient conditions for a graph to be k-cycle resonant were given. Recently, some necessary and sufficient conditions for a planar graph to be 1-cycle resonant and 2-cycle resonant were also given. In this paper, we investigate 1-cycle-resonant reducible (simply 1-CR-reducible) chains of planar 1-cycle resonant graphs. The upper and lower bounds of the numbers of 1-CR-reducible chains of planar 1-cycle resonant graphs are given. Consequently, it is shown that any planar 1-cycle resonant graph has an ear decomposition. Furthermore, a construction method of planar 1-cycle resonant graphs and an efficient algorithm for recognizing 1-cycle resonant graphs are established.
45226722
Enhancing Parallelism by Removing Cyclic Data Dependencies
The parallel execution of loop iterations often is inhibited by recurrence relations on scalar variables. Examples are the use of induction variables and recursive functions. Due to the cyclic dependence between the iterations, these loops have to be executed sequentially. A method is presented to convert a family of coupled linear recurrence relations into explicit functions of a loop index. When the cyclic dependency is the only factor preventing a parallel execution, the conversion effectively removes the dependency and allows the loop to be executed in parallel. The technique is based on constructing and solving a set of coupled linear difference equations at compile-time. The method is general for an arbitrary number of coupled scalar variables and can be implemented by a straight-forward algorithm. Results show that the parallelism of several sequential EISPACK do-loops is significantly enhanced by the converting them into do-all loops.
1083190
Streaming media caching algorithms for transcoding proxies
Streaming media is expected to become one of the most popular types of Web content in the future. Due to increasing variety of client devices and the range of access speeds to the Internet, multimedia contents may be required to be transcoded to match the client's capability. With transcoding, both the network and the proxy CPU are potential bottlenecks for streaming media delivery. This paper discusses and compares various caching algorithms designed for transcoding proxies. In particular we propose a new adaptive algorithm that dynamically selects an appropriate metric for adjusting the management policy. Experimental results show that the proposed algorithm significantly outperforms those that cache only untranscoded or only transcoded objects. Moreover motivated by the characteristics of many video compression algorithms, we investigate partitioning a video object into sections based on frame type and handling them individually for proxy caching. It is found that partitioning improves performance when CPU power rather than network bandwidth is the limiting resource, particularly when the reference pattern is not highly skewed.
15887745
The Rotation Graphs of Perfect Matchings of Plane Bipartite Graphs
Abstract In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC systems and perfect matchings in G.
2376990
Power-aware processor scheduling under average delay constraints
In this paper, voltage scaling strategies for scheduling aperiodic tasks under average delay constraints are studied. Dynamic voltage scaling in single processor systems is formulated as a constrained stochastic optimization problem for which the optimal solution can be obtained using a combination of Lagrange relaxation and the value iteration method. For multiprocessor systems, we present a two-phase approach. In the first phase, the speed settings and static workload distribution of the processors are optimized to minimize the total power dissipation. Dynamic voltage scaling techniques are then applied to each individual processor in the second phase. Both homogeneous and heterogeneous systems have been investigated. Based on queueing theory, the proposed algorithms guarantee conformity to the average delay constraint. Moreover, our simulation experiments have shown they are effective for minimizing power consumption.
29766053
Construction for bicritical graphs and k-extendable bipartite graphs
A graph G is said to be bicritical if G-u-v has a perfect matching for every choice of a pair of points u and v. Bicritical graphs play a central role in decomposition theory of elementary graphs with respect to perfect matchings. As Plummer pointed out many times, the structure of bicritical graphs is far from completely understood. This paper presents a concise structure characterization on bicritical graphs in terms of factor-critical graphs and transversals of hypergraphs. A connected graph G with at least 2k+2 points is said to be k-extendable if it contains a matching of k lines and every such matching is contained in a perfect matching. A structure characterization for k-extendable bipartite graphs is given in a recursive way. Furthermore, this paper presents an O(mn) algorithm for determining the extendability of a bipartite graph G, the maximum integer k such that G is k-extendable, where n is the number of points and m is the number of lines in G.