11215369
A note on the least number of edges of 3-uniform hypergraphs with upper chromatic number 2
The upper chromatic number @g@?(H) of a hypergraph H=(X,E) is the maximum number k for which there exists a partition of X into non-empty subsets X=X"1@?X"2@?...@?X"k such that for each edge at least two vertices lie in one of the partite sets. We prove that for every n>=3 there exists a 3-uniform hypergraph with n vertices, upper chromatic number 2 and @?n(n-2)/3@? edges which implies that a corresponding bound proved in [K. Diao, P. Zhao, H. Zhou, About the upper chromatic number of a co-hypergraph, Discrete Math. 220 (2000) 67-73] is best-possible.
5451258
Toughness and Perfect Matchings in Graphs
43698695
The fractional matching numbers of graphs
A fractional matching of a graph G is a function f that assigns to each edge a number in [0, 1] such that, for each vertex v, ∑ f(e) ≤ 1, where the sum is taken over all edges incident to v. The fractional matching number of G is the supremum of ∑e∈E(G)f(e) over all fractional matchings f. In this paper, we provide a new formula for calculating the fractional matching numbers of graphs using the Gallai–Edmonds Structure Theorem. Thus, we characterize graphs for which the fractional matching number equals the matching number and graphs for which the fractional matching number is the maximum possible (one-half the number of vertices). © 2002 Wiley Periodicals, Inc.
205876923
Number of maximum matchings of bipartite graphs with positive surplus
A bipartite graph G=(A,B) is said to have positive surplus (as viewed from A) if the number of neighbors of X is bigger than the size of X for any non-empty subset X of A. In this paper, two lower bounds on the number of maximum matchings in bipartite graphs with positive surplus are obtained. The enumeration problems for maximum matchings in special bipartite graphs are solved. From this, the number of perfect matchings of some elementary bipartite graphs is given.
1047063
Generalization of matching extensions in graphs
Abstract Let G be a graph with vertex set V(G) . Let n, k and d be non-negative integers such that n+2k+d⩽|V(G)|−2 and |V(G)|−n−d is even. A matching which covers exactly |V(G)|−d vertices of G is called a defect - d matching of G . If when deleting any n vertices of G the remaining subgraph contains a matching of k edges and every k -matching can be extended to a defect- d matching, then G is called a (n,k,d) - graph . In this paper a characterization of (n,k,d) -graphs is given and several properties (such as connectivity, minimum degree, hierarchy, etc.) of (n,k,d) -graphs are investigated.
26869429
Orthogonal (g, f)-factorizations in graphs
Abstract Let G be a graph and let F = F 1 , F 2 , …, F m and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with F i for all i, 1 ⩽ i ⩽ m , then we say that F is orthogonal to H . Let g and f be two integer-valued functions defined on V ( G ) such that g ( x ) ⩽ f ( x ) for every x ϵ V ( G ). In this paper it is proved that for any m -matching M of an ( mg + m − 1, mf − m + 1)-graph G, there exists a ( g , f )-factorization of G orthogonal to M .
232914
Active and real-time functionalities for electronic brokerage design
In this position paper, we discuss an architecture for developing next generation electronic brokerages using active and real-time functionalities. These electronic brokerages support timeliness requirements and allow users to express complex preferences. User preferences can be conveniently captured as event-condition-action (ECA) rules. The design allows pro-active monitoring of user preferences and execution of actions in a timely manner. A proof-of-concept prototype is implemented using Java in the context of online trading. The prototype consists of three major components: rule validator, active rule manager and event monitor.
8336028
Evaluation and optimization of clustering in gene expression data analysis
MOTIVATION
A measurement of cluster quality is needed to choose potential clusters of genes that contain biologically relevant patterns of gene expression. This is strongly desirable when a large number of gene expression profiles have to be analyzed and proper clusters of genes need to be identified for further analysis, such as the search for meaningful patterns, identification of gene functions or gene response analysis.


RESULTS
We propose a new cluster quality method, called stability, by which unsupervised learning of gene expression data can be performed efficiently. The method takes into account a cluster's stability on partition. We evaluate this method and demonstrate its performance using four independent, real gene expression and three simulated datasets. We demonstrate that our method outperforms other techniques listed in the literature. The method has applications in evaluating clustering validity as well as identifying stable clusters.


AVAILABILITY
Please contact the first author.
16951731
Network management information for light-path assessment: trade-off between performance and complexity
Network management information for light-path assessment to dynamically set up end-to-end lightpaths across administrative domains is investigated. Our focus is on investigating what performance can be possibly achieved given partial management information, and whether a small loss in performance can trade off with a large saving in management information. The partial information we consider includes aggregated characterization of subnetworks, and local states from wavelength converters. We cast the light-path assessment as a decision problem, and define the performance as the probability of an erroneous decision. We apply the decision theory to show that the optimal performance using the partial information is the Bayes probability of error. We derive an upper bound of the Bayes error in terms of the blocking probability. We evaluate the upper bound using both independent and dependent models of wavelength usage. Our study shows that there exits a "threshold effect": the Bayes error decreases exponentially to 0 with respect to the load when the load is either below or above a threshold value; and is nonnegligible when the load is in a small duration around the threshold. This suggests that a small percentage of error decisions can trade off with a large saving in management information.
5830047
A*Prune: an algorithm for finding K shortest paths subject to multiple constraints
We present a new algorithm, A*Prune, to list (in order of increasing length) the first K multiple-constrained-shortest-path (KMCSP) between a given pair of nodes in a digraph in which each are is associated with multiple quality of-service (QoS) metrics. The algorithm constructs paths starting at the source and going towards the destination. But, at each iteration, the algorithm gets rid of all paths that are guaranteed to violate the constraints, thereby keeping only those partial paths that have the potential to be turned into feasible paths, from which the optimal paths are drawn. The choice of which path to be extended first and which path can be pruned depend upon a projected path cost function, which is obtained by adding the cost already incurred to get to an intermediate node to an admissible cost to go the remaining distance to the destination. The Dijkstra's shortest path algorithm is a good choice to give a good admissible cost. Experimental results show that A*Prune is comparable to the current best known /spl epsiv/-approximate algorithms for most of randomly generated graphs, BA*Prune, which combines the A*Prune with any known polynomial time /spl epsiv/-approximate algorithms to give either optimal or /spl epsiv/-approximate solutions to the KMCSP problem, is also presented.
195706995
A Mobility-Aware Dynamic Database Caching Scheme for Wireless Mobile Computing and Communications
This paper describes a mobility-aware dynamic database caching scheme for wireless mobile computing and communications. A mobile-floating agent scheme is proposed, in which caching techniques are cognizant of the mobile nature of mobile users and the location-sensitive nature of mobile systems. The mobile-floating agent maintains a second class cache in the fixed network and employs Barbara’s “invalidation reports broadcasting” cache consistency strategies to maintain a dynamic cache consistent with the first class cache in the mobile client. The “invalidation reports broadcasting” scheme is combined with knowledge of the mobility behavior of each individual mobile user and broadcasts of invalidation reports only occur within the user’s mobility area. The evaluation results show that, for a large system (200 cells), this scheme can reduce the system cost by more than 87%, for even highly mobile users, compared with a fully replicated database system.