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.
7451094
Orthogonal (g, f)-factorizations in networks
Let G = (V,E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V . Let H1,H2, · · · ,Hk be subgraphs of G such that |E(Hi)| = m, 1 ≤ i ≤ k, and V (Hi) ∩ V (Hj) = ∅ when i 6= j. In this paper it is proved that every (mg + m − 1,mf −m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, · · · , k and shown that there are polynomial-time algorithms to find the desired (g, f)-factorizations.
35387631
A lower bound on connectivities of matroid base graphs
Abstract The connectivity of a graph G and the corank of a matroid M are denoted by κ ( G ) and ϱ , respectively. It is shown that if a graph G is the base graph of a simple matroid M , then κ ( G )⩾2 ϱ and the lower bound of 2 ϱ is best possible.
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 .
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.
5451258
Toughness and Perfect Matchings in Graphs
171789
A database and tool, IM Browser, for exploring and integrating emerging gene and protein interaction data for Drosophila
BackgroundBiological processes are mediated by networks of interacting genes and proteins. Efforts to map and understand these networks are resulting in the proliferation of interaction data derived from both experimental and computational techniques for a number of organisms. The volume of this data combined with the variety of specific forms it can take has created a need for comprehensive databases that include all of the available data sets, and for exploration tools to facilitate data integration and analysis. One powerful paradigm for the navigation and analysis of interaction data is an interaction graph or map that represents proteins or genes as nodes linked by interactions. Several programs have been developed for graphical representation and analysis of interaction data, yet there remains a need for alternative programs that can provide casual users with rapid easy access to many existing and emerging data sets.DescriptionHere we describe a comprehensive database of Drosophila gene and protein interactions collected from a variety of sources, including low and high throughput screens, genetic interactions, and computational predictions. We also present a program for exploring multiple interaction data sets and for combining data from different sources. The program, referred to as the Interaction Map (IM) Browser, is a web-based application for searching and visualizing interaction data stored in a relational database system. Use of the application requires no downloads and minimal user configuration or training, thereby enabling rapid initial access to interaction data. IM Browser was designed to readily accommodate and integrate new types of interaction data as it becomes available. Moreover, all information associated with interaction measurements or predictions and the genes or proteins involved are accessible to the user. This allows combined searches and analyses based on either common or technique-specific attributes. The data can be visualized as an editable graph and all or part of the data can be downloaded for further analysis with other tools for specific applications. The database is available at http://proteome.wayne.edu/PIMdb.htmlConclusionThe Drosophila Interactions Database described here places a variety of disparate data into one easily accessible location. The database has a simple structure that maintains all relevant information about how each interaction was determined. The IM Browser provides easy, complete access to this database and could readily be used to publish other sets of interaction data. By providing access to all of the available information from a variety of data types, the program will also facilitate advanced computational analyses.
1940922
On the scalability of network management information for inter-domain light-path assessment
We investigate the necessary amount of network management information for light-path assessment to dynamically set up end-to-end light-paths across administrative domains in optical networks. Our focus is on the scalability of partial management information. We pose light-path assessment as a decision problem, and define the performance as the Bayes probability of an erroneous decision. We then characterize the scalability of management information as its growth rate with respect to the total resources of the network to achieve a desired performance. Scalability is achieved if the management information needed is only a negligible fraction of the total network resources. Specifically, we consider in this work one type of partial information that grows only logarithmically with the number of wavelengths supported per link. We derive an upper bound for the Bayes error in terms of the blocking probability when a new call is presented at the entrance of the network. We evaluate the upper bound using both independent and dependent models of wavelength usage for intra- and inter-domain calls. Our study shows that there exists a "threshold effect": The Bayes error decreases to zero exponentially 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 the partial information considered can indeed provide the desired performance, and a small percentage of erroneous decisions can be traded off to achieve a large saving in the amount of management information.
26898961
A mobile virtual-distributed system architecture for supporting wireless mobile computing and communications
This paper describes a novel mobile virtual-distrubuted system architecture for supporting global mobile computing and communications. the principal contribution of this paper is to innovatively apply virtual memory concepts to mobile systems by deploying mobile-floating agents to de-couple services and resources from the underlying network and allow them to move around following their mobile users. The mobile-floating agents maintain data structures associated with a mobile user. By combining the mobile-floating agent functions with a predictive mobility management algorithm and location-aware caching and prefetching, services and user data structure are pre-connected and pre-assigned at the locations to which the user is moving. Thus, the users can maintain their data structures or immediately receive service with virtually the same efficiency as at the previous location.
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.
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.