9736348
Some Problems on Factorizations with Constraints in Bipartite Graphs
Let G = (X, Y, E(G)) be a bipartite graph with vertex set V(G) = X ∪ Y and edge set E(G) and let g and f be two non-negative integer-valued functions defined on V(G) such that g(x) ≤ f(x) for each x ∈ V(G). A (g, f)-factor of G is a spanning subgraph F of G such that g(x) ≤ dF(x) ≤ f(x) for each x ∈ V(F); a (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. In this paper it is proved that every bipartite (mg + m - 1, mf - m + 1)-graph has (g, f)-factorizations randomly k-orthogonal to any given subgraph with km edges if k ≤ g(x) for any x ∈ V(G) and has a (g, f)-factorization k-orthogonal to any given subgraph with km edges if k - 1 ≤ g(x) for any x ∈ V(G) and that every bipartite (mg, m f)-graph has a (g, f)-factorization orthogonal to any given m-star if 0 ≤ g(x) ≤ f(x) for any x ∈ V(G). Furthermore, it is shown that there are polynomial algorithms for finding the desired factorizations and the results in this paper are in some sense best possible.
5451258
Toughness and Perfect Matchings in Graphs
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.
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.
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.
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.
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.
14839466
Algorithms for large-scale genotyping microarrays
MOTIVATION
Analysis of many thousands of single nucleotide polymorphisms (SNPs) across whole genome is crucial to efficiently map disease genes and understanding susceptibility to diseases, drug efficacy and side effects for different populations and individuals. High density oligonucleotide microarrays provide the possibility for such analysis with reasonable cost. Such analysis requires accurate, reliable methods for feature extraction, classification, statistical modeling and filtering.


RESULTS
We propose the modified partitioning around medoids as a classification method for relative allele signals. We use the average silhouette width, separation and other quantities as quality measures for genotyping classification. We form robust statistical models based on the classification results and use these models to make genotype calls and calculate quality measures of calls. We apply our algorithms to several different genotyping microarrays. We use reference types, informative Mendelian relationship in families, and leave-one-out cross validation to verify our results. The concordance rates with the single base extension reference types are 99.36% for the SNPs on autosomes and 99.64% for the SNPs on sex chromosomes. The concordance of the leave-one-out test is over 99.5% and is 99.9% higher for AA, AB and BB cells. We also provide a method to determine the gender of a sample based on the heterozygous call rate of SNPs on the X chromosome. See http://www.affymetrix.com for further information. The microarray data will also be available from the Affymetrix web site.


AVAILABILITY
The algorithms will be available commercially in the Affymetrix software package.
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.
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.