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An Asymptotic Approximation Scheme for Multigraph Edge
"... Abstract The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges are allowed ..."
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Abstract The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges
Approximating Maximum Edge Coloring in Multigraphs
 In APPROX, volume 2462 of LNCS
, 2002
"... We study the complexity of the following problem that we call Max edge tcoloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G that ..."
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Cited by 8 (0 self)
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We study the complexity of the following problem that we call Max edge tcoloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G
A computational approach to edge detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal ..."
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Cited by 4621 (0 self)
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. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussiansmoothed image. We extend this simple detector using operators of several widths to cope
Sum Edge Colorings of Multigraphs . . .
"... We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the compl ..."
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of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, i.e. a partition of its edge set into matchings M1,..., Mt minimizing Pt i=1 iMi. This problem is APXhard, even in the case of bipartite graphs [Marx 2009]. This special case is closely related
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
A Guided Tour to Approximate String Matching
 ACM COMPUTING SURVEYS
, 1999
"... We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining t ..."
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Cited by 584 (38 self)
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We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices according to each case. We conclude with some future work directions and open problems.
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
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