349,106 research outputs found
On the approximability of the maximum induced matching problem
In this paper we consider the approximability of the maximum induced matching problem (MIM). We give an approximation algorithm with asymptotic performance ratio <i>d</i>-1 for MIM in <i>d</i>-regular graphs, for each <i>d</i>≥3. We also prove that MIM is APX-complete in <i>d</i>-regular graphs, for each <i>d</i>≥3
Maximum Likelihood Estimation and Graph Matching in Errorfully Observed Networks
Given a pair of graphs with the same number of vertices, the inexact graph
matching problem consists in finding a correspondence between the vertices of
these graphs that minimizes the total number of induced edge disagreements. We
study this problem from a statistical framework in which one of the graphs is
an errorfully observed copy of the other. We introduce a corrupting channel
model, and show that in this model framework, the solution to the graph
matching problem is a maximum likelihood estimator. Necessary and sufficient
conditions for consistency of this MLE are presented, as well as a relaxed
notion of consistency in which a negligible fraction of the vertices need not
be matched correctly. The results are used to study matchability in several
families of random graphs, including edge independent models, random regular
graphs and small-world networks. We also use these results to introduce
measures of matching feasibility, and experimentally validate the results on
simulated and real-world networks
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