Online request server matching
Theoretical Computer Science
Online matching for scheduling problems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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We consider a version of on-line maximum matching where an edge may be matched when either endpoint arrives. In contrast with previous work, we work with general undirected graphs with arbitrary edge weights. Our algorithms are inspired by the maxim "A bird in the hand is worth two in the bush". For the weighted case, we give a deterministic algorithm with a worst-case performance ratio of ${1 \over 4}$. We prove an upper bound on the worst case performance ratio of any deterministic on-line algorithm of ${1 \over 3}$. For the unweighted case, we prove a tight bound of ${2 \over 3}$ on the possible worst-case performance ratio of any deterministic on-line algorithm. All running times are small polynomials ($O(\size{V}\cdot\size{E})$) using naive implementations and no complicated data structures. As justified by previous work, problems of this nature are of practical importance.