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Dynamic Matchings in Convex Bipartite Graphs

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  • Department of Computer Science
  • Teoretisk naturvidenskab
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching in sub-linear time per operation, even in the amortized sense. Despite this difficulty, we develop a data structure which maintains the set of vertices that participate in a maximum matching in O(log2|V|) amortized time per update and reports the status of a vertex (matched or unmatched) in constant worst-case time. Our structure can report the mate of a matched vertex in the maximum matching in worst-case O( min { k log2|V| + log|V|, |V| log|V|}) time, where k is the number of update operations since the last query for the same pair of vertices was made. In addition, we give an O(Vlog2V) -time amortized bound for this pair query.
Original languageEnglish
Title of host publicationProc. 32nd International Symposium on Mathematical Foundations of Computer Science
EditorsLudek Kucera, Antonin Kucera
Number of pages12
Publication year2007
Publication statusPublished - 2007
Event32nd International Symposium on Mathematical Foundations of Computer Science - Providence, RI, United States
Duration: 20 Oct 200723 Oct 2007


Conference32nd International Symposium on Mathematical Foundations of Computer Science
LandUnited States
ByProvidence, RI
SeriesLecture Notes in Computer Science

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