Dynamic matchings in convex bipartite graphs

  • Authors:

  • Gerth Stølting Brodal;Loukas Georgiadis;Kristoffer Arnsfelt Hansen;Irit Katriel

  • Affiliations:

  • University of Aarhus, Århus, Denmark;Hewlett-Packard Laboratories, Palo Alto, CA;University of Chicago, Chicago, IL;Brown University, Providence, RI

  • Venue:
  • MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

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(√|V| log2 |V|)-time amortized bound for this pair query.