Maintaning maximal matching with lookahead

07/13/2018

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by   Kitti Gelle, et al.

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In this paper we study the problem of fully dynamic maximal matching with lookahead. In a fully dynamic n-vertex graph setting, we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph, preferably with a better time bound than that when running the trivial deterministic algorithm with worst-case time of O(m) (where m is the all-time maximum number of the edges) and recompute the matching from scratch each time a query arrives. We show that a maximal matching can be maintained in an (undirected) general graph with a deterministic amortized update cost of O( m), provided that a lookahead of length m is available, i.e. we can "take a peek" at the next m update operations in advance.