DFS is unsparsable and lookahead can help in maximal matching

Gelle, Kitti and Iván, Szabolcs: DFS is unsparsable and lookahead can help in maximal matching. Acta cybernetica, (23) 3. pp. 887-902. (2018)

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Abstract

In this paper we study two problems in the context of fully dynamic graph algorithms that is, when 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 a classical algorithm from scratch each time a query arrives. In the first part we show that there are dense (directed) graphs having no nontrivial strong certificates for maintaining a depth-first search tree, hence the so-called sparsification technique cannot be applied effectively to this problem. In the second part, we show that a maximal matching can be maintained in an (undirected) graph with a deterministic amortized update cost of O(log m) (where m is the all-time maximum number of the edges), provided that a lookahead of length m is available, i.e. we can “take a peek” at the next m update operations in advance.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2018
Volume: 23
Number: 3
Page Range: pp. 887-902
ISSN: 0324-721X
Uncontrolled Keywords: Gráf, Algoritmus
Additional Information: Bibliogr.: p. 901-902. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 08. 08:50
Last Modified: 2018. Nov. 08. 08:50
URI: http://acta.bibl.u-szeged.hu/id/eprint/55683

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