Small stretch spanners on dynamic graphs

Authors:
Giorgio Ausiello;Paolo G. Franciosa;Giuseppe F. Italiano
Affiliations:
Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Roma, Italy;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Roma, Italy;Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, Roma, Italy
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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Abstract

We present fully dynamic algorithms for maintaining 3- and 5-spanners of undirected graphs. For unweighted graphs we maintain a 3- or 5-spanner under insertions and deletions of edges in O(n) amortized time per operation over a sequence of Ω(n) updates. The maintained 3-spanner (resp., 5-spanner) has O(n3/2) edges (resp., O(n4/3) edges), which is known to be optimal. On weighted graphs with d different edge cost values, we maintain a 3- or 5-spanner in O(n) amortized time per operation over a sequence of Ω(dn) updates. The maintained 3-spanner (resp., 5-spanner) has O(dn3/2) edges (resp., O(dn4/3) edges). The same approach can be extended to graphs with real-valued edge costs in the range [1,C]. All our algorithms are deterministic and are substantially faster than recomputing a spanner from scratch after each update.