# Efficient Union-Find for Planar Graphs and other Sparse Graph Classes

Abstract : We solve the Union-Find problem (UF) efficiently for the case the input is restricted to several graph classes, namely partial k-trees for any fixed k, d-dimensional grids for any fixed dimension d and for planar graphs. For the later we develop a technique of decomposing such a graph into small subgraphs, patching, that might be useful for other algorithmic problems on planar graphs, too. By efficiency we do not only mean linear time'' in a theoretical setting but also a practical reorganization of memory such that a dynamic data structures for UF is allocated consecutively and thus to reduce the amount of page fault produced by UF implementations drastically.
Type de document :
Communication dans un congrès
d'Amore, Fabrizio and Franciosa, Paolo Giulio and Marchetti-Spaccamela, Alberto. Graph-Theoretic Concepts in Computer Science, 1996, Cadenabbia, Italy. SV, 1197, pp.181-195, 1997

https://hal.inria.fr/inria-00549672
Contributeur : Jens Gustedt <>
Soumis le : mercredi 22 décembre 2010 - 12:08:12
Dernière modification le : dimanche 20 mai 2018 - 20:20:10

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• HAL Id : inria-00549672, version 1

### Citation

Jens Gustedt. Efficient Union-Find for Planar Graphs and other Sparse Graph Classes. d'Amore, Fabrizio and Franciosa, Paolo Giulio and Marchetti-Spaccamela, Alberto. Graph-Theoretic Concepts in Computer Science, 1996, Cadenabbia, Italy. SV, 1197, pp.181-195, 1997. 〈inria-00549672〉

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