Paper by Erik D. Demaine

Therese C. Biedl, Prosenjit Bose, Erik D. Demaine, and Anna Lubiw, “Efficient Algorithms for Petersen's Matching Theorem”, in Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'99), Baltimore, Maryland, January 17–19, 1999, pages 130–139.

Petersen's theorem is a classic result in matching theory from 1891, stating that every 3-regular bridgeless graph has a perfect matching. Our work explores efficient algorithms for finding perfect matchings in such graphs. Previously, the only relevant matching algorithms were for general graphs, and the fastest algorithm ran in O(n3/2) time. We have developed an O(n log4 n)-time algorithm for matching in a 3-regular bridgeless graph. When the graph is also planar, we have as the main result of our paper an optimal O(n)-time algorithm. We present three applications of this result, terrain guarding, adaptive mesh refinement, and quadrangulation.

The paper is 10 pages and the talk is 20 minutes.

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Related papers:
MatchingJAlgorithms (Efficient Algorithms for Petersen's Matching Theorem)

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Last updated March 12, 2024 by Erik Demaine.