Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

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dc.creatorFekete, Sandor P.
dc.creatorMeijer, Henk
dc.creatorRohe, Andre
dc.creatorTietze, Walter
dc.date2002-12-16
dc.date.accessioned2026-07-25T16:37:52Z
dc.descriptionWe consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.
dc.description20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 2002
dc.identifierhttps://arxiv.org/abs/cs/0212044
dc.identifierhttp://arxiv.org/abs/cs/0212044
dc.identifierJournal of Experimental Algorithms, 7 (2002), article 11.
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/42605
dc.subjectData Structures and Algorithms
dc.subjectF.2.2; G.2.2
dc.titleSolving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
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