On Obtaining a Minimally-Valued Derangement in a Symmetric Cost Matrix

dc.creatorKleiman, Howard
dc.date2005-09-20
dc.date.accessioned2026-07-07T06:18:20Z
dc.date.available2026-07-07T06:18:20Z
dc.descriptionLet M be an n X n symmetric cost matrix. Assume that D is a derangement of edges in M, i.e., a set of point-disjoint cycles containing all of the n points of M.The modified Floyd-Warshall algorithm applied to ((D')^-1)A^- (where A is an asymmetric cost matrix containing D', a derangement)yielded a solution to the Assignment Problem in O((n^2)logn) running time. Here, applying a variation of the modified F-W algorithm to D^-1)M^-, we may possibly obtain a smaller-valued derangement than D consisting of entries in M. A minimally-valued derangement would be of great value as a good and natural lower bound for an optimal tour in M.
dc.descriptionIt appears that this paper does not generally obtain what I hoped it would: A minimally-valued derangement of edges in a symmetric cost matrix.There may be another procedure that may do so but it has a greater running time
dc.identifierhttps://arxiv.org/abs/math/0509443
dc.identifierhttp://arxiv.org/abs/math/0509443
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94702
dc.subjectCombinatorics
dc.titleOn Obtaining a Minimally-Valued Derangement in a Symmetric Cost Matrix
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