Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search

Andrei Nikolaev () and Anna Kozlova ()
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Andrei Nikolaev: P. G. Demidov Yaroslavl State University
Anna Kozlova: P. G. Demidov Yaroslavl State University

Journal of Combinatorial Optimization, 2021, vol. 42, issue 2, No 2, 212-230

Abstract: Abstract We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. A sufficient condition for vertex adjacency in the 1-skeleton of the traveling salesperson polytope can be formulated as the Hamiltonian decomposition problem in a 4-regular multigraph. We introduce a heuristic general variable neighborhood search algorithm for this problem based on finding a vertex-disjoint cycle cover of the multigraph through reduction to perfect matching and several cycle merging operations. The algorithm has a one-sided error: the answer “not adjacent” is always correct, and was tested on random directed and undirected Hamiltonian cycles and on pyramidal tours.

Keywords: Hamiltonian decomposition; Traveling salesperson polytope; 1-skeleton; Vertex adjacency; General variable neighborhood search; Variable neighborhood descent; Vertex-disjoint cycle cover; Perfect matching (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-020-00652-7

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