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

Author

Listed:
  • Andrei Nikolaev

    (P. G. Demidov Yaroslavl State University)

  • Anna Kozlova

    (P. G. Demidov Yaroslavl State University)

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.

Suggested Citation

  • Andrei Nikolaev & Anna Kozlova, 2021. "Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search," Journal of Combinatorial Optimization, Springer, vol. 42(2), pages 212-230, August.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:2:d:10.1007_s10878-020-00652-7
    DOI: 10.1007/s10878-020-00652-7
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