Combinatorial algorithms with performance guarantees for finding several Hamiltonian circuits in a complete directed weighted graph

• Published in: Discrete Applied Mathematics Vol. 196; pp. 54 - 61
• Main Authors: Gimadi, E.Kh, Glebov, A.N., Skretneva, A.A., Tsidulko, O.Yu, Zambalaeva, D.Zh
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 11-12-2015
• Subjects: Asymmetric [formula omitted]-Peripatetic Salesman Problem; Asymptotic optimality; Disjoint Hamiltonian circuits; Performance guarantees; Polynomial algorithm; Random inputs; Asymptotic optimality; Disjoint Hamiltonian circuits; Polynomial algorithm; Performance guarantees; Asymmetric m-Peripatetic Salesman Problem; Random inputs
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2015.03.007

In this paper we present two new polynomial algorithms for the asymmetric version of the m-Peripatetic Salesman Problem (m-APSP) which consists in finding m edge-disjoint Hamiltonian circuits of extremal total weight in a complete weighted digraph. The first algorithm solves the asymmetric 2-PSP on maximum. Its approximation ratio is equal to 2/3. The second algorithm deals with the minimization version of the asymmetric m-PSP on random instances. For this algorithm conditions for asymptotically exactness are presented.