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Problem Statements for k-Node Shortest Path and k-Node Shortest Cycle in a Complete Graph*

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Cybernetics and Systems Analysis Aims and scope

Abstract

The author formulates mixed Boolean linear programming problems to find the shortest route and the shortest cycle that pass through the given number of nodes in a complete graph. Their special cases provide formulations of problems for finding the shortest Hamiltonian path and the shortest Hamiltonian cycle. The problems include no more than 2n2 variables and no more than (n + 1)2 constraints, where n is the number of nodes of the complete graph.

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References

  1. N. Christofides, Graph Theory: An Algorithmic Approach, Acad. Press (1975).

  2. E. V. Alekseeva, Constructing Mathematical Models of Integer Linear Programming. Examples and Problems: A Handbook [in Russian], Novosibirsk. Gos. Univer., Novosibirsk (2012).

  3. Gurobi Optimization, Inc., Gurobi Optimizer Reference Manual (2014), http://www.gurobi.com.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    P. I. Stetsyuk

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  1. P. I. Stetsyuk
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Correspondence to P. I. Stetsyuk.

Additional information

*The study was financially supported by the NAS of Ukraine (Projects No. 0113U003146 and No. 0112U002251).

Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2016, pp. 78–82.

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Stetsyuk, P.I. Problem Statements for k-Node Shortest Path and k-Node Shortest Cycle in a Complete Graph* . Cybern Syst Anal 52, 71–75 (2016). https://doi.org/10.1007/s10559-016-9801-x

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  • DOI: https://doi.org/10.1007/s10559-016-9801-x

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