Cybernetics and Systems Analysis

, Volume 52, Issue 1, pp 71–75 | Cite as

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

Article

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.

Keywords

complete graph shortest path linear programming problem Hamiltonian path Hamiltonian cycle traveling salesman problem 

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References

  1. 1.
    N. Christofides, Graph Theory: An Algorithmic Approach, Acad. Press (1975).Google Scholar
  2. 2.
    E. V. Alekseeva, Constructing Mathematical Models of Integer Linear Programming. Examples and Problems: A Handbook [in Russian], Novosibirsk. Gos. Univer., Novosibirsk (2012).Google Scholar
  3. 3.
    Gurobi Optimization, Inc., Gurobi Optimizer Reference Manual (2014), http://www.gurobi.com.

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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