Communication: Integral polyhedra related to integer multicommodity flows on a cycle

Authors:
Kyungsik Lee
Affiliations:
School of Industrial and Management Engineering, Hankuk University of Foreign Studies, San 89 Yongin-si, Kyunggi-do, 449-791, Republic of Korea
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

The integer multicommodity flow problem on a cycle (IMFC) is to find a feasible integral routing of given demands between @k pairs of nodes on a link-capacitated undirected cycle, which is known to be polynomially solvable. Along with integral polyhedra related to IMFC, this paper shows that there exists a linear program, with a polynomial number of variables and constraints, which solves IMFC. Using the results, we also present a compact polyhedral description of the convex hull of feasible solutions to a certain class of instances of IMFC whose number of variables and constraints is O(@k), which in turn means that there exists a non-trivial special case for which a minimum cost integer multicommodity flow problem can be solved in polynomial time.