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The Steiner Traveling Salesman Polytope and Related Polyhedra

Baïou, Mourad; Mahjoub, Ali Ridha (2002), The Steiner Traveling Salesman Polytope and Related Polyhedra, SIAM Journal on Optimization, 13, 2, p. 498-507. http://dx.doi.org/10.1137/S1052623400322287

Type
Article accepté pour publication ou publié
Date
2002
Journal name
SIAM Journal on Optimization
Volume
13
Number
2
Publisher
SIAM
Pages
498-507
Publication identifier
Metadata
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Author(s)
Baïou, Mourad
Mahjoub, Ali Ridha
Abstract (EN)
In this paper we consider an extended formulation of the Steiner traveling salesman problem, that is, when variables are associated with both the edges and the nodes of the graph. We give a complete linear description of the associated polytope when the underlying graph is series-parallel. By projecting this polytope onto the edge variables, we obtain a characterization of the Steiner traveling salesman polytope in the same class of graphs. Both descriptions yield polynomial time (cutting plane) algorithms for the corresponding problems in that class of graphs.
Subjects / Keywords
Polyhedral combinatorics; Polytopes; Traveling salesman problem