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The Symmetric Generalized Travelling Salesman Polytope (1995)  (Make Corrections)  (4 citations)
Matteo Fischetti, Juan Jos
NETWORKS: Networks: An International Journal



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Abstract: The symmetric Generalized Travelling Salesman Problem (GTSP) is a variant of the classical symmetric Travelling Salesman Problem, in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster. A different version of the problem, called E-GTSP, arises when exactly one node for each cluster has to be visited. Both GTSP and E-GTSP are NP-hard problems, and find practical applications in routing and scheduling. In this paper we model GTSP and... (Update)

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...Steiner tree polyhedra for directed graphs. To our knowledge, there is no previous work on the GST polytope. Fischetti, Salazar and Toth [6] present a polyhedral analysis of a related polytope where the tree requirement is replaced by a cycle requirement . The paper is...

...Travelling Salesman Problem (GTSP) and nds practical applications in routing, scheduling and location routing. In a companion paper [5] we modeled GTSP as an integer linear program, and studied the facial structure of two polytopes associated with the problem. Here we...

Cited by:   More
A Branch-and-Cut Algorithm for the Undirected.. - Laporte..   (Correct)
On the Cycle Polytope of a Undirected Graph - González (1994)   (Correct)
A Branch-and-Cut Algorithm for the Symmetric.. - Fischetti.. (1995)   (Correct)

Active bibliography (related documents):   More   All
0.5:   A Polyhedral Study of the Asymmetric Travelling.. - Ascheuer, Fischetti, .. (1997)   (Correct)
0.5:   The m-Cost ATSP - Helmberg (1999)   (Correct)
0.3:   Solving the Orienteering Problem through Branch-and-Cut - Fischetti, González (1998)   (Correct)

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0.6:   Experiments with a multi-commodity formulation for.. - Fischetti.. (1995)   (Correct)
0.6:   Worst-case Comparison of Valid Inequalities for the TSP - Goemans (1995)   (Correct)
0.5:   The Median Cycle Problem - Labbé, Laporte, Martín, González (1999)   (Correct)

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2:   TSPLIB --- A Traveling Salesman Problem Library (context) - Reinelt - 1991
2:   Odd minimum cut-sets and b- matching (context) - Padberg, Rao - 1982
2:   A branch and cut algorithm for the symmetric generalized traveling salesman prob.. - Fischetti, Gonz'alez et al. - 1994

BibTeX entry:   (Update)

M. Fischetti, J.J. Salazar, P. Toth, \The Symmetric Generalized Travelling Salesman Polytope", Networks 26 (1995) 113-123. http://citeseer.ist.psu.edu/fischetti95symmetric.html   More

@article{ fischetti95symmetric,
    author = "Fischetti and Gonzalez and Toth",
    title = "The Symmetric Generalized Traveling Salesman Polytope",
    journal = "NETWORKS: Networks: An International Journal",
    volume = "26",
    year = "1995",
    url = "citeseer.ist.psu.edu/fischetti95symmetric.html" }
Citations (may not include all citations):
106   The Traveling Salesman Problem: A Guided Tour of Combinatori.. (context) - Lawler, Lenstra et al. - 1985
38   The Prize Collecting Traveling Salesman Problem (context) - Balas - 1989
16   A Branch-and-Cut Algorithm for the Symmetric Generalized Tra.. - Fischetti, Salazar et al. - 1993
16   The graphical relaxation: A new framework for the Symmetric .. (context) - Naddef, Rinaldi - 1993
11   A Lifting Procedure for the Asymmetric Traveling Salesman Po.. (context) - Balas, Fischetti - 1993
9   The Prize Collecting Traveling Salesman Problem: II (context) - Balas - 1993
8   Polyhedral theory (context) - Gr, Padberg
7   A note on zero{one programming (context) - Padberg - 1975
6   An Additive Approach for the Optimal Solution of the PrizeCo.. (context) - Fischetti, Toth - 1988
5   A Lagrangian Based Approach for the Asymmetric Generalized T.. (context) - Noon, Bean - 1991
2   Generalized Travelling Salesman Problem through n sets of no.. (context) - Laporte, Mercure et al. - 1987
2   The Symmetric Generalized Travelling Salesman Problem (context) - Sepehri - 1991
2   Generalized Travelling Salesman through n sets of nodes: an .. (context) - Laporte, Nobert - 1983
2   The Fixed-Outdegree 1-Arborescence Polytope (context) - Balas, Fischetti - 1992
2   Department of Industrial and Operations Research (context) - Noon, Traveling et al. - 1988
2   Algoritmi per il problema del Commesso Viaggiatore Generaliz.. (context) - Salazar - 1992
1   An Ecient Transformation of the Generalized Traveling Salesm.. (context) - Noon, Bean - 1993

Documents on the same site (http://webpages.ull.es/users/jjsalaza/gtsp.htm):
A Branch-and-Cut Algorithm for the Symmetric.. - Fischetti.. (1995)   (Correct)

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