Years and Authors of Summarized Original Work
-
2004; Deĭneko, Hoffmann, Okamoto, Woeginger
Problem Definition
In the traveling salesman problem (TSP) n cities 1, 2, \( { \dots } \), n together with all the pairwise distances d(i, j) between cities i and j are given. The goal is to find the shortest tour that visits every city exactly once and in the end returns to its starting city. The TSP is one of the most famous problems in combinatorial optimization, and it is well‐known to be NP-hard. For more information on the TSP, the reader is referred to the book by Lawler, Lenstra, Rinnooy Kan, and Shmoys [14].
A special case of the TSP is the so-called Euclidean TSP, where the cities are points in the Euclidean plane, and the distances are simply the Euclidean distances. A special case of the Euclidean TSP is the convex Euclidean TSP, where the cities are further restricted so that they lie in convex position. The Euclidean TSP is still NP-hard [4, 17], but the convex Euclidean TSP is...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
Děneko VG, Hoffmann M, Okamoto Y, Woeginger GJ (2006) The traveling salesman problem with few inner points. Oper Res Lett 31:106–110
Downey RG, Fellows MR (1999) Parameterized complexity. Monographs in computer science. Springer, New York
Flum J, Grohe M (2006) Parameterized complexity theory. Texts in theoretical computer science an EATCS series. Springer, Berlin
Garey MR, Graham RL, Johnson DS (1976) Some NP-complete geometric problems. In: Proceedings of 8th annual ACM symposium on theory of computing (STOC '76). Association for Computing Machinery, New York, pp 10–22
Grantson M (2004) Fixed-parameter algorithms and other results for optimal partitions. Lecentiate thesis, Department of Computer Science, Lund University
Grantson M, Borgelt C, Levcopoulos C (2005) A fixed parameter algorithm for minimum weight triangulation: analysis and experiments. Technical report 154, Department of Computer Science, Lund University
Grantson M, Borgelt C, Levcopoulos C (2005) Minimum weight triangulation by cutting out triangles. In: Deng X, Du D-Z (eds) Proceedings of the 16th annual international symposium on algorithms and computation (ISAAC). Lecture notes in computer science, vol 3827. Springer, New York, pp 984–994
Grantson M, Borgelt C, Levcopoulos C (2006) Fixed parameter algorithms for the minimum weight triangulation problem. Technical report 158, Department of Computer Science, Lund University
Grantson M, Levcopoulos C (2005) A fixed parameter algorithm for the minimum number convex partition problem. In: Akiyama J, Kano M, Tan X (eds) Proceedings of Japanese conference on discrete and computational geometry (JCDCG 2004). Lecture notes in computer science, vol 3742. Springer, New York, pp 83–94
Hoffmann M, Okamoto Y (2006) The minimum weight triangulation problem with few inner points. Comput Geom Theor Appl 34:149–158
Jansen K, Woeginger GJ (1993) The complexity of detecting crossingfree configurations in the plane. BIT 33:580–595
Knauer C, Spillner A (2006) Fixed-parameter algorithms for finding crossing-free spanning trees in geometric graphs. Technical report 06–07, Department of Computer Science, Friedrich-Schiller-Universität Jena
Knauer C, Spillner A (2006) A fixed-parameter algorithm for the minimum weight triangulation problem based on small graph separators. In: Proceedings of the 32nd international workshop on graph-theoretic concepts in computer science (WG). Lecture notes in computer science, vol 4271. Springer, New York, pp 49–57
Lawler E, Lenstra J, Rinnooy Kan A, Shmoys D (eds) (1985) The traveling salesman problem: a guided tour of combinatorial optimization. Wiley, Chichester
Mulzer W, Rote G (2006) Minimum weight triangulation is NP-hard. In: Proceedings of the 22nd annual ACM symposium on computational geometry (SoCG). Association for Computing Machinery, New York, pp 1–10
Niedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford lecture series in mathematics and its applications, vol 31. Oxford University Press, Oxford
Papadimitriou CH (1977) The Euclidean travelling salesman problem is NP-complete. Theor Comput Sci 4:237–244
Spillner A (2005) A faster algorithm for the minimum weight triangulation problem with few inner points. In: Broersma H, Johnson H, Szeider S (eds) Proceedings of the 1st ACiD workshop. Texts in algorithmics, vol 4. King's College, London, pp 135–146
Spillner A (2005) Optimal convex partitions of point sets with few inner points. In: Proceedings of the 17th Canadian conference on computational geometry (CCCG), pp 34–37
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this entry
Cite this entry
Okamoto, Y. (2016). Traveling Sales Person with Few Inner Points. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_426
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2864-4_426
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2863-7
Online ISBN: 978-1-4939-2864-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering