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Survivable networks, linear programming relaxations and the parsimonious property
1993
Mathematical programming
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Structural Properties of the Held-Karp Bound In this section, we consider the Held-Karp lower bound [13, 14] for the traveling salesman problem. ...
Under this probabilistic model, the Held-Karp lower bound is proved to have a similar asymptotic behavior as the traveling salesman problem or the 2-connected network design problem. ...
Appendix 2: Proof of Theorem 9 Using Theorem 8, we need to construct a family of instances for which the ratio XZO is arbitrarily close to 2 (k=l Pk.Pk-1). Let cak = Pk for k = 1, . .,p-1. ...
doi:10.1007/bf01580607
fatcat:rji3s5ponjbtzfvzkqt263ch4a
Estimating the Held-Karp lower bound for the geometric TSP
1997
European Journal of Operational Research
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The Held-Karp lower bound (HK) provides a very good problem-specific estimate of optimal tour length for the travelling salesman problem (TSP). ...
The Held-Karp lower bound (HK) provides a very good problem-specific estimate of optimal tour length for the travelling salesman problem (TSP). ...
Johnson of AT & T for his many helpful comments on our work. We are also indebted to the anonymous referees for their constructive criticism of our original submission. ...
doi:10.1016/s0377-2217(96)00214-7
fatcat:nzzcz4nuvjbqvhu3ab7hiwvohe
Computing in Combinatorial Optimization
[chapter]
2019
Lecture Notes in Computer Science
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We give a tour of this work, focusing on the early development of the subject and the central role played by linear programming. ...
The paper concludes with a short wish list of future research directions. ...
A central model is the traveling salesman problem, or TSP for short. It is simple to state. ...
doi:10.1007/978-3-319-91908-9_3
fatcat:zcyzrmfzrraa3cg53srp6gqnm4
Page 6223 of Mathematical Reviews Vol. , Issue 96j
[page]
1996
Mathematical Reviews
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Rothberg, Asymptotic experimental analysis for the Held- Karp traveling salesman bound (341-350); Claire Kenyon, Best-fit bin-packing with random order (359-364); Richa Agarwala, Vi- neet Bafna, Martin ...
and complexity (101-114); Jean Moulin Ollagnier, Algorithms and methods in differential algebra (115— 127); Jean-Jacques Risler, A bound for the degree of nonholonomy in the plane (129-136). ...
A Probabilistic Analysis of Christofides' Algorithm
[chapter]
2012
Lecture Notes in Computer Science
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As a first step towards obtaining an average case analysis of Christofides' algorithm, we provide a probabilistic analysis for the stochastic version of the algorithm for the Euclidean traveling salesman ...
Christofides' algorithm is a well known approximation algorithm for the metric travelling salesman problem. ...
for the Held-Karp relaxation of ETSP. ...
doi:10.1007/978-3-642-31155-0_20
fatcat:2ewyq64tbnca5dex34eukntwmy
Tabu search embedded simulated annealing for the shortest route cut and fill problem
2005
Journal of the Operational Research Society
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denotes the Held-Karp 1-tree lower bound. ...
Henderson er a/ calculated the Held-Karp 1- tree lower bound and used Lagrange multipliers to improve
these. ...
doi:10.1057/palgrave.jors.2601900
fatcat:qmlupe5klrektkohe3fuwu4lmu
Traveling salesman heuristics and embedding dimension in the Hopfield model
1989
International Joint Conference on Neural Networks
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We discuss methods for improving per3Pormance of the Hopfield-Tank quadratic minimization approach to TSP. ...
Implications concerning the nature of the Hopjeld energy sulface are discussed. ...
ACKNOWLEDGEMENTS The author would like to thank G. Hueter (UCSD Department of Physics and HNC, Inc.) and R. ...
doi:10.1109/ijcnn.1989.118627
fatcat:vyfeiwbhl5fi3jack3arwjproa
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
[article]
2002
arXiv
pre-print
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We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. ...
behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP. ...
Acknowledgments We thank Jens Vygen and Sylvia Boyd for helpful discussions, and Joe Mitchell for pointing out the paper [Tamir and Mitchell 1998 ]. ...
arXiv:cs/0212044v1
fatcat:evcr5cbvxne3bk5kwczgnheohy
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
[chapter]
2001
Lecture Notes in Computer Science
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Acknowledgments We thank Jens Vygen and Sylvia Boyd for helpful discussions, and Joe Mitchell for pointing out the paper [Tamir and Mitchell 1998 ]. ...
Two anonymous referees helped to improve the overall presentation by making various helpful suggestions. ...
Furthermore, the (relatively time-consuming) standard Held-Karp bound (see [Held and Karp 1971] ) is outperformed by our methods for most instances. ...
doi:10.1007/3-540-44808-x_1
fatcat:qpqlin3qmnhxnj42nb3zujzrb4
Combinatorial optimization and vehicle fleet planning: Perspectives and prospects
1981
Networks
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ACKNOWLEDGEMENTS I am grateful to Bruce Golden, Steve Graves, Jan Hammond, and Paul Mireault for their comments on an earlier version of this paper. ...
problem (Held and Karp [66] , [67] ). ...
When n his relaxaion reduces o he Held and Karp relaxaion NV = 1 and K > Z d i , this relaxation reduces to the Held and Karp relaxation i=l that we have mentioned previously for solving the traveling ...
doi:10.1002/net.3230110209
fatcat:kmmvt63wbjcppep5ak6zvhc7em
THE GUIDE TO NP-COMPLETENESS IS 40 YEARS OLD: AN HOMAGE TO DAVID S. JOHNSON
2020
Pesquisa Operacional
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Besides his contributions to the theory of NP-completeness, David S. Johnson also made important contributions to approximation algorithms and the experimental analysis of algorithms. ...
The book was written in the late 1970s, when problems solvable in polynomial time were linked to the concepts of efficiently solvable and tractability, and the complexity class NP was defined to capture ...
two chapters, Experimental Analysis of Heuristics for the STSP
and Experimental Analysis of Heuristics for the ATSP in a TSP book (Gutin & Punnen, 2002). ...
doi:10.1590/0101-7438.2020.040.00236329
fatcat:httrydnjczgwnaeufgvoeuhm6y
Solving a "Hard" problem to approximate an "Easy" one
2002
ACM Journal of Experimental Algorithmics
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Acknowledgments We thank Jens Vygen and Sylvia Boyd for helpful discussions, and Joe Mitchell for pointing out the paper [Tamir and Mitchell 1998 ]. ...
Two anonymous referees helped to improve the overall presentation by making various helpful suggestions. ...
Furthermore, the (relatively time-consuming) standard Held-Karp bound (see [Held and Karp 1971] ) is outperformed by our methods for most instances. ...
doi:10.1145/944618.944629
fatcat:kxo5roay5jczhlhxefnjwggpxe
Two Algorithmic Results for the Traveling Salesman Problem
1996
Mathematics of Operations Research
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The traveling salesperson problem (TSP) is a very well-known NP-hard combinatorial optimization problem. Many different integer programming formulations are known for the TSP. ...
A brief account of polyhedral analysis of different formulations of TSP is provided in subsection 2.1. Naddef (2007) succinctly summarizes the comparative strengths of the different models for STSP. ...
Acknowledgements The author thanks anonymous referees for their valuable suggestions for improved clarity of the presentation. The author thankfully acknowledges Dr. David Carfi and Prof. ...
doi:10.1287/moor.21.1.65
fatcat:revgcqn765bqheijf3i6o7tl7q
Dynamic Programming Approaches for the Traveling Salesman Problem with Drone
2017
Social Science Research Network
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Effectively combining a truck and a drone gives rise to a new planning problem that is known as the Traveling Salesman Problem with Drone (TSP-D). ...
This paper presents exact solution approaches for the TSP-D based on dynamic programming and provides an experimental comparison of these approach. ...
For the classic Traveling Salesman Problem (TSP), dynamic programming approaches were first proposed in Held and Karp (1962) ; Bellman (1962) . ...
doi:10.2139/ssrn.3035323
fatcat:t3bz6r37mnfqhfeydjdee5leoy
Designing and reporting on computational experiments with heuristic methods
1995
Journal of Heuristics
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The e ectiveness of any proposed methodology for solving a given class of problems can be demonstrated by theoretical analysis and empirical testing. ...
This report discusses the design of computational experiments to test heuristic methods and provides reporting guidelines for such experimentation. ...
We also thank the creators of the gures for allowing us to include their works, and Fred Glover for the opportunity t o b e a part of this important new journal. ...
doi:10.1007/bf02430363
fatcat:6awhdwau5nb5jfgd2ouvvah3ge
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