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Survivable networks, linear programming relaxations and the parsimonious property

Michel X. Goemans, Dimitris J. Bertsimas
1993 Mathematical programming  
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

Christine L. Valenzuela, Antonia J. Jones
1997 European Journal of Operational Research  
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]

William Cook
2019 Lecture Notes in Computer Science  
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  
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]

Markus Bläser, Konstatinos Panagiotou, B. V. Raghavendra Rao
2012 Lecture Notes in Computer Science  
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

A Lim, B Rodrigues, J Zhang
2005 Journal of the Operational Research Society  
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

Kahng
1989 International Joint Conference on Neural Networks  
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]

Sandor P. Fekete, Henk Meijer, Andre Rohe, Walter Tietze
2002 arXiv   pre-print
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]

Sándor P. Fekete, Henk Meijer, André Rohe, Walter Tietze
2001 Lecture Notes in Computer Science  
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

T. L. Magnanti
1981 Networks  
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

Luciana S. Buriol, Celina Figueiredo, Mauricio G. C. Resende, Eduardo Uchoa
2020 Pesquisa Operacional  
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

Sándor P. Fekete, Henk Meijer, André Rohe, Walter Tietze
2002 ACM Journal of Experimental Algorithmics  
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

Alexander I. Barvinok
1996 Mathematics of Operations Research  
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

Paul Bouman, Niels Agatz, Marie Schmidt
2017 Social Science Research Network  
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

Richard S. Barr, Bruce L. Golden, James P. Kelly, Mauricio G. C. Resende, William R. Stewart
1995 Journal of Heuristics  
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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