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A Gap-ETH-Tight Approximation Scheme for Euclidean TSP [article]

Sándor Kisfaludi-Bak, Jesper Nederlof, Karol Węgrzycki
2021 arXiv   pre-print
We complement our results with a matching Gap-ETH lower bound for Rectilinear Steiner Tree.  ...  We also show that a 2^o(1/ε^d-1)poly(n) algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH).  ...  Bodlaender for his double counting argument in Lemma 6.13, Artur Czumaj for sharing the full version of [17] with us, and Hung Le for answering multiple questions regarding spanners.  ... 
arXiv:2011.03778v2 fatcat:kkhvkz6ktrgznf3kw72ecxacgy

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms [article]

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 arXiv   pre-print
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  The first is the Gap Exponential Time Hypothesis (Gap-ETH), which is a strengthening of ETH.  ...  Despite these, Gap-ETH does give a strong inapproximability for DENSEST k-SUBGRAPH, as stated below: Theorem 8 ([36]). Assuming Gap-ETH, there is no k o(1) -FPT-approximation for DENSEST k-SUBGRAPH.  ... 
arXiv:2006.04411v1 fatcat:hjgu7f3s7zbydkcnioq3qlzgza

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 Algorithms  
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  Despite these, Gap-ETH does give a strong inapproximability for DENSEST k-SUBGRAPH, as stated below: Theorem 8 ([39]). Assuming Gap-ETH, there is no k o(1) -FPT-approximation for DENSEST k-SUBGRAPH.  ...  However, a PAS for Euclidean metrics both for the STEINER TREE and the TSP problems were shown to exist in the seminal work of Arora [167, 209] .  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

Maximum Scatter TSP in Doubling Metrics [article]

László Kozma, Tobias Mömke
2016 arXiv   pre-print
As a corollary we obtain (i) an efficient polynomial-time approximation scheme (EPTAS) for all constant dimensions d, (ii) a polynomial-time approximation scheme (PTAS) for dimension d = n/c, for a sufficiently  ...  Arkin et al. raised the question of whether a better approximation ratio can be obtained in the Euclidean plane.  ...  We would like to thank Karteek Sreenivasaiah for several helpful discussions.  ... 
arXiv:1512.02963v2 fatcat:o3n6ow6nszaklia2fsupkxx35q

The asymmetric bottleneck traveling salesman problem: Algorithms, complexity and empirical analysis

John LaRusic, Abraham P. Punnen
2014 Computers & Operations Research  
We also present a very efficient heuristic algorithm that produced provably optimal solutions for 270 out of 331 benchmark test instances.  ...  Our algorithms are applicable to the maxmin version of the problem, known as the maximum scatter TSP. Extensive experimental results on these instances are also given.  ...  Problem Size Tight LBs Best LB Best LB time Best LB sol. Opt. sol. Best gap (%) Avg. gap (%) Worst gap (%) Avg.  ... 
doi:10.1016/j.cor.2013.08.005 fatcat:y2bzmmqe7zgz7cfb7zhzmwc32i

Parameterized Complexity and Approximation Algorithms

D. Marx
2007 Computer journal  
We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type, and propose directions for future research.  ...  Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems.  ...  ACKNOWLEDGMENTS I would like to thank Mike Fellows for asking me to write this survey, and for the many ideas, comments, and references that were essential in compiling the material.  ... 
doi:10.1093/comjnl/bxm048 fatcat:6yukdt7tvja3jf76zyuxfm536q

Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

Jeff Erickson, Philip N. Klein, Dániel Marx, Claire Mathieu, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 16221 "Algorithms for Optimization Problems in Planar Graphs". The seminar was held from May 29 to June 3, 2016.  ...  This report contains abstracts for the recent developments in planar graph algorithms discussed during the seminar as well as summaries of open problems in this area of research.  ...  Our PTAS for planar group Steiner tree implies the first PTAS for geometric Euclidean group Steiner tree with obstacles, as well as a (2 + ε)-approximation algorithm for group TSP with obstacles, improving  ... 
doi:10.4230/dagrep.6.5.94 dblp:journals/dagstuhl-reports/EricksonKMM16 fatcat:wasdfgivt5fqdppfxo3iqqs2ta

Geometric Optimization Revisited [chapter]

Pankaj K. Agarwal, Esther Ezra, Kyle Fox
2019 Lecture Notes in Computer Science  
Instead of discussing many problems, we focus on a few problems, namely, set cover, hitting set, independent set, and computing maps between point sets.  ...  We review the progress made in recent years on a number of such geometric optimization problems, with an emphasis on how geometry has been exploited to develop better algorithms.  ...  We thank Timothy Chan, Sariel Har-Peled, and Micha Sharir for their helpful comments.  ... 
doi:10.1007/978-3-319-91908-9_5 fatcat:3l3jwv5bevhkvoyi3gtb65g7ae

Inapproximability of Clustering in Lp Metrics

Vincent Cohen-Addad, Karthik C. S.
2019 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)  
This improves on a result of Lee-Schmidt-Wright (IPL'17) who proved hardness of approximation for a factor of 1.0013.  ...  In this paper, we take a significant step to improve the hardness of approximation of the k-means problem in various L-p metrics, and more particularly on Manhattan (L-1), Euclidean (L-2), Hamming (L-0  ...  S. was a Ph. D. student at the Weizmann Institute of Science.  ... 
doi:10.1109/focs.2019.00040 dblp:conf/focs/Cohen-AddadS19 fatcat:h3cbi6u7ozgj7ozvvtslxjqfte

A branch-and-cut algorithm for the hub location and routing problem

Inmaculada Rodríguez-Martín, Juan-José Salazar-González, Hande Yaman
2014 Computers & Operations Research  
Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities.  ...  We devise separation routines for these inequalities and develop a branch-andcut algorithm which is tested on CAB and AP instances from the literature.  ...  The branch-and-cut scheme for integer programming problems combines a branch-and-bound method for exploring a decision tree and a cutting plane method for computing bounds.  ... 
doi:10.1016/j.cor.2014.04.014 fatcat:emuvqxlo2zbdnacs3gxyy2mqaa

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  Particularly, for the Euclidean TSP the complexity o f the algorithm is On 3 .  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Algorithms for Optimization Problems in Planar Graphs

Glencora Borradaile, Philip Klein, Dániel Marx, Claire Mathieu, Glencora Borradaile, Philip Klein, Dániel Marx, Claire Mathieu, Glencora Borradaile, Philip Klein, Dániel Marx, Claire Mathieu (+1 others)
Report from Dagstuhl Seminar   unpublished
There has recently been a growing interest in addressing combinatorial optimization problems using algorithms that exploit embeddings on surfaces to achieve provably higher-quality output or provably faster  ...  This report documents the program and the outcomes of Dagstuhl Seminar 13421 "Algorithms for Optimization Problems in Planar Graphs". The seminar was held from October 13 to October 18, 2013.  ...  I then turn to the traveling salesman problem (TSP) in planar graphs with edge-weights. I discuss a framework in which one can obtain a linear-time approximation scheme for TSP.  ... 
fatcat:g2fjt6hfa5ebvbrytjofdqjbla

Approximation Algorithms for some Min-max Vehicle Routing Problems

Amin Jorati
2013
Then, we explore the possibility of Polynomial time approximation schemes on the Euclidean metric. We rule out this possibility by giving an APX-hardness reduction.  ...  We improve on the approximation ratios of these problems by giving a (16/3 + )-approximation algorithm for the unrooted min-max k-tour cover problem and a (7 + )-approximation algorithm for rooted version  ...  The ETH states that the latter is a sound assumption. This motivates the definition of a QPTAS, similar to a PTAS as follows. Quasi-Polynomial Time Approximation Scheme (QPTAS).  ... 
doi:10.7939/r3pt1q fatcat:pvmiabhdh5e7nc5c22o2qzhjpe

A route-neighborhood-based metaheuristic for vehicle routing problem with time windows

Fuh-Hwa Franklin Liu, Sheng-Yuan Shen
1999 European Journal of Operational Research  
In addition, when there are only a few unrouted customers left, we design a special procedure for handling them. Computational results for 60 benchmark problems are reported.  ...  Unlike the conventional methods for parallel route construction, we construct routes in a nested parallel manner to obtain higher solution quality.  ...  Thangiah for providing many reference papers on the VRPTW area, Wen-Chyuan Chiang and Robert A.  ... 
doi:10.1016/s0377-2217(98)00315-4 fatcat:tqqrc77o6rcnfednb3rvldeq7y

Scientific Visualization (Dagstuhl Seminar 11231) Outdoor and Large-Scale Real-World Scene Analysis. 15th Workshop Theoretic Foundations of Computer Vision

Min Chen, Hans Hagen, Charles Hansen, Arie Kaufman, Martin Dyer, Uriel Feige, Alan Frieze, Marek Karpinski, Frank Dellaert, Jan-Michael Frahm, Marc Pollefeys, Bodo Rosenhahn
2011 unpublished
Thanks go to Mathias Hauptmann for his help in collecting abstracts of the talks and other related materials for these Proceedings.  ...  We thank Annette Beyer and Angelika Mueller-von Brochowski for their continuous support and help in organizing this workshop.  ...  We apply our framework to obtain smoothed analyses of Dyer and Frieze's partitioning algorithm for Euclidean matching, Karp's partitioning scheme for the TSP, a heuristic for Steiner trees, and a heuristic  ... 
fatcat:jzxttttmrvda3caw6dy4q2kw6i
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