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Maximum ATSP with Weights Zero and One via Half-Edges [article]

Katarzyna Paluch
2014 arXiv   pre-print
We present a fast combinatorial 3/4-approximation algorithm for the maximum asymmetric TSP with weights zero and one.  ...  Our algorithm first computes a maximum size matching and a maximum weight cycle cover without certain cycles of length two but possibly with half-edges - a half-edge of a given edge e is informally speaking  ...  Introduction We study the maximum asymmetric traveling salesman problem with weights zero and one (Max (0,1)-ATSP), which is defined as follows.  ... 
arXiv:1408.1431v1 fatcat:rs5ogz3azba2tk3afbsjjhnq3y

A 3/4-Approximation Algorithm for Maximum ATSP with Weights Zero and One [chapter]

Markus Bläser
2004 Lecture Notes in Computer Science  
We present a polynomial time 3/4-approximation algorithm for the maximum asymmetric TSP with weights zero and one.  ...  As applications, we get a 5/4-approximation algorithm for the (minimum) asymmetric TSP with weights one and two and a 3/4-approximation algorithm for the Maximum Directed Path Packing Problem.  ...  Let MaxATSP(0, 1) be the following problem: Given a directed complete loopless graph with edge weights zero and one, compute a TSP tour of maximum weight.  ... 
doi:10.1007/978-3-540-27821-4_6 fatcat:blp2kdhbcrgvpkpijpzt3impbm

Simpler Approximation of the Maximum Asymmetric Traveling Salesman Problem

Katarzyna Paluch, Khaled Elbassioni, Anke Van Zuylen, Marc Herbstritt
2012 Symposium on Theoretical Aspects of Computer Science  
Our algorithm is simple to analyze, and contrary to previous approaches, which need an optimal solution to a linear program, our algorithm is combinatorial and only uses maximum weight perfect matching  ...  ACM Subject Classification I.1.2 Algorithms Keywords and phrases approximation algorithm, maximum asymmetric traveling salesman problem  ...  Acknowledgements The authors thank Marcin Mucha for useful comments on an earlier version of this paper. S TA C S ' 1 2  ... 
doi:10.4230/lipics.stacs.2012.501 dblp:conf/stacs/PaluchEZ12 fatcat:2yn5oyiy6vhcvkfoup6nznr5sy

Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

Markus Bläser, Bodo Manthey
2005 Algorithmica  
Given a complete directed graph with edge weights zero and one, Max-k-DCC(0, 1) is the problem of finding a k-cycle cover with maximum weight.  ...  Instances of the latter problem are complete directed graphs with edge weights one and two. The goal is to find a k-cycle cover with minimum weight.  ...  For directed graphs (asymmetric TSP, ATSP), we call the former with distances zero and one Max-ATSP(0, 1) and the latter with distances one and two Min-ATSP (1, 2) .  ... 
doi:10.1007/s00453-004-1131-0 fatcat:6rw4rlft3jf7ziwqytqic7kaam

WAOA 2015 Special Issue on TOCS

Laura Sanità, Martin Skutella
2018 Theory of Computing Systems  
Katarzyna Paluch, in her contribution Maximum ATSP with Weights Zero and One via Half-Edges, gives a fast combinatorial 3/4-approximation algorithm for the maximum asymmetric TSP problem, with weights  ...  zero and one.  ... 
doi:10.1007/s00224-018-9850-9 fatcat:ulo7cobavfelzjctlackzjne7e

Optimal Control-Based UAV Path Planning with Dynamically-Constrained TSP with Neighborhoods [article]

Dae-Sung Jang, Hyeok-Joo Chae, Han-Lim Choi
2016 arXiv   pre-print
vehicle dynamics, this problem is regarded as a dynamically-constrained traveling salesman problem with neighborhoods.  ...  This paper addresses path planning of an unmanned aerial vehicle (UAV) with remote sensing capabilities (or wireless communication capabilities).  ...  to a neighborhood in Ns, and vs is connected with all of its intersection nodes via a zero-weight path.  ... 
arXiv:1612.06008v1 fatcat:raux3liowbgghguvsk4lhk6564

From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization [article]

Lukas Behrendt, Katrin Casel, Tobias Friedrich, J.A. Gregor Lagodzinski, Alexander Löser, Marcus Wilhelm
2020 arXiv   pre-print
We generalize the tree doubling and Christofides algorithm, the two most common approximations for TSP, to parameterized approximations for ATSP.  ...  Both algorithms are also stated in the form of additive lossy kernelizations, which allows to combine them with known polynomial time approximations for ATSP.  ...  Finally, we connect every vertex pair that is not yet connected with an edge with cost m + 1, where m is the maximum edge cost in G.  ... 
arXiv:1911.02453v2 fatcat:rhztdvx35zawzf5nezfgivnoiy

New facets of the STS polytope generated from known facets of the ATS polytope

Egon Balas, Robert Carr, Matteo Fischetti, Neil Simonetti
2006 Discrete Optimization  
While it had been known for a long time how to transform an asymmetric traveling salesman (ATS) problem on the complete graph with n vertices into a symmetric traveling salesman (STS) problem on an incomplete  ...  The procedure exploits the structure of the tight STS tours and organizes them into a suitable tree structure.  ...  The third author was partially supported by MIUR and CNR, Italy, and by the EU project ADONET.  ... 
doi:10.1016/j.disopt.2005.10.001 fatcat:rdqkntwy6jej7inaynpqcbsu7a

New Approximation Algorithms for (1,2)-TSP

Anna Adamaszek, Matthias Mnich, Katarzyna Paluch, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The algorithm is based on combining three copies of a minimum-cost cycle cover of the input graph together with a relaxed version of a minimum weight matching, which allows using "half-edges".  ...  Our main results are two approximation algorithms for (1, 2)-TSP, one with approximation factor 8/7 and run time O(n 3 ) and the other having an approximation guarantee of 7/6 and run time O(n 2.5 ).  ...  Later, Paluch [22] used half-edges to improve the approximation guarantee to 3/4 for the special case of Max-ATSP where all edge costs are either zero or one. Recently, Dudycz et al.  ... 
doi:10.4230/lipics.icalp.2018.9 dblp:conf/icalp/AdamaszekMP18 fatcat:ekfhs336xndavg6hnglih672bu

New Approximation Algorithms for Maximum Asymmetric Traveling Salesman and Shortest Superstring [article]

Katarzyna Paluch
2020 arXiv   pre-print
In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum  ...  It is based on techniques of eliminating and diluting problematic subgraphs with the aid of half-edges and a method of edge coloring.  ...  Introduction In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph G = (V, E) with nonnegative weights on the edges and we wish to compute a traveling salesman  ... 
arXiv:2005.10800v2 fatcat:jrfdjplqxndenntqfh6io4smgi

Analysis of Evolutionary Diversity Optimization for Permutation Problems

Anh Viet Do, Mingyu Guo, Aneta Neumann, Frank Neumann
2022 ACM Transactions on Evolutionary Learning and Optimization  
Additionally, experiments are carried out on QAPLIB and synthetic instances in unconstrained and constrained settings, and reveal much more optimistic practical performances, while corroborating the theoretical  ...  This work contributes to this line of research with an investigation on evolutionary diversity optimization for three of the most well-studied permutation problems, namely the Traveling Salesperson Problem  ...  ACKNOWLEDGMENTS This work was supported by the Phoenix HPC service at the University of Adelaide, and by the Australian Research Council through grant DP190103894.  ... 
doi:10.1145/3561974 fatcat:irpuqt7ix5he7plwcry6qjsili

New inapproximability bounds for TSP

Marek Karpinski, Michael Lampis, Richard Schmied
2015 Journal of computer and system sciences (Print)  
One of our main tools, which may be of independent interest, is a new construction of a bounded degree wheel amplifier used in the proof of our results. $ A preliminary version of this paper appeared in  ...  The best up to now known hardness of approximation bounds were 185/184 for the symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to Papadimitriou and Vempala).  ...  Observe that this sum contains half the weight of edges with one endpoint in V but the full weight for edges with both endpoints in V .  ... 
doi:10.1016/j.jcss.2015.06.003 fatcat:57sot2dxejcg3m5yqurtd3aany

An Experimental Evaluation of the Best-of-Many Christofides' Algorithm for the Traveling Salesman Problem [article]

Kyle Genova, David P. Williamson
2015 arXiv   pre-print
One then runs Christofides' algorithm on the tree by computing a minimum-cost matching on the odd-degree vertices in the tree, and shortcutting the resulting Eulerian graph to a tour.  ...  The algorithm involves sampling a spanning tree from the solution the standard LP relaxation of the TSP, subject to the condition that each edge is sampled with probability at most its value in the LP  ...  Acknowledgments We thank Shayan Oveis Gharan for generously sharing his maximum entropy code with us; we used many of his implementation ideas in coding our own algorithm.  ... 
arXiv:1506.07776v1 fatcat:fwayjvj6ljgknimfcymda6albu

An O(log n/log log n)-Approximation Algorithm for the Asymmetric Traveling Salesman Problem

Arash Asadpour, Michel X. Goemans, Aleksander Mądry, Shayan Oveis Gharan, Amin Saberi
2017 Operations Research  
The key ingredient of our approach is a new connection between the approximability of the ATSP and the notion of so-called thin trees.  ...  To exploit this connection, we employ maximum entropy rounding -a novel method of randomized rounding of LP relaxations of optimization problems.  ...  Claim 8.4 Let γ : E → R that has at least one gap. Let T max be a maximum spanning tree of G with respect to weights γ, i.e., T max = argmax T γ(T ).  ... 
doi:10.1287/opre.2017.1603 fatcat:krwti2dm55bcfdrylbzspqcv5m

On Approximation Lower Bounds for TSP with Bounded Metrics [article]

Marek Karpinski, Richard Schmied
2012 arXiv   pre-print
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds.  ...  In particular, we prove the best known lower bound for TSP with bounded metrics for the metric bound equal to 4.  ...  Further Research We have improved (modestly) the best known approximation lower bounds for TSP with bounded metrics problems.  ... 
arXiv:1201.5821v2 fatcat:jq2orj3ky5cmzi4xvclg4p5wkq
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