Improved approximation algorithms for metric MaxTSP

Chen, Zhizhong; Nagoya, Takayuki

doi:10.1007/s10878-006-9023-7

Cited by 12 publications

(4 citation statements)

References 9 publications

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“…This algorithm had later been derandomized by Chen and Nagoya [1], at a cost of a slightly worse approximation factor of…”

Section: Ifmentioning

confidence: 99%

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The Maximum Hamilton Path Problem with Parameterized Triangle Inequality

Li¹,

Li²,

Qiao³

et al. 2013

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“…This algorithm had later been derandomized by Chen and Nagoya [1], at a cost of a slightly worse approximation factor of…”

Section: Ifmentioning

confidence: 99%

“…Based on the idea of Chen et al [2] and the propertiesof a folklore partition of the edges of a 2n-vertex complete undirected graph into 2 perfect matchings, Chen and Nagoya [1] derandomize Hassin & Rubinstein's algorithm mat a cost of a slightly worse approximation factor of…”

Section: Modified Randomized Kostochka and Serdyukov's Algorithmmentioning

confidence: 99%

The Maximum Hamilton Path Problem with Parameterized Triangle Inequality

Li¹,

Li²,

Qiao³

et al. 2013

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“…A special case of the cycle cover problem is the traveling salesman problem (TSP), where the goal is to determine a Hamiltonian cycle of maximum or minimum weight. The problem of cycle partitioning is an important tool for the design of approximation algorithms for different variants of the TSP [30][31][32]65]. Computing cycle partitions is an important task in the fields of information science, graph theory and combinatorial optimization [75,81].…”

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confidence: 99%

Paths, Cycles and Related Partitioning Problems in Graphs

Zhang¹

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P a t h s , Cy c l e s a n d Re l a t e d P a r t i t i o n i n g P r o b l e ms i n Gr a p h s P a t h s , Cy c l e s a n d Re l a t e d P a r t i t i o n i n g P r o b l e ms i n Gr a p h s Paths, Cycles and Related Partitioning Problems in Graphs Zanbo ZhangThe research was supported by and carried out in the group of Formal Methods and Tools, in the Faculty of Electrical Engineering, Mathematics and Computer Science of the University of Twente, the Netherlands. The financial support from the University of Twente for this research work and its publication is gratefully acknowledged.The research was also supported by the National Natural Science Foundation of China (NSFC, 11471003 and 11471342) Copyright c⃝2017 Zanbo Zhang, Enschede, the Netherlands. All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission from the copyright owner. PATHS, CYCLES AND RELATED PARTITIONING PROBLEMS IN GRAPHS DISSERTATION PrefaceThis thesis is based on joint work of the author with several different collaborators during the last five years. It is composed of a short introductory chapter, followed by five technical chapters. These five chapters are all based on associated research papers that are in different stages of submission, refereeing, acceptance or publication, and that are listed below together with several other joint publications of the author.The underlying research papers as well as the corresponding chapters in this thesis are the result of continuous part-time research efforts of the author, in collaboration with other researchers, on paths and cycles in graphs.The first chapter contains a brief introduction, with some background and motivation for the research in this field, and with some remarks on earlier work that inspired the author to contribute to this field. The details of the author's contributions are presented in the subsequent five chapters, that are all self-contained. The second chapter deals with the extremal digraphs one has to exclude when relaxing a classical degree condition for the existence of Hamiltonian cycles in digraphs. The third and fourth chapter deal with sufficient conditions for path extendability and cycle extendability in digraphs, respectively. In the fifth chapter, in the context of path and cycle properties, we study the number of 2-paths in oriented graphs and tournaments. We also present some applications to demonstrate the relevance of conditions in terms of the number of 2-paths. In the sixth chapter, we study monochromatic clique and multicolored cycle partitioning problems in edge-colored graphs, from the perspective of computational complexity and algorithmic solutions. i ii PrefaceThe thesis has been written as a collection of independent papers. To guarantee the independence and readability of the chapters, we chose to maintain the structure of journal papers, with a short introduction and background, and th...

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“…A cycle cover of a graph is a spanning subgraph that consists solely of cycles such that every vertex is part of exactly one cycle. Cycle covers are an important tool for the design of approximation algorithms for different variants of the traveling salesman problem [3,5,6,[9][10][11][12]21], for the shortest common superstring problem from computational biology [8,28], and for vehicle routing problems [18].…”

Section: Introductionmentioning

confidence: 99%

Minimum-Weight Cycle Covers and Their Approximability

Manthey

Graph-Theoretic Concepts in Computer Science

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A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle.An L-cycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N.We investigate how well L-cycle covers of minimum weight can be approximated. For undirected graphs, we devise non-constructive polynomial-time approximation algorithms that achieve constant approximation ratios for all sets L. On the other hand, we prove that the problem cannot be approximated with a factor of 2 − ε for certain sets L.For directed graphs, we devise non-constructive polynomial-time approximation algorithms that achieve approximation ratios of O(n), where n is the number of vertices. This is asymptotically optimal: We show that the problem cannot be approximated with a factor of o(n) for certain sets L.To contrast the results for cycle covers of minimum weight, we show that the problem of computing L-cycle covers of maximum weight can, at least in principle, be approximated arbitrarily well.

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Improved approximation algorithms for metric MaxTSP

Abstract: We present two polynomial-time approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is 27 35 . The other is for undirected graphs and its approximation ratio is

Cited by 12 publications

References 9 publications

The Maximum Hamilton Path Problem with Parameterized Triangle Inequality

The Maximum Hamilton Path Problem with Parameterized Triangle Inequality

Paths, Cycles and Related Partitioning Problems in Graphs

Minimum-Weight Cycle Covers and Their Approximability

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