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ON APPROXIMATING MULTICRITERIA TSP
 SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
"... We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP), whose performances are independent of the number k of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized appro ..."
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Cited by 6 (2 self)
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We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP), whose performances are independent of the number k of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized approximation algorithms for multicriteria maximum traveling salesman problems (MaxTSP). For multicriteria MaxSTSP, where the edge weights have to be symmetric, we devise an algorithm that achieves an approximation ratio of 2/3 − ε. For multicriteria MaxATSP, where the edge weights may be asymmetric, we present an algorithm with an approximation ratio of 1/2 − ε. Our algorithms work for any fixed number k of objectives. To get these ratios, we introduce a decomposition technique for cycle covers. These decompositions are optimal in the sense that no decomposition can always yield more than a fraction of 2/3 and 1/2, respectively, of the weight of a cycle cover. Furthermore, we present a deterministic algorithm for bicriteria MaxSTSP that achieves an approximation ratio of 61/243 ≈ 1/4. Finally, we present a randomized approximation algorithm for the asymmetric multicriteria
APPROXIMATING MULTICRITERIA MaxTSP
, 2008
"... We present randomized approximation algorithms for multicriteria MaxTSP. For MaxSTSP with k> 1 objective functions, we obtain an approximation ratio of 1 − ε for arbitrarily small ε> 0. For k MaxATSP with k objective functions, we obtain a ratio of − ε. ..."
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Cited by 4 (3 self)
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We present randomized approximation algorithms for multicriteria MaxTSP. For MaxSTSP with k> 1 objective functions, we obtain an approximation ratio of 1 − ε for arbitrarily small ε> 0. For k MaxATSP with k objective functions, we obtain a ratio of − ε.
MultiCriteria TSP: Min and Max Combined
, 2009
"... We present randomized approximation algorithms for multicriteria traveling salesman problems (TSP), where some objective functions should be minimized while others should be maximized. For the symmetric multicriteria TSP (STSP), we present an algorithm that computes (2/3 − ε, 4 + ε) approximate Pa ..."
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Cited by 1 (0 self)
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We present randomized approximation algorithms for multicriteria traveling salesman problems (TSP), where some objective functions should be minimized while others should be maximized. For the symmetric multicriteria TSP (STSP), we present an algorithm that computes (2/3 − ε, 4 + ε) approximate Pareto curves. Here, the first parameter is the approximation ratio for the objectives that should be maximized, and the second parameter is the ratio for the objectives that should be minimized. For the asymmetric multicriteria TSP (ATSP), we present an algorithm that computes (1/2 − ε, log 2 n + ε) approximate Pareto curves. In order to obtain these results, we simplify the existing approximation algorithms for multicriteria MaxSTSP and MaxATSP. Finally, we give algorithms with improved ratios for some special cases.
Single approximation for Biobjective Max TSP ∗†
"... We mainly study Max TSP with two objective functions. We propose an algorithm which returns a single Hamiltonian cycle with performance guarantee on both objectives. The algorithm is analysed in three cases. When both (resp. at least one) objective 5 function(s) fulfill(s) the triangle inequality, t ..."
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We mainly study Max TSP with two objective functions. We propose an algorithm which returns a single Hamiltonian cycle with performance guarantee on both objectives. The algorithm is analysed in three cases. When both (resp. at least one) objective 5 function(s) fulfill(s) the triangle inequality, the approximation ratio is 12 − ε ≈ 0.41 −ε). When the triangle inequality is not assumed on any objective function, the
www.stacsconf.org ON APPROXIMATING MULTICRITERIA TSP
, 2009
"... Abstract. We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP), whose performances are independent of the number k of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomi ..."
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Abstract. We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP), whose performances are independent of the number k of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized approximation algorithms for multicriteria maximum traveling salesman problems (MaxTSP). For multicriteria MaxSTSP, where the edge weights have to be symmetric, we devise an algorithm that achieves an approximation ratio of 2/3 − ε. For multicriteria MaxATSP, where the edge weights may be asymmetric, we present an algorithm with an approximation ratio of 1/2 − ε. Our algorithms work for any fixed number k of objectives. To get these ratios, we introduce a decomposition technique for cycle covers. These decompositions are optimal in the sense that no decomposition can always yield more than a fraction of 2/3 and 1/2, respectively, of the weight of a cycle cover. Furthermore, we present a deterministic algorithm for bicriteria MaxSTSP that achieves an approximation ratio of 61/243 ≈ 1/4. Finally, we present a randomized approximation algorithm for the asymmetric multicriteria
Salesman
"... We apply a multicolor extension of the BeckFiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2approximable on directed graphs and randomized 2/3approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satis ..."
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We apply a multicolor extension of the BeckFiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2approximable on directed graphs and randomized 2/3approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiabilty problem is 1/2approximable.