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The Greedy Algorithm for the Symmetric TSP
"... We corrected proofs of two results on the greedy algorithm for the Symmetric TSP and answered a question in Gutin and Yeo, Oper. Res. Lett. 30 (2002), 97–99. ..."
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We corrected proofs of two results on the greedy algorithm for the Symmetric TSP and answered a question in Gutin and Yeo, Oper. Res. Lett. 30 (2002), 97–99.
Better differential approximation for symmetric TSP
, 2007
"... In this paper, we study the approximability properties of symmetric TSP under an approximation measure called the differential ratio. More precisely, we improve up to 3/4 − ε (for any ε> 0) the best differential ratio of 2/3 known so far, given in Hassin ..."
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In this paper, we study the approximability properties of symmetric TSP under an approximation measure called the differential ratio. More precisely, we improve up to 3/4 − ε (for any ε> 0) the best differential ratio of 2/3 known so far, given in Hassin
A better differential approximation ratio for symmetric TSP
"... In this paper, we study the approximability properties of symmetric TSP under an approximation measure called the differential ratio. More precisely, we improve up to 3/4 − ε (for any ε> 0) the best differential ratio of 2/3 known so far, given in Hassin ..."
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In this paper, we study the approximability properties of symmetric TSP under an approximation measure called the differential ratio. More precisely, we improve up to 3/4 − ε (for any ε> 0) the best differential ratio of 2/3 known so far, given in Hassin
On Asymmetric TSP: Transformation to Symmetric TSP and Performance Bound
"... We show that an instance of traveling salesman problem (TSP) of size n with an asymmetric distance matrix can be transformed into an instance of TSP of size 2n with a symmetric distance matrix. This is an improvement over earlier transformations of this kind which triple the size of the problem. Nex ..."
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Cited by 4 (0 self)
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We show that an instance of traveling salesman problem (TSP) of size n with an asymmetric distance matrix can be transformed into an instance of TSP of size 2n with a symmetric distance matrix. This is an improvement over earlier transformations of this kind which triple the size of the problem
Improved LargeStep Markov Chain Variants for the Symmetric TSP
 JOURNAL OF HEURISTICS
, 1995
"... The largestep Markov chain (LSMC) approach is the most effective known heuristic for large symmetric TSP instances; cf. recent results of Martin et al. [17] and Johnson [12]. In this report, we examine relationships among (i) the underlying local optimization engine within the LSMC approach, (ii ..."
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Cited by 11 (4 self)
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The largestep Markov chain (LSMC) approach is the most effective known heuristic for large symmetric TSP instances; cf. recent results of Martin et al. [17] and Johnson [12]. In this report, we examine relationships among (i) the underlying local optimization engine within the LSMC approach
Improved LargeStep Markov Chain Variants for the Symmetric TSP
"... Abstract. The largestep Markov chain (LSMC) approach is the most effective known heuristic for large symmetric TSP instances; cf. recent results of [Martin, Otto and Felten, 1991] and [Johnson, 1990]. In this paper, we examine relationships among (i) the underlying local optimization engine within ..."
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Abstract. The largestep Markov chain (LSMC) approach is the most effective known heuristic for large symmetric TSP instances; cf. recent results of [Martin, Otto and Felten, 1991] and [Johnson, 1990]. In this paper, we examine relationships among (i) the underlying local optimization engine within
Improving the Efficiency of Helsgaun’s LinKernighan Heuristic for the Symmetric TSP
, 2007
"... ..."
Ant Colony System: A cooperative learning approach to the traveling salesman problem
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1997
"... This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a pher ..."
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Cited by 1000 (53 self)
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ACS3opt, a version of the ACS augmented with a local search procedure, to some of the best performing algorithms for symmetric and asymmetric TSP’s.
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for Kcolorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability of a solution changes abruptly from near 0 to near 1. It is the high density of wellseparated almost solutions (local minima) at this boundary that cause search algorithms to "thrash". This boundary is a type of phase transition and we show that it is preserved under mappings between problems. We show that for some P problems either there is no phase transition or it occurs for bounded N (and so bound...
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