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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 are in # d , the running time increases to O(n(log n) (O( # dc)) d-1 ). For every fixed c, d the running time is n poly(log n), i.e., nearly linear in n. The algorithm can be derandomized,... (Update)
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BibTeX entry: (Update)
S. Arora, Polynomial time approximation schemes for Euclidean TSP and other geometric problems, Manuscript, March 30, 1996. Appears in Proc. 37th Annu. IEEE Sympos. Found. Comput. Sci.(1996), pp. 2--12. http://citeseer.ist.psu.edu/article/arora96polynomial.html More
@article{ arora98polynomial,
author = "Sanjeev Arora",
title = "Polynomial time approximation schemes for {Euclidean} traveling salesman and other geometric problems",
journal = "Journal of the ACM",
volume = "45",
number = "5",
pages = "753--782",
year = "1998",
url = "citeseer.ist.psu.edu/article/arora96polynomial.html" }
Citations (may not include all citations):773 Reducibility among combinatorial problems (context) - Karp - 1972
318 Approximation Algorithms for NP-hard problems (context) - Hochbaum - 1996
293 Approximation algorithms for combinatorial problems (context) - Johnson - 1974
289 Approximation schemes for the Euclidean k- medians and relat.. - Arora, Raghavan et al. - 1998
212 Probabilistic Checking of Proofs: A new characterization of .. - Arora, Safra - 1992
203 Approximating clique is almost NP-complete (context) - Feige, Goldwasser et al. - 1991
193 The traveling salesman problem (context) - Lawler, Lenstra et al. - 1985
187 Polynomial-time approximation schemes for Euclidean TSP and .. - Arora - 1996
173 Proof verification and intractability of approximation probl.. (context) - Arora, Lund et al. - 1992
170 Bounds for certain multiprocessing anomalies (context) - Graham - 1966
127 Guillotine subdivisions approximate polygonal subdivisions: .. - Mitchell - 1996
127 Guillotine subdivisions approximate polygonal subdivisions: .. - Mitchell - 1996
107 complete approximation problems (context) - Sahni, Gonzales - 1976
102 Computer solutions for the traveling salesman problem (context) - Lin - 1965
96 Fast approximation algorithms for the knapsack and sum of su.. (context) - Ibarra, Kim - 1975
84 How easy is local search (context) - Johnson, Papadimitriou et al. - 1988
79 Extensions of Lipschitz mappings into Hilbert space (context) - Johnson, Lindenstrauss - 1984
78 Fast algorithms for geometric traveling salesman problem (context) - Bentley - 1992
77 Worst-case analysis of a new heuristic for the traveling sal.. (context) - Christofides - 1976
68 Steiner minimal trees (context) - Gilbert, Pollak - 1968
61 The shortest path through many points (context) - Beardwood, Halton et al. - 1959
61 The Steiner problem with edge lengths 1 and (context) - Bern, Plassmann - 1989
56 The Traveling Salesman Problem: A Case Study in Local Optimi.. (context) - Johnson, McGeoch - 1997
50 Approximation algorithms for geometric problems - Bern, Eppstein
48 Approximation Algorithms for Geometric tour and network prob.. - Mata, Mitchell - 1995
47 approximation for the minimum tree spanning k vertices (context) - Garg - 1996
47 Probabilistic analysis of partitioning algorithms for the TS.. (context) - Karp - 1977
45 approximation algorithm for the network Steiner Problem (context) - Zelikovsky - 1993
43 Iterated nearest neighbors and finding minimal polytopes - Eppstein, Erickson - 1994
41 of Computer and System Sciences (context) - Papadimitriou, Yannakakis et al. - 1991
41 ective heuristic algorithm for the traveling salesman proble.. (context) - Lin, Kernighan - 1973
33 A constant-factor approximation for the k- MST problem in th.. (context) - Blum, Chalasani et al. - 1995
27 When Hamming meets Euclid: the approximability of geometric .. - Trevisan - 1997
26 Finding cuts in the TSP (context) - Applegate, Bixby et al.
26 An approximation scheme for planar graph TSP - Grigni, Koutsoupias et al. - 1995
25 Some NP-complete geometric problems (context) - Garey, Graham et al. - 1976
24 Parallel construction of quadtree and quality triangulations - Bern, Eppstein et al. - 1993
23 cardinality treecomplexity and polyhedral structure (context) - Jornsten, Weighted et al. - 1994
21 A polynomial-time approximation scheme for weighted planar g.. - Arora, Grigni et al. - 1998
21 Analyzing the Held-Karp TSP bound: A monotonicity property w.. (context) - Shmoys, Williamson - 1990
20 Better approximation bounds for the network and Euclidean St.. - Zelikovsky - 1996
16 linear programming and branch and bound (context) - Wolsey - 1980
15 the problem of Steiner (context) - Melzak - 1961
14 Euclidean TSP is NP-complete (context) - Papadimitriou - 1977
14 Worst-case comparison of valid inequalities for the TSP - Goemans - 1995
13 TSPLIB--A travelling salesman problem library (context) - Reinelt - 1991
13 The complexity of the Lin-Kernighan heuristic for the travel.. (context) - Papadimitriou - 1992
12 Personal communication (context) - Graham - 1996
9 Personal communication (context) - Klein, Karger - 1996
9 cient approximation scheme for the onedimensional bin-packin.. (context) - Karmarkar, Karp - 1982
9 Covering Points in the Plane by k-Tours: Towards a Polynomia.. (context) - Asano, Katoh et al. - 1997
8 point MST approximation (context) - Eppstein, k-
8 A proof of Gilbert-Pollak's conjecture on the Steiner ratio (context) - Du, Hwang - 1992
7 New results for the old K-OPT algorithm for the TSP - Chandra, Karlo et al. - 1994
6 Bin packing can be solved within 1+# in linear time (context) - de la, Lueker - 1981
5 Approximating geometric graphs via (context) - Rao, Smith - 1998
5 Euclidean MST and bichromatic closest pairs (context) - Agarwal, Edelsbrunner et al. - 1991
4 parameter in Arora's TSP algorithm the best possible (context) - Wang - 1996
4 th IEEE Symposium on Foundations of Computer Science (context) - Krentel, locally et al. - 1989
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.densis.fee.unicamp.br/~moscato/TSPBIB_home.html): More
An Approximation Scheme for Planar Graph TSP - Grigni, Koutsoupias.. (1995) (Correct)
Relaxed Tours and Path Ejections for the Traveling Salesman Problem - Rego (1996) (Correct)
The Traveling Salesrep Problem, Edge Assembly Crossover, and 2-opt - Ross (1998) (Correct)
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