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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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to Christofides) achieves a 3/2approximation in polynomial time. We also give similar approximation schemes for some other NPhard Euclidean problems: Minimum Steiner Tree, kTSP, and kMST. (The running times of the algorithm for kTSP and kMST involve an additional multiplicative factor k.) The previous best
Approximating TSP Solution by MST Based Graph Pyramid
, 2007
"... The traveling salesperson problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution of an input with a large number of cities, the problem is approximated into a simpler form containing smaller number of cities, which is then solved optimal ..."
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Cited by 4 (2 self)
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The traveling salesperson problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution of an input with a large number of cities, the problem is approximated into a simpler form containing smaller number of cities, which is then solved
Guillotine subdivisions approximate polygonal subdivisions: Part II  A simple polynomialtime approximation scheme for geometric kMST, TSP, and related problems
, 1996
"... this paper, thereby achieving essentially the same results that we report here, using decomposition schemes that are somewhat similar to our own. Arora's remarkable results predate this paper by several weeks, and his discovery was done independently of this work. 2 mGuillotine Subdivisions ..."
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Cited by 187 (12 self)
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this paper, thereby achieving essentially the same results that we report here, using decomposition schemes that are somewhat similar to our own. Arora's remarkable results predate this paper by several weeks, and his discovery was done independently of this work. 2 mGuillotine Subdivisions
The Power of Recourse for Online MST and TSP
, 2012
"... We consider the online MST and TSP problems with recourse. The nodes of an unknown graph with metric edge cost appear one by one and must be connected in such a way that the resulting tree or tour has low cost. In the standard online setting, with irrevocable decisions, no algorithm can guarantee ..."
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Cited by 4 (0 self)
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We consider the online MST and TSP problems with recourse. The nodes of an unknown graph with metric edge cost appear one by one and must be connected in such a way that the resulting tree or tour has low cost. In the standard online setting, with irrevocable decisions, no algorithm can guarantee
Nearly Linear Time Approximation Schemes for Euclidean TSP and other Geometric Problems
, 1997
"... We present a randomized polynomial time approximation scheme for Euclidean TSP in ! 2 that is substantially more efficient than our earlier scheme in [2] (and the scheme of Mitchell [21]). For any fixed c ? 1 and any set of n nodes in the plane, the new scheme finds a (1+ 1 c )approximation to ..."
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Cited by 93 (3 self)
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was an open problem (our earlier algorithm in [2] ran in superpolynomial time for d 3). The algorithm generalizes to the same set of Euclidean problems handled by the previous algorithm, including Steiner Tree, kTSP, kMST, etc, although for kTSP and kMST the running time gets multiplied by k. We also
When Hamming Meets Euclid: The Approximability of Geometric TSP and MST (Extended Abstract)
, 1997
"... We prove that the Traveling Salesperson Problem (MIN TSP) and the Minimum Steiner Tree Problem (MIN ST) are Max SNPhard (and thus NPhard to approximate within some constant r ? 1) even if all cities (respectively, points) lie in the geometric space R n (n is the number of cities/points) and ..."
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Cited by 45 (1 self)
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that this dependance is necessary unless NP has subexponential algorithms. We also prove, as an intermediate step, the hardness of approximating MIN TSP and MIN ST in Hamming spaces. The reduction for MIN TSP uses errorcorrecting codes and random sampling; the reduction for MIN ST uses the integrality property
Approximation Algorithms for Directed Steiner Problems
 Journal of Algorithms
, 1998
"... We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work we ..."
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Cited by 177 (8 self)
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We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work
Approximating TSP on Metrics with Bounded Global Growth ∗
"... The Traveling Salesman Problem (TSP) is a canonical NPcomplete problem which is known to be MAXSNP hard even on Euclidean metrics (of high dimensions) [40]. In order to circumvent this hardness, researchers have been developing approximation schemes for lowdimensional metrics [4, 39] (under diffe ..."
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Cited by 7 (0 self)
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first show that we can solve TSP (and other optimization problems) on these metrics in time 2 O( √ n); then we take advantage of the global nature of TSP (and the global nature of our definition) to give a (1+ε)approximation algorithm that runs in subexponential time: i.e., in 2 O(nδ ε −4 dim C
Abstract Approximating TSP on Metrics with Bounded Global Growth ∗
"... The Traveling Salesman Problem (TSP) is a canonical NPcomplete problem which is known to be MAXSNP hard even on (highdimensional) Euclidean metrics [39]. In order to circumvent this hardness, researchers have been developing approximation schemes for lowdimensional metrics [4, 38] (under differe ..."
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containing uniform submetrics of size √ n. We first show, using a somewhat “local” argument, that one can solve TSP on these metrics in time 2 O( √ n) ; we then take advantage of the global nature of TSP (and the global nature of our definition) to give a (1 + ε)approximation algorithm that runs in sub
Results 1  10
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1,443