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644,245
Approximation guarantees for fictitious play
 In Proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing
, 2009
"... Abstract—Fictitious play is a simple, wellknown, and oftenused algorithm for playing (and, especially, learning to play) games. However, in general it does not converge to equilibrium; even when it does, we may not be able to run it to convergence. Still, we may obtain an approximate equilibrium. I ..."
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Cited by 5 (0 self)
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then consider the possibility that the players fail to choose the same r. We show how to obtain the optimal approximation guarantee when both the opponent’s r and the game are adversarially chosen (but there is an upper bound R on the opponent’s r), using a linear program formulation. We show that if the action
Mixed Bregman clustering with approximation guarantees
 In: ECML PKDD ’08: Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases—Part II
, 2008
"... Abstract. Two recent breakthroughs have dramatically improved the scope and performance of kmeans clustering: squared Euclidean seeding for the initialization step, and Bregman clustering for the iterative step. In this paper, we first unite the two frameworks by generalizing the former improvement ..."
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Cited by 20 (9 self)
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improvement to Bregman seeding — a biased randomized seeding technique using Bregman divergences — while generalizing its important theoretical approximation guarantees as well. We end up with a complete Bregman hard clustering algorithm integrating the distortion at hand in both the initialization
New approximation guarantee for chromatic number
 STOC'06
, 2006
"... We describe how to color every 3colorable graph with O(n0.2111) colors, thus improving an algorithm of Blum and Karger from almost a decade ago. Our analysis uses new geometric ideas inspired by the recent work of Arora, Rao, and Vazirani on SPARSEST CUT, and these ideas show promise of leading to ..."
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Cited by 31 (3 self)
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We describe how to color every 3colorable graph with O(n0.2111) colors, thus improving an algorithm of Blum and Karger from almost a decade ago. Our analysis uses new geometric ideas inspired by the recent work of Arora, Rao, and Vazirani on SPARSEST CUT, and these ideas show promise of leading to further improvements.
Better approximation guarantees for jobshop scheduling
 SIAM Journal on Discrete Mathematics
, 1997
"... Abstract. Jobshop scheduling is a classical NPhard problem. Shmoys, Stein, and Wein presented the first polynomialtime approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work and present further impro ..."
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Cited by 32 (2 self)
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Abstract. Jobshop scheduling is a classical NPhard problem. Shmoys, Stein, and Wein presented the first polynomialtime approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work and present further
Heuristic Contraction Hierarchies with Approximation Guarantee
"... We present a new heuristic pointtopoint shortest path algorithm based on contraction hierarchies (CH). Given an ε ≥ 0, we can prove that the length of the path computed by our algorithm is at most (1 + ε) times the length of the optimal (shortest) path. Exact CH is based on node contraction: remov ..."
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We present a new heuristic pointtopoint shortest path algorithm based on contraction hierarchies (CH). Given an ε ≥ 0, we can prove that the length of the path computed by our algorithm is at most (1 + ε) times the length of the optimal (shortest) path. Exact CH is based on node contraction: removing nodes from a network and adding shortcuts to preserve shortest path distances. Our heuristic CH tries to avoid adding shortcuts even when a replacement path is (1 + ε) times longer. However, we cannot avoid all such shortcuts, as we need to ensure that errors do not stack. Combinations with goaldirected techniques bring further speedups.
Improved Approximation Guarantees for Packing and Covering Integer Programs
 SIAM J. Comput
, 1995
"... Several important NPhard combinatorial optimization problems can be posed as packing/covering integer programs; the randomized rounding technique of Raghavan & Thompson is a powerful tool to approximate them well. We present one elementary unifying property of all these integer programs (IPs), ..."
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Cited by 49 (5 self)
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), and use the FKG correlation inequality to derive an improved analysis of randomized rounding on them. This also yields a pessimistic estimator, thus presenting deterministic polynomialtime algorithms for them with approximation guarantees significantly better than those known. Keywords.Approximation
Expected Approximation Guarantees for the Demand Matching Problem
, 2006
"... The objective of the demand matching problem is to obtain the subset � of edges which is feasible and where the sum of the profits of each of the edges is maximized. The set � is feasible if for each vertex � the total demand of edges in � incident to � is at most ��. In the case where each of the e ..."
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bipartite graphs. We demonstrate that an expected ���approximation guarantee and �approximation guarantee is achieveable for bipartite graphs and nonbipartite graphs and give some connections to the independent set and weighted independent set problem. 1
Improved Approximation Guarantees for SublinearTime Fourier Algorithms
, 2010
"... In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse Fourier transforms to higher dimensional settings are develope ..."
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Cited by 13 (4 self)
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In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse Fourier transforms to higher dimensional settings
Improved Approximation Guarantees for LowerBounded Facility Location ⋆
"... Abstract. We consider the lowerbounded facility location (LBFL) problem, which is a generalization of uncapacitated facility location (UFL), where each open facility is required to serve a certain minimum amount of demand. The current best approximation ratio for LBFL is 448 [17]. We substantially ..."
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Cited by 4 (0 self)
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Abstract. We consider the lowerbounded facility location (LBFL) problem, which is a generalization of uncapacitated facility location (UFL), where each open facility is required to serve a certain minimum amount of demand. The current best approximation ratio for LBFL is 448 [17]. We substantially
Results 1  10
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644,245