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An Approximation Ratio for Biclustering
, 2007
"... The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying oneway clustering algorithm ..."
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Cited by 7 (1 self)
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algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worstcase approximation ratio of 1+ √ 2 under L1norm for 0–1 valued matrices, and of 2 under L2norm for real valued matrices. Keywords: Approximation algorithms; Biclustering; One
THE BEST RANKONE APPROXIMATION RATIO
"... Abstract. In this paper we define the best rankone approximation ratio of a tensor space. It turns out that in the finite dimensional case this provides an upper bound for the quotient of the residual of the best rankone approximation of any tensor in that tensor space and the norm of that tensor. ..."
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Abstract. In this paper we define the best rankone approximation ratio of a tensor space. It turns out that in the finite dimensional case this provides an upper bound for the quotient of the residual of the best rankone approximation of any tensor in that tensor space and the norm of that tensor
An Improved Approximation Ratio for the Minimum Latency Problem
 Mathematical Programming
, 1996
"... Given a tour visiting n points in a metric space, the latency of one of these points p is the distance traveled in the tour before reaching p. The minimum latency problem asks for a tour passing through n given points for which the total latency of the n points is minimum; in effect, we are seekin ..."
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Cited by 89 (2 self)
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such algorithm, obtaining an approximation ratio of 144. In this work, we present an algorithm which improves this ratio to 21:55. The dev...
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 776 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
Tight bounds for the approximation ratio of the hypervolume indicator
 In Proc. 11th International Conference 29 Problem Solving from Nature (PPSN XI), volume 6238 of LNCS
, 2010
"... Abstract The hypervolume indicator is widely used to guide the search and to evaluate the performance of evolutionary multiobjective optimization algorithms. It measures the volume of the dominated portion of the objective space which is considered to give a good approximation of the Pareto front. ..."
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Cited by 7 (5 self)
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. There is surprisingly little theoretically known about the quality of this approximation. We examine the multiplicative approximation ratio achieved by twodimensional sets maximizing the hypervolume indicator and prove that it deviates significantly from the optimal approximation ratio. This provable gap is even
A better approximation ratio for the vertex cover problem
, 2005
"... We reduce the approximation factor for Vertex Cover to 2 − Θ ( 1 √ log n) (instead of the previous log log n 2 − Θ ( log n), obtained by BarYehuda and Even [2], and by Monien and Speckenmeyer [10]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao, ..."
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Cited by 65 (0 self)
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We reduce the approximation factor for Vertex Cover to 2 − Θ ( 1 √ log n) (instead of the previous log log n 2 − Θ ( log n), obtained by BarYehuda and Even [2], and by Monien and Speckenmeyer [10]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao
Approximation Ratios of Multicast Lighttrees in WDM Networks
, 2010
"... Alloptical multicast routing (AOMR) is implemented by the concept of lighttree in WDM networks. The costoptimal multicast lighttree is NPhard to compute, especially when taking sparse splitting into account. Thus many heuristic algorithms have been proposed. In this paper, the approximation rati ..."
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Cited by 1 (1 self)
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ratios of two classical heuristic AOMR algorithms for sparse splitting WDM network are studied. Let K be the number of destinations in a multicast session, it is proved that ReroutetoSource (R2S) algorithm [4] achieves a tight approximation ratio equal to K in the nonequallyweighted WDM network while
On the Smoothed Approximation Ratio of the 2Opt Heuristic for the TSP
"... The 2Opt heuristic is a simple, easytoimplement local search heuristic for the traveling salesman problem. While it usually provides good approximations to the optimal tour in experiments, its worstcase performance is poor. In an attempt to explain the approximation performance of 2Opt, we prov ..."
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prove an upper bound of exp(O( log(1/σ))) for the smoothed approximation ratio of 2Opt. As a lower bound, we prove that the worstcase lower bound of Ω ( lognlog logn) for the approximation ratio holds for σ = O(1/ n). Our main technical novelty is that, different from existing smoothed analyses, we do
Stee. Absolute approximation ratios for packing rectangles into bins
 Journal of Scheduling
, 2009
"... Abstract. We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles have to be packed nonoverlapping and orthogonal, i.e., axisparallel. We present an algorithm with an absolute worstcase ratio of 2 for the ..."
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Cited by 6 (3 self)
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for the case where the rectangles can be rotated by 90 degrees. This is optimal provided P 6 = NP. For the case where rotation is not allowed, we prove an approximation ratio of 3 for the algorithm Hybrid First Fit which was introduced by Chung, Gary & Johnson [1982] and whose running time is slightly
A comparative analysis of selection schemes used in genetic algorithms
 Foundations of Genetic Algorithms
, 1991
"... This paper considers a number of selection schemes commonly used in modern genetic algorithms. Specifically, proportionate reproduction, ranking selection, tournament selection, and Genitor (or «steady state") selection are compared on the basis of solutions to deterministic difference or d ..."
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Cited by 531 (31 self)
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or differential equations, which are verified through computer simulations. The analysis provides convenient approximate or exact solutions as well as useful convergence time and growth ratio estimates. The paper recommends practical application of the analyses and suggests a number of paths for more detailed
Results 1  10
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