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A Randomized Approximation Scheme for Metric MAX-CUT

W. Fernandez de la Vega, Claire Kenyon
2001 Journal of computer and system sciences (Print)  
We show that metric MAX-CUT has a polynomial time randomized approximation scheme.  ...  Metric MAX-CUT is the problem of dividing a set of points in metric space into two parts so as to maximize the sum of the distances between points belonging to distinct parts.  ...  Acknowledgement We wish to thank Marek Karpinski and Richard Kenyon for fruitful discussions, and the second author wishes to thank Oded Schramm for babysitting on May 4.  ... 
doi:10.1006/jcss.2001.1772 fatcat:3trn5u6paral5irdfdf4jkxp6m

A randomized approximation scheme for metric MAX-CUT

W. Fernandez de la Vega, C. Kenyon
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)  
We show that metric MAX-CUT is NP-complete but has a polynomial time randomized approximation scheme.  ...  Metric MAX-CUT is the problem of dividing a set of points in metric space into two parts so as to maximize the sum of the distances between points belonging to distinct parts.  ...  We also thank Marek Karpinski, Frédéric Magniez, and Richard Kenyon for fruitful discussions.  ... 
doi:10.1109/sfcs.1998.743497 dblp:conf/focs/VegaK98 fatcat:mytgawn6dzdhrasmiwie65fgcy

Approximation Schemes for Metric Clustering Problems [chapter]

Claire Kenyon
2004 Lecture Notes in Computer Science  
Unfortunately, only poor approximation guarantees are possible [16,12]. initiated the study of the problem in metrics. Schulman [20] gave probabilistic algorithms for 2 2 k-Clustering.  ...  We consider a set V of n points endowed with a distance function δ.  ...  of Metric 2-Clustering (polynomial time approximation scheme for metric Max Cut [8] ).  ... 
doi:10.1007/978-3-540-24749-4_1 fatcat:polwvhawircyjeint5q3bt4un4

Page 8183 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Fernandez [Fernandez de la Vega, Wenceslao| (F-PARISI1-RI; Orsay) ; Kenyon, Claire (F-PARIS11-RI; Orsay) A randomized approximation scheme for metric MAX-CUT.  ...  We show that metric MAX-CUT is NP-complete but has a polynomial time randomized approximation scheme.” 2004j:68192 68W20 60C05 68M10 Rao, Nageswara S.  ... 

Approximation Algorithms for Multicommodity-Type Problems with Guarantees Independent of the Graph Size

Ankur Moitra
2009 2009 50th Annual IEEE Symposium on Foundations of Computer Science  
ACKNOWLEDGMENTS We would like to thank Yossi Azar, Tom Leighton, Harald Räcke, Satish Rao and Mohit Singh for many helpful discussions.  ...  Neumann's Min-Max Theorem, we can bound the game value by bounding the cost of P1's best response to any fixed, randomized strategy for P2.  ...  Such papers approach approximating terminal cuts via matroid theory, and here we consider the problem of approximating all terminal cuts via metric geometry.  ... 
doi:10.1109/focs.2009.28 dblp:conf/focs/Moitra09 fatcat:cyr2pizykzeibp6ujitruyy74q

Vertex Sparsification and Oblivious Reductions

Ankur Moitra
2013 SIAM journal on computing (Print)  
These results allow us to derive a more general theory of Steiner cut and flow problems, and allow us to obtain approximation algorithms with guarantees independent of the size of the graph for a number  ...  Given an undirected, capacitated graph G = (V, E) and a set K ⊂ V of terminals of size k, we construct an undirected, capacitated graph G = (K, E ) for which the cut-function approximates the value of  ...  We would like to thank Tom Leighton, Harald Räcke and Satish Rao for many helpful discussions.  ... 
doi:10.1137/100787337 fatcat:6yu5mn6o55frlencngvg7dcjzy

Genus and the geometry of the cut graph: [extended abstract] [chapter]

James R. Lee, Anastasios Sidiropoulos
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
Using these geometric primitives, we present exponentially improved dependence on genus for a number of problems like approximate max-flow/mincut theorems, approximations for uniform and nonuniform Sparsest  ...  In particular, we give optimal bounds for random partitioning schemes, as well as various types of embeddings.  ...  Speaking to the power of such random partitions, this has a number of applications to, e.g. approximate max-flow/min-cut theorems, approximations for uniform and non-uniform Sparsest Cut, treewidth approximation  ... 
doi:10.1137/1.9781611973075.18 dblp:conf/soda/LeeS10 fatcat:ykjbuujnyzemxdjiur2ixfui4y

Approximation schemes for clustering problems

W. Fernandez de la Vega, Marek Karpinski, Claire Kenyon, Yuval Rabani
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
We give polynomial time approximation schemes for the following three clustering problems: Metric k-Clustering, 2 2 k-Clustering, and 2 2 k-Median.  ...  For the first two problems, our results are the first polynomial time approximation schemes. For the third problem, the running time of our algorithms is a vast improvement over previous work.  ...  Our algorithm uses, as a black box, an approximation scheme for Metric Max-k-Cut which is already known in the litterature.  ... 
doi:10.1145/780542.780550 dblp:conf/stoc/VegaKKR03 fatcat:a6loscrgi5ajzb7p3xabyjnogq

Assessing physical network vulnerability under random line-segment failure model

Xiaoliang Wang, Xiaohong Jiang, Achille Pattavina, Sanglu Lu
2012 2012 IEEE 13th International Conference on High Performance Switching and Routing  
Disconnection Probability, three commonly used metrics for statistical vulnerability assessment.  ...  In this paper, we focus on the network vulnerability assessment under the geographically correlated region failure(s) caused by a random "line-segment" cut, an important region failure model that can efficiently  ...  For any point u in a given grid partition Z n , we define a cut which maximizes the value of a specific performance metric by Δ * n (u), i.e., Δ * n (u) = arg max u∈Z n Δ n (u).  ... 
doi:10.1109/hpsr.2012.6260838 dblp:conf/hpsr/WangJPL12 fatcat:nrf53halyjapbl2b2fc747r4ca

Semidefinite programming in combinatorial optimization

Michel X. Goemans
1997 Mathematical programming  
(it) the automatic generation of strong valid inequalities, (iii) the maximum cut problem and related problems, and (iv) the embedding of finite metric spaces and its relationship to the sparsest cut problem  ...  We discuss the use of semidefinite programming for combinatorial optimization problems.  ...  Thanks also to Dan Spielman for stimulating disct,ssions on coding theory and the sparsest cut problem.  ... 
doi:10.1007/bf02614315 fatcat:tm7kei3wuje6vc5vecggkit52e

A Novel Low-Complexity Low-Latency Power Efficient Collision Detection Algorithm for Wireless Sensor Networks

Fawaz Alassery, Walid K. M. Ahmed, Mohsen Sarraf, Victor Lawrence
2015 Wireless Sensor Network  
In addition, we present a complexity and power-saving comparison between our novel algorithms and conventional full-decoding (for select coding schemes) to demonstrate the significant power and complexity  ...  In this paper, we propose a suite of novel, yet simple and power-efficient algorithms to detect a collision without the need for full-decoding of the received packet.  ...  Figure 13 . 13 The PDF (simulation versus fitted) of the metric value, when treated as a random variable (over snapshots): MAX-MIN based metric.  ... 
doi:10.4236/wsn.2015.76006 fatcat:5bsgfqvtzzbmfetr7j57c4bmwi

Bilu–Linial Stable Instances of Max Cut and Minimum Multiway Cut [chapter]

Konstantin Makarychev, Yury Makarychev, Aravindan Vijayaraghavan
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
We also study a relaxed notion of weak stability and present algorithms for weakly stable instances of Max Cut and Minimum Multiway Cut.  ...  We prove that there is no robust polynomialtime algorithm for γ-stable instances of Max Cut when γ < α SC (n/2), where α SC is the best approximation factor for Sparsest Cut with non-uniform demands.  ...  Other known rounding schemes for Multiway Cut achieve a better approximation; e.g. the rounding scheme of Cȃlinescu, Karloff, and Rabani [15] gives a 3/2 approximation.  ... 
doi:10.1137/1.9781611973402.67 dblp:conf/soda/MakarychevMV14 fatcat:oqqa2far5vctjim565rlz47uvu

Bilu-Linial Stable Instances of Max Cut and Minimum Multiway Cut [article]

Konstantin Makarychev, Yury Makarychev, Aravindan Vijayaraghavan
2013 arXiv   pre-print
We prove that there is no robust polynomial-time algorithm for γ-stable instances of Max Cut when γ < α_SC(n/2), where α_SC is the best approximation factor for Sparsest Cut with non-uniform demands.  ...  We show that the standard SDP relaxation for Max Cut (with ℓ_2^2 triangle inequalities) is integral if γ≥ D_ℓ_2^2→ℓ_1(n), where D_ℓ_2^2→ℓ_1(n) is the least distortion with which every n point metric space  ...  Note that in general this rounding scheme gives only a 2 approximation for Multiway Cut.  ... 
arXiv:1305.1681v3 fatcat:uqj7a2il35egjjjnwtcflpdggq

Polynomial Time Approximation Schemes for Dense Instances of NP-Hard Problems

Sanjeev Arora, David Karger, Marek Karpinski
1999 Journal of computer and system sciences (Print)  
We present a uni ed framework for designing polynomial time approximation schemes (PTASs) for \dense" instances of many NP-hard optimization problems, including maximum cut, graph bisection, graph separation  ...  However, recent results show that unless P = NP, PTASs do not exist for many NP-hard problems, including all MAX-SNP-hard problems such as vertex cover, maximum 3-satis ability, maximum cut, metric TSP  ...  However, the operation of taking the complement of a sparse graph yields a dense graph, for which we have just given approximation algorithms for MAX-CUT.  ... 
doi:10.1006/jcss.1998.1605 fatcat:zs4vsyd67ndzpkhishjweru3jm

Similarity estimation techniques from rounding algorithms

Moses S. Charikar
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
Such a scheme leads to a compact representation of objects so that similarity of objects can be estimated from their compact sketches, and also leads to efficient algorithms for approximate nearest neighbor  ...  We show that rounding algorithms for LPs and SDPs used in the context of approximation algorithms can be viewed as locality sensitive hashing schemes for several interesting collections of objects.  ...  They used the random hyperplane rounding technique to round vector solutions for the MAX-CUT problem.  ... 
doi:10.1145/509961.509965 fatcat:oiiuclwjrfabldyjbokqxdxvru
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