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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.  ...  dense instance of MAX-CUT.  ... 
doi:10.1006/jcss.2001.1772 fatcat:3trn5u6paral5irdfdf4jkxp6m

Approximability of the Minimum Bisection Problem: An Algorithmic Challenge [chapter]

Marek Karpinski
2002 Lecture Notes in Computer Science  
We survey some recent results on the complexity of computing approximate solutions for instances of the Minimum Bisection problem and formulate some very intriguing and still open questions about the approximability  ...  status of that problem.  ...  Their method followed the earlier work ofFernandez de la Vega and Karpinski FK98a] on existence of a PTAS on dense weighted instances of MAX-CUT.  ... 
doi:10.1007/3-540-45687-2_4 fatcat:k7art7ukvrgshkquf65he4juha

Sampling Methods Applied to Dense Instances of Non-Boolean Optimization Problems [chapter]

Gunnar Andersson, Lars Engebretsen
1998 Lecture Notes in Computer Science  
We generalize earlier sampling methods and thereby construct a randomized polynomial time approximation scheme for instances with Θ(n k ) functions where n is the number of variables occurring in the functions  ...  We study dense instances of optimization problems with variables taking values in Zp.  ...  Introduction Arora, Karger and Karpinski [1] have constructed a randomized polynomial time approximation scheme for dense instances of a number of Max-SNP problems, including Max Cut.  ... 
doi:10.1007/3-540-49543-6_28 fatcat:a2qgylovrzbfvix75wugm4bozm

Page 2112 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
(D-BONN-C; Bonn) Polynomial time approximation of dense weighted instances of MAX-CUT. (English summary) Random Structures Algorithms 16 (2000), no. 4, 314—332.  ...  It is shown for MAX- CUT and MAX-BISECTION that the problem of finding such schemes is achievable for dense classes, while for nondense classes the problem is not tractable, given the standard assumptions  ... 

On Weighted vs Unweighted Versions of Combinatorial Optimization Problems

Pierluigi Crescenzi, Riccardo Silvestri, Luca Trevisan
2001 Information and Computation  
For an appropriate (and very general) definition of niceness, we show that if a nice weighted problem is hard to approximate within r , then its polynomially bounded weighted version is hard to approximate  ...  Then we turn our attention to specific problems, and we show that the unweighted versions of MIN VERTEX COVER, MIN SAT, MAX CUT, MAX DICUT, MAX 2SAT, and MAX EXACT kSAT are exactly as hard to approximate  ...  ACKNOWLEDGMENTS We thank Viggo Kann for having read a preliminary version of this paper and for suggesting some useful modifications.  ... 
doi:10.1006/inco.2000.3011 fatcat:pqvgcjfopjdxfnbaar67uhcuda

Edge covering with budget constrains [article]

Rajiv Gandhi, G. Kortsarz
2013 arXiv   pre-print
The best approximation guarantee known for this instance of dense k-subgraph is O(n^2/9) BCCFV.  ...  We improve the NP-completeness of GH97 by proving the pronlem are APX-hard unless a well-known instance of the dense k-subgraph admits a constant ratio.  ...  Since minimum s-t cut can be computed in polynomial time, our algorithm runs in polynomial time.  ... 
arXiv:1311.0713v1 fatcat:lf4npevzunf3zfohslilibzpkq

Page 6624 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
Summary: “Given a directed graph G and an edge weight func- tion w: A(G) — R*, the maximum directed cut problem (MAX DICUT) is that of finding a directed cut d(S) with maximum total weight.  ...  We also consider the MAX 4-DENSE-SUBGRAPH problem, i.e., de- termine a block of half the number of vertices from a weighted undirected graph such that the sum of the edge weights, within For the web version  ... 

Novel Dense Subgraph Discovery Primitives: Risk Aversion and Exclusion Queries [article]

Charalampos E. Tsourakakis, Tianyi Chen, Naonori Kakimura, Jakub Pachocki
2019 arXiv   pre-print
We formulate both problems mathematically as special instances of dense subgraph discovery in graphs with negative weights.  ...  Is the problem still solvable in polynomial time? Also, why should we care about the densest subgraph problem in the presence of negative weights? In this work we answer the aforementioned question.  ...  Despite the fact we do not know the max cut, we can perform this step in polynomial time by repeating the following procedure for all possible pairs of nodes; if we cannot find a positive cut for any of  ... 
arXiv:1904.08178v1 fatcat:5q3kcvzzcvfpzg6tu5kg6h7a4e

On size-constrained minimum s–t cut problems and size-constrained dense subgraph problems

Wenbin Chen, Nagiza F. Samatova, Matthias F. Stallmann, William Hendrix, Weiqin Ying
2016 Theoretical Computer Science  
We present a polynomial time algorithm for DalkS when k is bounded by some constant c. We also present two approximation algorithms for DamkS.  ...  In this paper, we consider size-constrained minimum s-t cut problems and size-constrained dense subgraph problems.  ...  For the densest subgraph problem of directed graphs, Khuller and Saha proposed a polynomial time algorithm based on max-flow technology, as well as a greedy algorithm with approximation ratio 2.  ... 
doi:10.1016/j.tcs.2015.10.031 fatcat:62n5kfmhwbatrhbajrmgyjwtie

On greedy construction heuristics for the MAX-CUT problem

Sera Kahruman, Elif Kolotoglu, Sergiy Butenko, Illya V. Hicks
2007 International Journal of Computational Science and Engineering (IJCSE)  
Given a graph with non-negative edge weights, the MAX-CUT problem is to partition the set of vertices into two subsets so that the sum of the weights of edges with endpoints in different subsets is maximized  ...  This paper compares the performance of several greedy construction heuristics for MAX-CUT problem.  ...  Acknowledgements The research of Illya V. Hicks was partially supported by NSF grant DMI-0217265  ... 
doi:10.1504/ijcse.2007.017827 fatcat:xh4cchrbczcdpcz3hp7trsy5cq

In Search of the Densest Subgraph

András Faragó, Zohre R. Mojaveri
2019 Algorithms  
While this problem has been the subject of active research for over half of a century, with many proposed variants and solutions, new results still continuously emerge in the literature.  ...  In this survey paper, we review various concepts of graph density, as well as associated theorems and algorithms.  ...  With non-negative edge weights, let w in (S) be the total weight of internal edges, and w cut (S) be the total weight of cut edges.  ... 
doi:10.3390/a12080157 fatcat:7rht55sor5errh2zkyvildkmhi

Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

Jeff Erickson, Philip N. Klein, Dániel Marx, Claire Mathieu, Marc Herbstritt
2016 Dagstuhl Reports  
This report contains abstracts for the recent developments in planar graph algorithms discussed during the seminar as well as summaries of open problems in this area of research.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 16221 "Algorithms for Optimization Problems in Planar Graphs". The seminar was held from May 29 to June 3, 2016.  ...  Weighted Max Cut Background: The problem can be solved in polynomial time when g = 0 [13] and in 2 O(g) poly(|G|) time when g = O(1) and all edge weights are equal [10] .  ... 
doi:10.4230/dagrep.6.5.94 dblp:journals/dagstuhl-reports/EricksonKMM16 fatcat:wasdfgivt5fqdppfxo3iqqs2ta

Approximation Algorithms for NP-Hard Problems

Ravindran Kannan, Marek Karpinski
2004 Oberwolfach Reports  
One of the great recent successes in that area has been the discovery of a new paradigm connecting probabilistic proof verification theory to the theory of approximate computation as well as some new probabilistic  ...  An important mean for surmounting this intractability barrier is that of approximate computation, where the answer is guaranteed to be within some small fraction of optimality.  ...  Polynomial Time Approximation Schemes for Some Dense Instances of NP-Hard Problems. Algorithmica 30 (2001), pp. 386-397. [RZ00a] G. Robins and A. Zelikovsky.  ... 
doi:10.4171/owr/2004/28 fatcat:fwbs36pgpjev5gk6cfeb7ylukm

Commute Times in Dense Graphs [chapter]

Francisco Escolano, Manuel Curado, Edwin R. Hancock
2016 Lecture Notes in Computer Science  
In our experiments we analyze the implications of densification in the estimation of commute times.  ...  After motivating the need of densification, we review the fundamentals of graph densifiers based on cut similarity and then analyze their associated optimization problems.  ...  This study is motivated by the fact that certain NP-hard problems have a PTAS (Polynomial Time Approximation Scheme) when their associated graphs are dense.  ... 
doi:10.1007/978-3-319-49055-7_22 fatcat:7cinj4e5nretdk3nzp3vhysscy

Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems

Yuichi Yoshida, Yuan Zhou
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
Though they are NP-Hard in general, if the instance is "dense" or "locally dense", then they are known to have approximation schemes that run in polynomial time or quasi-polynomial time.  ...  In this paper, we give a unified method of showing these approximation schemes based on the Sherali-Adams linear programming relaxation hierarchy.  ...  However, de la Vega [19] showed that there is a polynomial-time approximation scheme for Max-Cut if the input graph is dense, i.e., it has Ω(n 2 ) edges.  ... 
doi:10.1145/2554797.2554836 dblp:conf/innovations/YoshidaZ14 fatcat:s5jn2jbg7bdqznmyt6vybzatda
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