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Approximating Vertex Cover using Structural Rounding [article]

Brian Lavallee, Hayley Russell, Blair D. Sullivan, Andrew van der Poel
2019 arXiv   pre-print
We find that in this setting, structural rounding significantly outperforms standard 2-approximations.  ...  In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms.  ...  Lifting Algorithms In this section, we describe different lifting strategies for using structural rounding on Vertex Cover.  ... 
arXiv:1909.04611v2 fatcat:ur45ov6tcvc5fbnfzanz5hofcy

Fully Dynamic (1+ϵ)-Approximate Matchings [article]

Manoj Gupta, Richard Peng
2013 arXiv   pre-print
Our main result is a data structure that maintains a (1+ϵ) approximation of maximum matching under edge insertions/deletions in worst case O(√(m)ϵ^-2) time per update.  ...  We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update.  ...  vertex cover on G ′ using ApproxCover(G') The vertex cover returned by this procedure will be used for the next round.  ... 
arXiv:1304.0378v2 fatcat:n4e372ma7jbvlmuq2keevs77qa

Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, Andrew Van Der Poel, Michael Wagner
2019 European Symposium on Algorithms  
We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback  ...  We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common  ...  We first use our structural rounding framework with vertex deletions to obtain the following approximation results.  ... 
doi:10.4230/lipics.esa.2019.37 dblp:conf/esa/DemaineGKLLSVP19 fatcat:sa6gr2pm3rggpdb5pehdxtmk6e

Set Cover Revisited: Hypergraph Cover with Hard Capacities [chapter]

Barna Saha, Samir Khuller
2012 Lecture Notes in Computer Science  
Chuzhoy and Naor [FOCS 2002], first studied the special case of unweighted vertex cover with hard capacities and developed an elegant 3 approximation for it based on rounding a natural LP relaxation.  ...  The set cover hardness precludes the possibility of a constant factor approximation for the hard-capacitated vertex cover problem on weighted graphs.  ...  Theorem 3 is also crucially used to obtain an O(f )-approximation algorithm for the set cover and partial cover problem with arbitrary multiplicities.  ... 
doi:10.1007/978-3-642-31594-7_64 fatcat:mbuh2m6f45cx7fwnphlw6curda

Experimental Analysis of Approximation Algorithms for the Vertex Cover and Set Covering Problems

Fernando C. Gomes, Cláudio N. Meneses, Panos M. Pardalos, Gerardo Valdisio R. Viana
2006 Computers & Operations Research  
We conduct a controlled empirical study of approximation algorithms for the Vertex Cover and the Set Covering Problems. Many authors have proposed approximation algorithms for those problems.  ...  Several approximation algorithms with proven performance guarantees have been proposed to find approximate solutions to classical combinatorial optimization problems.  ...  Due to this we used the same data structures on all algorithms, and we do not use any compile options.  ... 
doi:10.1016/j.cor.2005.03.030 fatcat:ihma7yx6tvbylmeioqurxq7hhe

Approximated Distributed Minimum Vertex Cover Algorithms for Bounded Degree Graphs [chapter]

Yong Zhang, Francis Y. L. Chin, Hing-Fung Ting
2010 Lecture Notes in Computer Science  
For the weighted case, we give a 4-approximation algorithm with round complexity O(∆). Related Works: Minimum vertex cover is a very well studied problem in theoretical computer science.  ...  In this paper, two distributed algorithms for the minimum vertex cover problem are given.  ...  This gives us an heuristic to improve the approximation ratio by modifying the length-2 paths in G ′ .  ... 
doi:10.1007/978-3-642-14031-0_13 fatcat:jofflwpkxbhmvkuxlxmdvm3n2e

Fast Distributed Approximation for TAP and 2-Edge-Connectivity [article]

Keren Censor-Hillel, Michal Dory
2019 arXiv   pre-print
approximation algorithms, and an O(h_MST+√(n)^*n)-round 3-approximation algorithm for the weighted case, where h_MST is the height of the MST of the graph.  ...  In this paper, we provide the first fast distributed approximations for TAP. We present a distributed 2-approximation for weighted TAP which completes in O(h) rounds, where h is the height of T.  ...  Note that using the labels of an edge e, a vertex v knows if this edge covers {v, p(v)} using LCA computations.  ... 
arXiv:1711.03359v2 fatcat:xfainfkm6vcr5mkojqcklolxce

A randomized 1.885903-approximation algorithm for the minimum vertex cover problem [article]

Majid Zohrehbandian
2022 Zenodo  
In this paper, by a combination of a well-known semidefinite programming formulation and a rounding procedure, along with satisfying new properties, we introduce an approximation algorithm for the vertex  ...  Vertex cover problem is a famous combinatorial problem, which its complexity has been heavily studied over the years and we know that there is not any mathematical formulation that approximates it better  ...  The rest of the paper is structured as follows. Section 2 is about the vertex cover problem and introduces new properties and new techniques which lead to a -approximation ratio on special graphs.  ... 
doi:10.5281/zenodo.6512073 fatcat:sokwy77oynddzkkrxuytgqtfmq

New insight into introducing a (2-ℇ)-approximation ratio for minimum vertex cover problem [article]

Majid Zohrehbandian
2021 Zenodo  
Vertex cover problem is a famous combinatorial problem, which its complexity has been heavily studied over the years.  ...  Then, by a combination of semidefinite programming and a rounding procedure, along with satisfying the proposed assumptions, we introduce an approximation algorithm with a performance ratio of on arbitrary  ...  The rest of the paper is structured as follows. Section 2 is about the vertex cover problem and introduces new properties and new techniques which lead to a -approximation ratio on special graphs.  ... 
doi:10.5281/zenodo.5831865 fatcat:f5e2qmgcvfa5tix26kv32y2pyi

Distributed Vertex Cover Algorithms for Wireless Sensor Networks

Vedat Kavalci, Aybars Ural, Orhan Dagdeviren
2014 International Journal of Computer Networks & Communications  
The second algorithm finds a vertex cover from graph matching where Hoepman's weighted matching algorithm is used.  ...  The first algorithm, which is an adaption of the Parnas & Ron's algorithm, is a greedy approach that finds a vertex cover by using the degrees of the nodes.  ...  But contrarily, our aim is to approximate a distributed vertex cover in an unweighted graph, so we do not use edge weights. Our implementation is realized through certain assumptions as well.  ... 
doi:10.5121/ijcnc.2014.6107 fatcat:zhrooqkcgfhpjgufigdaajtm2q

New insight into introducing a (2-ℇ)-approximation ratio for minimum vertex cover problem [article]

Majid Zohrehbandian
2021 Zenodo  
In this paper, by a combination of a well-known semidefinite programming formulation and a rounding procedure, along with satisfying new properties, we introduce an approximation algorithm for the vertex  ...  Vertex cover problem is a famous combinatorial problem, which its complexity has been heavily studied over the years and we know that there is not any mathematical formulation that approximates it better  ...  The rest of the paper is structured as follows. Section 2 is about the vertex cover problem and introduces new properties about it.  ... 
doi:10.5281/zenodo.5831874 fatcat:ywlhvlleabdtlgdiwj3yb32umy

Mildly Exponential Time Approximation Algorithms for Vertex Cover, Balanced Separator and Uniform Sparsest Cut

Pasin Manurangsi, Luca Trevisan, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
algorithm for Vertex Cover that runs in exp n 2 r 2 n O(1) time.  ...  An O(r)-approximation algorithms for Uniform Sparsest Cut and Balanced Separator that runs in exp n 2 r 2 n O(1) time. Our algorithm for Vertex Cover improves upon Bansal et al.'  ...  A positive result would show that, in a precise sense, (7/8 + ε) approximation of Max 3SAT is "harder" than (2 − ε) approximation for Vertex Cover (since the former requires poly(ε) • n rounds while the  ... 
doi:10.4230/lipics.approx-random.2018.20 dblp:conf/approx/ManurangsiT18 fatcat:4ylzjfoesjc4dngajskiqxwbha

A fault-containing self-stabilizing (3−2Δ+1)-approximation algorithm for vertex cover in anonymous networks

Volker Turau, Bernd Hauck
2011 Theoretical Computer Science  
For trees the algorithm computes a 2-approximation of a minimum vertex cover.  ...  This paper presents a deterministic self-stabilizing algorithm to compute a (3 − 2 ∆+1 )approximation of a minimum vertex cover in anonymous networks.  ...  The same approach is used by Polishchuk and Suomela to develop a local algorithm that finds a 3-approximation vertex cover in anonymous networks [16] .  ... 
doi:10.1016/j.tcs.2010.11.010 fatcat:ckaujf3yw5aebpnubc34noa6me

LP Rounding for k-Centers with Non-uniform Hard Capacities [article]

Marek Cygan, MohammadTaghi Hajiaghayi, Samir Khuller
2012 arXiv   pre-print
Our algorithm uses an LP rounding approach to solve this problem, and works for the case of non-uniform hard capacities, when multiple copies of a node may not be chosen and can be extended to the case  ...  We develop the first constant factor approximation algorithm for this problem.  ...  Rounding safe caterpillar structures In this section we describe how to round the c-feasible solution (x , y ) using the set of vertex disjoint safe caterpillar structures S from Lemma 26.  ... 
arXiv:1208.3054v1 fatcat:5esduijwuzc4bfdsjzwg4cicpa

Distributed Approximation of Minimum k-edge-connected Spanning Subgraphs [article]

Michal Dory
2018 arXiv   pre-print
Our first contribution is an O(D + √(n))-round O(n)-approximation for 2-ECSS, for a graph with n vertices and diameter D.  ...  For larger constant values of k we give an O(n)-round O(n)-approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D ^3n) rounds.  ...  We show that using the labels we can understand the structure of cuts of size 2 in a graph, and compute how many cuts are covered by an edge in O(D) rounds.  ... 
arXiv:1805.07764v1 fatcat:jx7545iicjemblyqfks2hsspeq
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