Results 11  20
of
64
Distributed Weighted Vertex Cover via Maximal Matchings
, 2004
"... In this paper we consider the problem of computing a minimumweight vertexcover in an nnode, weighted, undirected graph G = (V,E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expe ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
In this paper we consider the problem of computing a minimumweight vertexcover in an nnode, weighted, undirected graph G = (V,E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O(logn + log ˆW) communication rounds, where ˆW is the average vertexweight. The previous best algorithm for this problem requires O(logn(log n + log ˆW)) rounds and it is not fully distributed. For a maximal matching M in G it is a wellknown fact that any vertexcover in G needs to have at least M  vertices. Our algorithm is based on a generalization of this combinatorial lowerbound to the weighted setting.
Integrality gaps of semidefinite programs for Vertex Cover and relations to ℓ1 embeddability of negative type metrics
"... ..."
(Show Context)
EWLS: A New Local Search for Minimum Vertex Cover
 PROCEEDINGS OF THE TWENTYFOURTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI10)
, 2010
"... A number of algorithms have been proposed for the Minimum Vertex Cover problem. However, they are far from satisfactory, especially on hard instances. In this paper, we introduce Edge Weighting Local Search (EWLS), a new local search algorithm for the Minimum Vertex Cover problem. EWLS is based on t ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
A number of algorithms have been proposed for the Minimum Vertex Cover problem. However, they are far from satisfactory, especially on hard instances. In this paper, we introduce Edge Weighting Local Search (EWLS), a new local search algorithm for the Minimum Vertex Cover problem. EWLS is based on the idea of extending a partial vertex cover into a vertex cover. A key point of EWLS is to find a vertex set that provides a tight upper bound on the size of the minimum vertex cover. To this purpose, EWLS employs an iterated local search procedure, using an edge weighting scheme which updates edge weights when stuck in local optima. Moreover, some sophisticated search strategies have been taken to improve the quality of local optima. Experimental results on the broadly used DIMACS benchmark show that EWLS is competitive with the current best heuristic algorithms, and outperforms them on hard instances. Furthermore, on a suite of difficult benchmarks, EWLS delivers the best results and sets a new record on the largest instance.
Harnessing Genetic Algorithm for Vertex Cover Problem
 International Journal on Computer Science and Engineering (IJCSE
"... Abstract: The problem of finding a minimum vertex cover is an NP hard optimization problem. Some approximation algorithms for the problem have been proposed but most of them are neither optimal nor complete. The work proposes the use of the theory of natural selection via Genetic Algorithms (GAs) fo ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
(Show Context)
Abstract: The problem of finding a minimum vertex cover is an NP hard optimization problem. Some approximation algorithms for the problem have been proposed but most of them are neither optimal nor complete. The work proposes the use of the theory of natural selection via Genetic Algorithms (GAs) for solving the problem. The proposed work has been tested for some constrained inputs and the results were encouraging. The paper also discusses the application of genetic algorithms to the solution and the requisite analysis. The approach presents a Genetic Algorithms based solution to a problem.
Vertex Cover resists SDPs tightened by local hypermetric inequalities
, 2007
"... We consider the standard semidefinite programming (SDP) relaxation for the vertex cover problem to which all hypermetric inequalities supported on at most k vertices are added and show that the integrality gap for such SDPs remains 2 − o(1) even for k = O ( � log n / loglog n). This extends results ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
We consider the standard semidefinite programming (SDP) relaxation for the vertex cover problem to which all hypermetric inequalities supported on at most k vertices are added and show that the integrality gap for such SDPs remains 2 − o(1) even for k = O ( � log n / loglog n). This extends results by KleinbergGoemans, Charikar and Hatami et al. who considered vertex cover SDPs tightened using the triangle and pentagonal inequalities, respectively. Our result is complementary to a recent result by Georgiou et al. proving integrality gaps for vertex cover SDPs in the LovászSchrijver hierarchy. However, the SDPs we consider are incomparable to the SDPs analyzed by Georgiou et al. In particular we show that vertex cover SDPs in the LovászSchrijver hierarchy fail to satisfy any hypermetric constraints supported on an independent set of the input graph. This constrasts with the LP LovászSchrijver hierarchy where all local LP constraints are derived.
Tight Gaps for Vertex Cover in the SheraliAdams SDP Hierarchy
, 2011
"... We give the first tight integrality gap for Vertex Cover in the SheraliAdams SDP system. More precisely, we show that for every ɛ> 0, the standard SDP for Vertex Cover that is strengthened with the level6 SheraliAdams system has integrality gap 2 − ɛ. To the best of our knowledge this is the f ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We give the first tight integrality gap for Vertex Cover in the SheraliAdams SDP system. More precisely, we show that for every ɛ> 0, the standard SDP for Vertex Cover that is strengthened with the level6 SheraliAdams system has integrality gap 2 − ɛ. To the best of our knowledge this is the first nontrivial tight integrality gap for the SheraliAdams SDP hierarchy for a combinatorial problem with hard constraints. For our proof we introduce a new tool to establish LocalGlobal Discrepancy which uses simple facts from highdimensional geometry. This allows us to give SheraliAdams solutions with objective value n(1/2 + o(1)) for graphs with small (2 + o(1)) vector chromatic number. Since such graphs with no linear size independent sets exist, this immediately gives a tight integrality gap for the SheraliAdams system for superconstant number of tightenings. In order to obtain a SheraliAdams solution that also satisfies semidefinite conditions, we reduce semidefiniteness to a condition on the Taylor expansion of a reasonably simple function that we are able to establish up to constantlevel SDP tightenings. We conjecture that this condition holds even for superconstant levels which would imply that in fact our solution is valid for superconstant level SheraliAdams SDPs.
NuMVC: An efficient local search algorithm for minimum vertex cover
 J. Artif. Intell. Res. (JAIR
, 2013
"... The Minimum Vertex Cover (MVC) problem is a prominent NPhard combinatorial optimization problem of great importance in both theory and application. Local search has proved successful for this problem. However, there are two main drawbacks in stateoftheart MVC local search algorithms. First, they ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
The Minimum Vertex Cover (MVC) problem is a prominent NPhard combinatorial optimization problem of great importance in both theory and application. Local search has proved successful for this problem. However, there are two main drawbacks in stateoftheart MVC local search algorithms. First, they select a pair of vertices to exchange simultaneously, which is timeconsuming. Secondly, although using edge weighting techniques to diversify the search, these algorithms lack mechanisms for decreasing the weights. To address these issues, we propose two new strategies: twostage exchange and edge weighting with forgetting. The twostage exchange strategy selects two vertices to exchange separately and performs the exchange in two stages. The strategy of edge weighting with forgetting not only increases weights of uncovered edges, but also decreases some weights for each edge periodically. These two strategies are used in designing a new MVC local search algorithm, which is referred to as NuMVC. We conduct extensive experimental studies on the standard benchmarks, namely DIMACS and BHOSLIB. The experiment comparing NuMVC with stateoftheart heuristic algorithms show that NuMVC is at least competitive with the nearest competitor namely PLS on the DIMACS benchmark, and clearly dominates all competitors on the BHOSLIB benchmark. Also, experimental results indicate that NuMVC finds an optimal solution much faster than the current best exact algorithm for Maximum Clique on random instances as well as some structured ones. Moreover, we study the effectiveness of the two strategies and the runtime behaviour through experimental analysis. 1.
Distance scales, embeddings, and metrics of negative type
 Symposium on Discrete Algorithms (SODA
, 2005
"... We introduce a new number of new techniques for the construction of lowdistortion embeddings of a finite metric space. These include a generic Gluing Lemma which avoids the overhead typically incurred from the naïve concatenation of maps for different scales of a space. We also give a significantly ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
We introduce a new number of new techniques for the construction of lowdistortion embeddings of a finite metric space. These include a generic Gluing Lemma which avoids the overhead typically incurred from the naïve concatenation of maps for different scales of a space. We also give a significantly improved and quantitatively optimal version of the main structural theorem of Arora, Rao, and Vazirani on separated sets in metrics of negative type. The latter result offers a simple hyperplane rounding algorithm for the computation of an O ( √ log n)approximation to the Sparsest Cut problem with uniform demands, and has a number of other applications to embeddings and approximation algorithms. 1
A (2  c(log N/N)) Approximation Algorithm for the Stable Marriage Problem
, 2006
"... An instance of the classical stable marriage problem requires all participants to submit a strictly ordered preference list containing all members of the opposite sex. However, considering applications in realworld, we can think of two natural relaxations, namely, incomplete preference lists and ti ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
An instance of the classical stable marriage problem requires all participants to submit a strictly ordered preference list containing all members of the opposite sex. However, considering applications in realworld, we can think of two natural relaxations, namely, incomplete preference lists and ties in the lists. Either variation leaves the problem polynomially solvable, but it is known that finding a maximum cardinality stable matching is NPhard when both variations are allowed. It is easy to see that the size of any two stable matchings differ by at most a factor of two, and so, an approximation algorithm with a factor two is trivial. A few approximation algorithms have been proposed with approximation ratio better than two, but they are only for restricted instances, such as restricting occurrence of ties and/or lengths of ties. Up to the present, there is no known approximation algorithm with ratio better than two for general inputs. In this paper, we give the first nontrivial result for approximation of factor less than two for general instances. Our algorithm achieves the log N ratio 2 − c N for an arbitrarily positive constant c, where N denotes the number of men in an input.
A PrimalDual Bicriteria Distributed Algorithm for Capacitated Vertex Cover
, 2008
"... In this paper we consider the capacitated vertex cover problem which is the variant of vertex cover where each node is allowed to cover a limited number of edges. We present an efficient, deterministic, distributed approximation algorithm for the problem. Our algorithm computes a (2 + ǫ)approximate ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
In this paper we consider the capacitated vertex cover problem which is the variant of vertex cover where each node is allowed to cover a limited number of edges. We present an efficient, deterministic, distributed approximation algorithm for the problem. Our algorithm computes a (2 + ǫ)approximate solution which violates the capacity constraints by a factor of (4 + ǫ) in a polylogarithmic number of communication rounds. On the other hand, we also show that every efficient distributed approximation algorithm for this problem must violate the capacity constraints. Our result is achieved in two steps. We first develop a 2approximate, sequential primaldual algorithm that violates the capacity constraints by a factor of 2. Subsequently, we present a distributed version of this algorithm. We demonstrate that the sequential algorithm has an inherent need for synchronization which forces any naive distributed implementation to use a linear number of communication rounds. The challenge in this step is therefore to achieve a reduction of the communication complexity to a polylogarithmic number of rounds without worsening the approximation guarantee too much.