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Compact vs. Exponentialsize LP Relaxations
 OPERATIONS RESEARCH LETTERS
, 2000
"... In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomialsize) LP relaxations in place of exponentialsize models requiring separation algorithms. In the same vein as a celebrated theorem by Grötschel, Lovász and Schrijver, we state the equivalence of ..."
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Cited by 7 (3 self)
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In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomialsize) LP relaxations in place of exponentialsize models requiring separation algorithms. In the same vein as a celebrated theorem by Grötschel, Lovász and Schrijver, we state the equivalence
Algorithms Based on LP Relaxations for Combinatorial Optimization Problems
"... We survey the main results presented in the author's Ph.D Thesis [12], which addresses the use of Linear Programming (LP) relaxations within exact and heuristic algorithms for the solution of some Combinatorial Optimization (CO) problems arising from reallife applications. It is well known ..."
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Cited by 1 (0 self)
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We survey the main results presented in the author's Ph.D Thesis [12], which addresses the use of Linear Programming (LP) relaxations within exact and heuristic algorithms for the solution of some Combinatorial Optimization (CO) problems arising from reallife applications. It is well known
1 Integrality Gap 1.1 LP Relaxation
, 2008
"... The LP relaxation for the Priority Steiner Tree is similar to the relaxation used before for the Steiner Tree. Again, say a set S ⊆ V crosses the set R if S ∩ R � = ∅ and R \S � = ∅ there is at least one terminal in S and one not in S. For j ≤ k, let Sj be the collection of all sets which cross R ..."
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The LP relaxation for the Priority Steiner Tree is similar to the relaxation used before for the Steiner Tree. Again, say a set S ⊆ V crosses the set R if S ∩ R � = ∅ and R \S � = ∅ there is at least one terminal in S and one not in S. For j ≤ k, let Sj be the collection of all sets which cross
Learning Bayesian Network Structure using LP Relaxations
"... We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty aris ..."
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Cited by 58 (2 self)
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arises from the global constraint that the graph structure has to be acyclic. We cast the structure learning problem as a linear program over the polytope defined by valid acyclic structures. In relaxing this problem, we maintain an outer bound approximation to the polytope and iteratively tighten
A simple LP relaxation for the Asymmetric Traveling Salesman Problem
"... A longstanding conjecture in Combinatorial Optimization is that the integrality gap of the HeldKarp LP relaxation for the Asymmetric Traveling Salesman Problem (ATSP) is a constant. In this paper, we give a simpler LP relaxation for the ASTP. The integrality gaps of this relaxation and of the Hel ..."
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Cited by 3 (0 self)
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A longstanding conjecture in Combinatorial Optimization is that the integrality gap of the HeldKarp LP relaxation for the Asymmetric Traveling Salesman Problem (ATSP) is a constant. In this paper, we give a simpler LP relaxation for the ASTP. The integrality gaps of this relaxation
Equivalence of LP Relaxation and MaxProduct for Weighted Matching in General Graphs
, 2007
"... Maxproduct belief propagation is a local, iterative algorithm to find the mode/MAP estimate of a probability distribution. While it has been successfully employed in a wide variety of applications, there are relatively few theoretical guarantees of convergence and correctness for general loopy gra ..."
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Cited by 10 (1 self)
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probability distribution whose mode corresponds to the optimal matching, and then running maxproduct. Weighted matching can also be posed as an integer program, for which there is an LP relaxation. This relaxation is not always tight. In this paper we show that 1) If the LP relaxation is tight, then max
Approximate Constraint Satisfaction Requires Large LP Relaxations
"... We prove superpolynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomialsized linear programs are exactly as powerful as programs arising from a constant number of rounds of the S ..."
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Cited by 16 (2 self)
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We prove superpolynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomialsized linear programs are exactly as powerful as programs arising from a constant number of rounds
Analysis of LP relaxations for multiway and multicut problems
 M.C. COSTA ET AL. / EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 1999
"... We introduce in this paper an exact nonlinear formulation of the multiway cut problem. By simple linearizations of this formulation, we derive several wellknown and new formulations for the problem. We further establish a connection between the multiway cut and the maximumweighted independent set ..."
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Cited by 2 (0 self)
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We introduce in this paper an exact nonlinear formulation of the multiway cut problem. By simple linearizations of this formulation, we derive several wellknown and new formulations for the problem. We further establish a connection between the multiway cut and the maximumweighted independent set problem. This leads to the study of several instances of the multiway cut problem through the theory of perfect graphs. We also introduce a new randomized rounding argument to study the
On the LP relaxation of the asymmetric traveling salesman path problem
 Theory of Computing
, 2008
"... Abstract: This is a comment on the article “An O(logn) Approximation Ratio for the ..."
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Abstract: This is a comment on the article “An O(logn) Approximation Ratio for the
Results 11  20
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708