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Semidefinite Programming Relaxations in Timetabling
, 2011
"... This paper extends semidefinite programming relaxations of graph colouring to bounded graph colouring and extensions encountered in timetabling, where room sizes, room features, room stability, and preallocated assignments are considered. A matrixfree implementation of an augmented Lagrangian met ..."
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This paper extends semidefinite programming relaxations of graph colouring to bounded graph colouring and extensions encountered in timetabling, where room sizes, room features, room stability, and preallocated assignments are considered. A matrixfree implementation of an augmented Lagrangian
Semidefinite Programming Relaxations for Semialgebraic Problems
, 2001
"... A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The mai ..."
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Cited by 365 (23 self)
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A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility
Semidefinite Programming Relaxation
"... Today, we talk the use of Semidefinite Programming in the design of approximation algorithms. This technique was invented by Goemans and Williamson in 1995. It is because of this technique both of them won the Fulkerson Prize in 2000. I’ll talk about this technique in the context of the ..."
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Today, we talk the use of Semidefinite Programming in the design of approximation algorithms. This technique was invented by Goemans and Williamson in 1995. It is because of this technique both of them won the Fulkerson Prize in 2000. I’ll talk about this technique in the context of the
Semidefinite Programming Relaxation for the Independent Set Problem
, 1999
"... This report contains a study on the weighted independent set problem. In particular, it deals with solving this problem by parallel branchandbound algorithms, in which the evaluation of the nodes is based on positive semidefinite programming relaxation ..."
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This report contains a study on the weighted independent set problem. In particular, it deals with solving this problem by parallel branchandbound algorithms, in which the evaluation of the nodes is based on positive semidefinite programming relaxation
Strengthened Semidefinite Programming Relaxations for the MAXCUT Problem
"... In this paper we summarize recent results on finding tight semidefinite programming relaxations for the MaxCut problem and hence tight upper bounds on its optimal value. Our results hold for every instance of MaxCut and in particular we make no assumptions on the edge weights. We present two stren ..."
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In this paper we summarize recent results on finding tight semidefinite programming relaxations for the MaxCut problem and hence tight upper bounds on its optimal value. Our results hold for every instance of MaxCut and in particular we make no assumptions on the edge weights. We present two
Semidefinite Programming Relaxations in Timetabling (Abstract)
 PATAT 2010
, 2010
"... Semidefinite programming has recently gained much attention as a powerful method for deriving both strong lower bounds and approximation algorithms in combinatorial optimisation. There have not been, however, any applications to timetabling. We show one reason to believe that this could well change ..."
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Semidefinite programming has recently gained much attention as a powerful method for deriving both strong lower bounds and approximation algorithms in combinatorial optimisation. There have not been, however, any applications to timetabling. We show one reason to believe that this could well
On Linear and Semidefinite Programming Relaxations for Hypergraph Matching
"... The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a wellstudied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. I ..."
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Cited by 16 (0 self)
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. In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method. Our main results are the following: • We consider the standard linear programming relaxation of the problem. We provide an algorithmic
Convex Quadratic and Semidefinite Programming Relaxations in Scheduling
 Journal of the ACM
, 1999
"... We consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs. The main contribution of this paper is a provably good convex quadratic programming relaxation of strongly polynomial size for this problem. The be ..."
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Cited by 33 (3 self)
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. Finally, for the special case of two machines we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by Goemans and Williamson for the MAXCUT problem
Semidefinite Programming Relaxations For Set Partitioning Problems
, 1996
"... We present a relaxation for the set partitioning problem that combines the standard linear programming relaxation with a semidefinite programming relaxation. We include numerical results that illustrate the strength and efficiency of this relaxation. Contents 1 INTRODUCTION 2 1.1 Background . . . ..."
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Cited by 1 (0 self)
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We present a relaxation for the set partitioning problem that combines the standard linear programming relaxation with a semidefinite programming relaxation. We include numerical results that illustrate the strength and efficiency of this relaxation. Contents 1 INTRODUCTION 2 1.1 Background
An Improved Semidefinite Programming Relaxation for the Satisfiability Problem
, 2002
"... The satisfiability (SAT) problem is a central problem in mathematical logic, computing theory, and artificial intelligence. An instance of SAT is specified by a set of boolean variables and a propositional formula in conjunctive normal form. Given such an instance, the SAT problem asks whether there ..."
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Cited by 13 (3 self)
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unsatisfiability. In this paper we introduce a new SDP relaxation for the satisfiability problem. This SDP relaxation arises from the recently introduced paradigm of “higher liftings” for constructing semidefinite programming relaxations of discrete optimization problems.
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