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143
A Note on Polyhedral Relaxations for the Maximum Cut Problem
"... We consider three wellstudied polyhedral relaxations for the maximum cut problem: the metric polytope of the complete graph, the metric polytope of a general graph, and the relaxation of the bipartite subgraph polytope. The metric polytope of the complete graph can be described with a polynomial nu ..."
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Cited by 1 (1 self)
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We consider three wellstudied polyhedral relaxations for the maximum cut problem: the metric polytope of the complete graph, the metric polytope of a general graph, and the relaxation of the bipartite subgraph polytope. The metric polytope of the complete graph can be described with a polynomial
Combining Semidefinite and Polyhedral Relaxations for Integer Programs
, 1995
"... We present a general framework for designing semidefinite relaxations for constrained 01 quadratic programming and show how valid inequalities of the cutpolytope can be used to strengthen these relaxations. As examples we improve the #function and give a semidefinite relaxation for the quadrati ..."
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Cited by 17 (11 self)
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We present a general framework for designing semidefinite relaxations for constrained 01 quadratic programming and show how valid inequalities of the cutpolytope can be used to strengthen these relaxations. As examples we improve the #function and give a semidefinite relaxation
Solving MaxCut to optimality by intersecting semidefinite and polyhedral relaxations
, 2008
"... We present a method for finding exact solutions of MaxCut, the problem of finding a cut of maximum weight in a weighted graph. We use a BranchandBound setting, that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly opti ..."
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Cited by 33 (3 self)
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optimal” solution of the basic semidefinite MaxCut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the MaxCut problem, which has to be done several times during the bounding process. We review other solution
Higharity Interactions, Polyhedral Relaxations, and Cutting Plane Algorithm for Soft Constraint Optimisation (MAPMRF)
"... LP relaxation approach to soft constraint optimisation (i.e. MAPMRF) has been mostly considered only for binary problems. We present its generalisation to nary problems, including a simple algorithm to optimise the LP bound, nary maxsum diffusion. As applications, we show that a hierarchy of gra ..."
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of gradually tighter polyhedral relaxations of MAPMRF is obtained by adding zero interactions. We propose a cutting plane algorithm, where cuts correspond to adding zero interactions and the separation problem to finding an unsatisfiable constraint satisfaction subproblem. Next, we show that certain high
A branch and bound algorithm for maxcut based on combining semidefinite and polyhedral relaxations
 INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION 2007
, 2006
"... In this paper we present a method for finding exact solutions of the MaxCut problem max x T Lx such that x ∈ {±1} n. We use a semidefinite relaxation combined with triangle inequalities, which we solve with the bundle method. This approach is due to Fischer, Gruber, Rendl, and Sotirov [12] and uses ..."
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Cited by 11 (3 self)
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In this paper we present a method for finding exact solutions of the MaxCut problem max x T Lx such that x ∈ {±1} n. We use a semidefinite relaxation combined with triangle inequalities, which we solve with the bundle method. This approach is due to Fischer, Gruber, Rendl, and Sotirov [12
Fences are Futile: On Relaxations for the Linear Ordering Problem
"... We study polyhedral relaxations for the linear ordering problem. ..."
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Cited by 9 (3 self)
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We study polyhedral relaxations for the linear ordering problem.
Generating textures on arbitrary surfaces using reactiondiffusion
 Computer Graphics
, 1991
"... This paper describes a biologically motivated method of texture synthesis called reactiondiffusion and demonstrates how these textures can be generated in a manner that directly matches the geometry of a given surface. Reactiondiffusion is a process in which two or more chemicals diffuse at unequa ..."
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Cited by 283 (5 self)
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, this paper introduces a method by which reactiondiffusion textures are created to match the geometry of an arbitrary polyhedral surface. This is accomplished by creating a mesh over a given surface and then simulating the reactiondiffusion process directly on this mesh. This avoids the often difficult task
Polyhedral approaches to machine scheduling
, 1996
"... We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition ..."
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Cited by 41 (8 self)
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We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition
ON THE DERIVATIVE CONES OF POLYHEDRAL CONES
, 2011
"... Hyperbolic polynomials elegantly encode a rich class of convex cones that includes polyhedral and spectrahedral cones. Hyperbolic polynomials are closed under taking polars and the corresponding cones – the derivative cones – yield relaxations for the associated optimization problem and exhibit in ..."
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Cited by 7 (2 self)
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Hyperbolic polynomials elegantly encode a rich class of convex cones that includes polyhedral and spectrahedral cones. Hyperbolic polynomials are closed under taking polars and the corresponding cones – the derivative cones – yield relaxations for the associated optimization problem and exhibit
Polyhedral Combinatorics of Benzenoid Problems
 Lect. Notes Comput. Sci
, 1998
"... Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational results, that solving the ..."
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Cited by 1 (0 self)
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the linear programming relaxation always yields integral solutions. We prove this conjecture showing that the constraint matrices of these problems are unimodular. This establishes the integrality of the relaxation polyhedra since the linear programs are in standard form. However, the matrices are not
Results 1  10
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143