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58
An Improved Tight Closure Algorithm for Integer Octagonal Constraints ⋆
"... Abstract. Integer octagonal constraints (a.k.a. Unit Two Variables Per Inequality or UTVPI integer constraints) constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of softw ..."
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Cited by 7 (1 self)
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. The latter is called tight closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n 3) algorithm to compute the tight closure of a set of UTVPI integer constraints. 1
Iterating octagons
, 2009
"... In this paper we prove that the transitive closure of a nondeterministic octagonal relation using integer counters can be expressed in Presburger arithmetic. The direct consequence of this fact is that the reachability problem is decidable for flat counter automata with octagonal transition relatio ..."
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Cited by 17 (4 self)
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In this paper we prove that the transitive closure of a nondeterministic octagonal relation using integer counters can be expressed in Presburger arithmetic. The direct consequence of this fact is that the reachability problem is decidable for flat counter automata with octagonal transition
PTIME Computation of Transitive Closures of Octagonal Relations
"... Abstract. Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we study difference bounds and octagonal relations and prove that their transitive closure is a PTIMEcomputable formula in the existential fragment of Presburge ..."
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Abstract. Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we study difference bounds and octagonal relations and prove that their transitive closure is a PTIMEcomputable formula in the existential fragment
Tightened Transitive Closure of Integer Addition Constraints
, 2009
"... We present algorithms for testing the satisfiability and finding the tightened transitive closure of conjunctions of addition constraints of the form ±x ± y ≤ d and bound constraints of the form ±x ≤ d where x and y are integer variables and d is an integer constrant. The running time of these algor ..."
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Cited by 1 (0 self)
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We present algorithms for testing the satisfiability and finding the tightened transitive closure of conjunctions of addition constraints of the form ±x ± y ≤ d and bound constraints of the form ±x ≤ d where x and y are integer variables and d is an integer constrant. The running time
An Efficient Decision Procedure . . . Constraints
, 2005
"... A unit two variable per inequality (UTVPI) constraint is of the form a.x+b.y ≤ d where x and y are integer variables, the coefficients a, b ∈ {−1, 0, 1} and the bound d is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given m such constraints over ..."
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n variables, the procedure checks the satisfiability of the constraints in O(n.m) time and O(n+m) space. This improves upon the previously known O(n 2.m) time and O(n 2) space algorithm based on transitive closure. Our decision procedure is also equality generating, proof generating, and model
Semidefinite relaxations for nonconvex quadratic mixedinteger programming
, 2010
"... We present semidefinite relaxations for unconstrained nonconvex quadratic mixedinteger optimization problems. These relaxations yield tight bounds and are computationally easy to solve for mediumsized instances, even if some of the variables are integer and unbounded. In this case, the problem co ..."
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Cited by 5 (1 self)
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We present semidefinite relaxations for unconstrained nonconvex quadratic mixedinteger optimization problems. These relaxations yield tight bounds and are computationally easy to solve for mediumsized instances, even if some of the variables are integer and unbounded. In this case, the problem
Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation
"... We consider two approaches for solving the classical minimum vertex coloring problem, that is the problem of coloring the vertices of a graph so that adjacent vertices have different colors, minimizing the number of used colors, namely Constraint Programming and Column Generation. Constraint Program ..."
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Programming is able to solve very efficiently many of the benchmarks, but suffers from the lack of effective bounding methods. On the contrary, Column Generation provides tight lower bounds by solving the fractional vertex coloring problem exploited in a BranchandPrice algorithm, as already proposed
Performance optimization of latency insensitive systems through buffer queue sizing of communication channels
 in Proc. Int. Conf. Computer Aided Design
, 2003
"... This paper proposes for latency insensitive systems a performance optimization technique called channel buffer queue sizing, which is performed after relay station insertion in the physical design stage. It can be shown that proper queue sizing can reduce or even completely avoid the performance los ..."
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Cited by 24 (1 self)
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on mixed integer linear programming is proposed. Experimental results show that queue sizing is effective in improving the performance of latency insensitive systems even under tight area constraints. Moreover, the proposed algorithm is sufficiently efficient in obtaining the optimal solution for systems
A Branch and Bound Algorithm for the Minimum StorageTime Sequencing Problem
, 1998
"... The minimum storagetime sequencing problem generalizes many well known problems in Combinatorial Optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propos ..."
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Cited by 1 (0 self)
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propose a new lower bound, based on a Lagrangian relaxation, which can be computed very efficently. To improve upon this lower bound, we employ a bundle optimization algorithm. We also show that the best bound obtainable by this approach equals the one obtainable from the linear relaxation computed on a
An inout approach to disjunctive optimization
 FS10] [GM12] [Gom63] [HCS11] [JT96
, 2010
"... Abstract. Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to provide tight bounds for MixedInteger Programs (MIPs). This is obtained by embedding a cutseparation module within a search scheme. The importance of a sound search ..."
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Cited by 6 (2 self)
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Abstract. Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to provide tight bounds for MixedInteger Programs (MIPs). This is obtained by embedding a cutseparation module within a search scheme. The importance of a sound
Results 1  10
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