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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 11 (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
The Octagon Abstract Domain
"... ... domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on DifferenceBound Matrices and allows us to represent invariants of the form (±x ± y ≤ c), where x and y are program variables and c is a real constant. We focus on giving an efficient re ..."
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Cited by 327 (24 self)
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representation based on DifferenceBound Matrices—O(n²) memory cost, where n is the number of variables—and graphbased algorithms for all common abstract operators—O(n³) time cost. This includes a normal form algorithm to test equivalence of representation and a widening operator to compute least fixpoint
The Omega Test: a fast and practical integer programming algorithm for dependence analysis
 Communications of the ACM
, 1992
"... The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method ..."
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Cited by 521 (15 self)
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The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worstcase exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...
Constraint Networks
, 1992
"... Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expression ..."
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Cited by 1149 (43 self)
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Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
"... ..."
The Viterbi algorithm
 Proceedings of the IEEE
, 1973
"... vol. 6, no. 8, pp. 211220, 1951. [7] J. L. Anderson and J. W..Ryon, “Electromagnetic radiation in accelerated systems, ” Phys. Rev., vol. 181, pp. 17651775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an accelerated system of reference, ” Phys. Reu., vol. 134, pp. A ..."
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Cited by 985 (3 self)
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vol. 6, no. 8, pp. 211220, 1951. [7] J. L. Anderson and J. W..Ryon, “Electromagnetic radiation in accelerated systems, ” Phys. Rev., vol. 181, pp. 17651775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an accelerated system of reference, ” Phys. Reu., vol. 134, pp. A799A804, 1964. [9] T. C. Mo, “Theory of electrodynamics in media in noninertial frames and applications, ” J. Math. Phys., vol. 11, pp. 25892610, 1970.
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Theory and Practice of Constraint Handling Rules
, 1998
"... Constraint Handling Rules (CHR) are our proposal to allow more flexibility and applicationoriented customization of constraint systems. CHR are a declarative language extension especially designed for writing userdefined constraints. CHR are essentially a committedchoice language consisting of mu ..."
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Cited by 459 (36 self)
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property, confluence, of CHR programs and define a tight integration of CHR with constraint logic programming languages. This survey then describes implementations of the language before we review several constraint solvers  both traditional and non standard ones  written in the CHR language. Finally we
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas
Results 1  10
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90,727