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On Approximation Algorithms for Hierarchical MAXSAT
, 1997
"... We prove upper and lower bounds on performance guarantees of approximation algorithms for the Hierarchical MAXSAT (HMAXSAT) problem. This problem is representative of a broad class of PSPACEhard problems involving graphs, Boolean formulas and other structures that are defined succinctly. Our fir ..."
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Cited by 4 (0 self)
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We prove upper and lower bounds on performance guarantees of approximation algorithms for the Hierarchical MAXSAT (HMAXSAT) problem. This problem is representative of a broad class of PSPACEhard problems involving graphs, Boolean formulas and other structures that are defined succinctly. Our
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
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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o(1)) ln n), and previous results of Lund and Yannakakis, that showed hardness of approximation within a ratio of (log 2 n)=2 ' 0:72 lnn. For max kcover we show an approximation threshold of (1 \Gamma 1=e) (up to low order terms), under the assumption that P != NP .
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 782 (12 self)
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for the efficient approximability of many optimization problems studied previously. In particular, for MaxE2Sat, MaxCut, MaxdiCut, and Vertex cover. Warning: Essentially this paper has been published in JACM and is subject to copyright restrictions. In particular it is for personal use only.
Approximation algorithms for MaxSAT
"... The main aim of NPcompleteness theory is the analysis of intractability. Many optimization problems were first proved to be NPhard. Since the complete solution of these problems requires exponential time, polynomial time algorithms to find "nearoptimal" solutions, i.e., approximation al ..."
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The main aim of NPcompleteness theory is the analysis of intractability. Many optimization problems were first proved to be NPhard. Since the complete solution of these problems requires exponential time, polynomial time algorithms to find "nearoptimal" solutions, i.e., approximation
Optimally relaxing partialorder plans with MaxSAT
 In Proceedings of the 22nd International Conference on Automated Planning and Scheduling
, 2012
"... Partialorder plans (POPs) are attractive because of their least commitment nature, providing enhanced plan flexibility at execution time relative to sequential plans. Despite the appeal of POPs, most of the recent research on automated plan generation has focused on sequential plans. In this paper ..."
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Cited by 4 (2 self)
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we examine the task of POP generation by relaxing or modifying the action orderings of a plan to optimize for plan criteria that promotes flexibility in the POP. Our approach relies on a novel partial weighted MaxSAT encoding of a plan that supports the minimization of deordering or reordering
Optimization of PartialOrder Plans via MaxSAT
"... Partialorder plans (POPs) are attractive because of their least commitment nature, providing enhanced plan flexibility at execution time relative to sequential plans. Despite the appeal of POPs, most of the recent research on automated plan generation has focused on sequential plans. In this paper ..."
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Cited by 2 (1 self)
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we examine the task of POP generation by relaxing or modifying the action orderings of a sequential plan to optimize for plan criteria that promote flexibility in the POP. Our approach relies on a novel partial weighted MaxSAT encoding of a sequential plan that supports the minimization of deordering
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
A New Method for Solving Hard Satisfiability Problems
 AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
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Cited by 734 (21 self)
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We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, Nqueens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a modelfinding procedure. Its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theoremproving problems as modelfinding tasks.
Results 1  10
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