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Kakuro as a Constraint Problem
"... In this paper we describe models of the logic puzzle Kakuro as a constraint problem with finite domain variables. We show a basic model expressing the constraints of the problem and present various improvements to enhance the constraint propagation, and compare alternatives using MILP and SAT solve ..."
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Cited by 45 (1 self)
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In this paper we describe models of the logic puzzle Kakuro as a constraint problem with finite domain variables. We show a basic model expressing the constraints of the problem and present various improvements to enhance the constraint propagation, and compare alternatives using MILP and SAT solvers. Results for different puzzle collections are given. We also propose a grading scheme predicting the difficulty of a puzzle for a human and show how problems can be tightened by removing hints.
Measuring the Hardness of SAT Instances
, 2008
"... The search of a precise measure of what hardness of SAT instances means for stateoftheart solvers is a relevant research question. Among others, the space complexity of treelike resolution (also called hardness), the minimal size of strong backdoors and of cyclecutsets, and the treewidth can be ..."
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Cited by 7 (1 self)
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The search of a precise measure of what hardness of SAT instances means for stateoftheart solvers is a relevant research question. Among others, the space complexity of treelike resolution (also called hardness), the minimal size of strong backdoors and of cyclecutsets, and the treewidth can be used for this purpose. We propose the use of the treelike space complexity as a solid candidate to be the best measure for solvers based on DPLL. To support this thesis we provide a comparison with the other mentioned measures. We also conduct an experimental investigation to show how the proposed measure characterizes the hardness of random and industrial instances.
Rational deployment of CSP heuristics
 In IJCAI
, 2011
"... Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy ..."
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Cited by 5 (0 self)
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Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solutioncount estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction. 1
Using expectation maximization to find likely assignments for solving csp’s
 In AAAI (2007
"... We present a new probabilistic framework for finding likely variable assignments in difficult constraint satisfaction problems. Finding such assignments is key to efficient search, but practical efforts have largely been limited to random guessing and heuristically designed weighting systems. In con ..."
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Cited by 4 (0 self)
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We present a new probabilistic framework for finding likely variable assignments in difficult constraint satisfaction problems. Finding such assignments is key to efficient search, but practical efforts have largely been limited to random guessing and heuristically designed weighting systems. In contrast, we derive a new version of Belief Propagation (BP) using the method of Expectation Maximization (EM). This allows us to differentiate between variables that are strongly biased toward particular values and those that are largely extraneous. Using EM also eliminates the threat of nonconvergence associated with regular BP. Theoretically, the derivation exhibits appealing primal/dual semantics. Empirically, it produces an “EMBP”based heuristic for solving constraint satisfaction problems, as illustrated with respect to the Quasigroup with Holes domain. EMBP outperforms existing techniques for guiding variable and value ordering during backtracking search on this problem.
Proceedings of the TwentySecond International Joint Conference on Artificial Intelligence Rational Deployment of CSP Heuristics
"... Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy ..."
Abstract
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Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some wellknown heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solutioncount estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction. 1
Rational Metareasoning in ProblemSolving Search
, 2013
"... ___________________________________________________________________Approved by the advisor ..."
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___________________________________________________________________Approved by the advisor