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Algorithms and Complexity Results for #SAT and Bayesian Inference
 IN 44TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2004
"... Bayesian inference is an important problem with numerous applications in probabilistic reasoning. Counting satisfying assignments is a closely related problem of fundamental theoretical importance. In this paper, we show that plain old DPLL equipped with memoization (an algorithm we call #DPLLCache) ..."
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Cited by 66 (6 self)
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Bayesian inference is an important problem with numerous applications in probabilistic reasoning. Counting satisfying assignments is a closely related problem of fundamental theoretical importance. In this paper, we show that plain old DPLL equipped with memoization (an algorithm we call #DPLLCache) can solve both of these problems with time complexity that is at least as good as stateoftheart exact algorithms, and that it can also achieve the best known timespace tradeoff. We then proceed to show that there are instances where #DPLLCache can achieve an exponential speedup over existing algorithms.
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 61 (9 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward messagepassing and using backward messagepassing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our messagepassing ...
Enhancing Davis Putnam with Extended Binary Clause Reasoning
, 2002
"... The backtracking based Davis Putnam (DPLL) procedure remains the dominant method for deciding the satisfiability of a CNF formula. In recent years there has been much work on improving the basic procedure by adding features like improved heuristics and data structures, intelligent backtracking, ..."
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Cited by 55 (4 self)
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The backtracking based Davis Putnam (DPLL) procedure remains the dominant method for deciding the satisfiability of a CNF formula. In recent years there has been much work on improving the basic procedure by adding features like improved heuristics and data structures, intelligent backtracking, clause learning, etc. Reasoning with binary clauses in DPLL has been a much discussed possibility for achieving improved performance, but to date solvers based on this idea have not been competitive with the best unit propagation based DPLL solvers. In this paper we experiment with a DPLL solver called 2CLS+EQ that makes more extensive use of binary clause reasoning than has been tried before. The results are very encouraging2CLS+EQ is competitive with the very best DPLL solvers. The techniques it uses also open up a number of other possibilities for increasing our ability to solve SAT problems.
Using Weighted MaxSat Engines to Solve MPE
 Proc. 18th Nat’l Conf. Artificial Intelligence
, 2002
"... Logical and probabilistic reasoning are closely related. Many examples in each group have natural analogs in the other. One example is the strong relationship between weighted MAXSAT and MPE. This paper presents a simple reduction of MPE to weighted MAXSAT. It also investigates approximating MPE b ..."
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Cited by 50 (0 self)
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Logical and probabilistic reasoning are closely related. Many examples in each group have natural analogs in the other. One example is the strong relationship between weighted MAXSAT and MPE. This paper presents a simple reduction of MPE to weighted MAXSAT. It also investigates approximating MPE by converting it to a weighted MAXSAT problem, then using the incomplete methods for solving weighted MAXSAT to generate a solution. We show that converting MPE problems to MAXSAT problems and using a method designed for MAXSAT to solve them often produces solutions that are vastly superior to the previous local search methods designed directly for the MPE problem. SAT is the problem of taking a set of clauses with associated weights, and finding the instantiation that produces the largest sum of the weights of satisfied clauses. Weighted MAXSAT is used for example to resolve conflicts in a knowledge base. Finding approximate solutions to weighted MAXSAT has received significant research attention, and novel algorithms have been developed that have proved to be very successful. This paper investigates using local search algorithms developed for weighted MAXSAT and applying them to approximately solve MPE. Local search is a general optimization technique which can be used alone or as a method for improving solutions found by other approximation methods. We compare two successful local search algorithms in the MAXSAT domain ( Discrete Lagrangian Multipliers (Wah & Shang 1997), and Guided Local Search (Mills & Tsang 2000) ) to the local search method proposed for MPE (Kask &Dechter 1999). For large problems, the MAXSAT algorithms proved to be significantly more powerful, typically providing instantiations that are orders of magnitude more probable. The paper is organized as follows: First, we formally introduce the MPE and MAXSAT problems. Then we present the reduction of MPE to MAXSAT. We then introduce the MAXSAT algorithms that will be evaluated. Finally, we provide experimental results comparing the solution quality of MPE approximations using the MAXSAT methods to the previously proposed local search method developed for MPE.
Value Elimination: Bayesian Inference via Backtracking Search
 IN UAI03
, 2003
"... We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially bet ..."
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Cited by 49 (2 self)
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We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially better, irrespective of the variable ordering used by these algorithms. Value Elimination
Optimizing Exact Genetic Linkage Computations
, 2003
"... Genetic linkage analysis is a challenging application which requires Bayesian networks consisting of thousands of vertices. Consequently, computing the likelihood of data, which is needed for learning linkage parameters, using exact inference procedures calls for an extremely efficient implementatio ..."
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Cited by 37 (2 self)
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Genetic linkage analysis is a challenging application which requires Bayesian networks consisting of thousands of vertices. Consequently, computing the likelihood of data, which is needed for learning linkage parameters, using exact inference procedures calls for an extremely efficient implementation that carefully optimizes the order of conditioning and summation operations. In this paper we present the use of stochastic greedy algorithms for optimizing this order. Our algorithm has been incorporated into the newest version of superlink, which is currently the fastest genetic linkage program for exact likelihood computations in general pedigrees. We demonstrate an order of magnitude improvement in run times of likelihood computations using our new optimization algorithm, and hence enlarge the class of problems that can be handled effectively by exact computations.
Practical PartitionBased Theorem Proving for Large Knowledge Bases
, 2003
"... Query answering over commonsense knowledge bases typically employs a firstorder logic theorem prover. While firstorder inference is intractable in general, provers can often be handtuned to answer queries with reasonable performance in practice. ..."
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Cited by 31 (4 self)
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Query answering over commonsense knowledge bases typically employs a firstorder logic theorem prover. While firstorder inference is intractable in general, provers can often be handtuned to answer queries with reasonable performance in practice.
Theorem proving with structured theories (full report
, 2001
"... Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graphbased techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We prese ..."
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Cited by 29 (6 self)
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Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graphbased techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We present messagepassing algorithms that reason over these theories using consequence finding, specializing our algorithms for the case of firstorder resolution, and for batch and concurrent theorem proving. We provide an algorithm that restricts the interaction between subtheories by exploiting the polarity of literals. We attempt to minimize the reasoning within each individual partition by exploiting existing algorithms for focused incremental and general consequence finding. Finally, we propose an algorithm that compiles each subtheory into one in a reduced sublanguage. We have proven the soundness and completeness of all of these algorithms. 1
MBDPOP: A new memorybounded algorithm for distributed optimization
 In Proceedings of IJCAI
, 2007
"... In distributed combinatorial optimization problems, dynamic programming algorithms like DPOP ([Petcu and Faltings, 2005]) require only a linear number of messages, thus generating low communication overheads. However, DPOP’s memory requirements are exponential in the induced width of the constraint ..."
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Cited by 26 (6 self)
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In distributed combinatorial optimization problems, dynamic programming algorithms like DPOP ([Petcu and Faltings, 2005]) require only a linear number of messages, thus generating low communication overheads. However, DPOP’s memory requirements are exponential in the induced width of the constraint graph, which may be prohibitive for problems with large width. We present MBDPOP, a new hybrid algorithm that can operate with bounded memory. In areas of low width, MBDPOP operates like standard DPOP (linear number of messages). Areas of high width are explored with bounded propagations using the idea of cyclecuts [Dechter, 2003]. We introduce novel DFSbased mechanisms for determining the cyclecutset, and for grouping cyclecut nodes into clusters. We use caching between clusters to reduce the complexity to exponential in the largest number of cycle cuts in a single cluster. We compare MBDPOP with ADOPT [Modi et al., 2005], the current state of the art in distributed search with bounded memory. MBDPOP consistently outperforms ADOPT on 3 problem domains, with respect to 3 metrics, providing speedups of up to 5 orders of magnitude. 1
SatEx: A Webbased Framework for SAT Experimentation
 Electronic Notes in Discrete Mathematics
, 2001
"... SatEx is a web site devoted to SAT experimentation. It is not only a front end to a database gathering an exhaustive number of executions, but it also allows dynamic results synthesis as well as detailed explorations of experimentation results. Being dynamically generated and constantly updated ..."
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Cited by 20 (6 self)
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SatEx is a web site devoted to SAT experimentation. It is not only a front end to a database gathering an exhaustive number of executions, but it also allows dynamic results synthesis as well as detailed explorations of experimentation results. Being dynamically generated and constantly updated and improved, this site can be considered as an almost always uptodate SAT experimentation paper. To the current time, SatEx presents the results of more than 450 CPU days on a recent machine. In a few months, this site has been well received by the SAT community and has reached more than 20000 hits. SatEx site is available at http://www.lri.fr/simon/satex/satex.php3. 1