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17
Bucket Elimination: A Unifying Framework for Reasoning
"... Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination ..."
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Cited by 270 (59 self)
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Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucketelimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and space exponential in the inducedwidth of the problem's interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called "conditioning search" require only linear space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucketelimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade space for time.
Minibuckets: A general scheme for bounded inference
 Journal of the ACM (JACM
"... Abstract. This article presents a class of approximation algorithms that extend the idea of boundedcomplexity inference, inspired by successful constraint propagation algorithms, to probabilistic inference and combinatorial optimization. The idea is to bound the dimensionality of dependencies create ..."
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Cited by 57 (20 self)
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Abstract. This article presents a class of approximation algorithms that extend the idea of boundedcomplexity inference, inspired by successful constraint propagation algorithms, to probabilistic inference and combinatorial optimization. The idea is to bound the dimensionality of dependencies created by inference algorithms. This yields a parameterized scheme, called minibuckets, that offers adjustable tradeoff between accuracy and efficiency. The minibucket approach to optimization problems, such as finding the most probable explanation (MPE) in Bayesian networks, generates both an approximate solution and bounds on the solution quality. We present empirical results demonstrating successful performance of the proposed approximation scheme for the MPE task, both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding.
MiniBuckets: A General Scheme for Approximating Inference
 Journal of ACM
, 1998
"... The paper presents a class of approximation algorithms that extend the idea of bounded inference, inspired by successful constraint propagation algorithms, to probabilistic inference and combinatorial optimization. The idea is to bound the dimensionality of dependencies created by inference algor ..."
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Cited by 45 (16 self)
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The paper presents a class of approximation algorithms that extend the idea of bounded inference, inspired by successful constraint propagation algorithms, to probabilistic inference and combinatorial optimization. The idea is to bound the dimensionality of dependencies created by inference algorithms. This yields a parameterized scheme, called minibuckets, that offers adjustable levels of accuracy and efficiency. The minibucket approach generates both an approximate solution and a bound on the solution quality. We present empirical results demonstrating successful performance of the proposed approximation scheme for probabilistic tasks, both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding. 1 Introduction Automated reasoning tasks such as constraint satisfaction and optimization, probabilistic inference, decisionmaking, and planning are generally hard (NPhard). One way to cope This work was partially supported...
Efficient Solution Techniques for Disjunctive Temporal Reasoning Problems
, 2002
"... Over the past few years, a new constraintbased formalism for temporal reasoning has been developed to represent and reason about Disjunctive Temporal Problems (DTPs). The class of DTPs is significantly more expressive than other problems previously studied in constraintbased temporal reasoning. In ..."
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Cited by 45 (12 self)
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Over the past few years, a new constraintbased formalism for temporal reasoning has been developed to represent and reason about Disjunctive Temporal Problems (DTPs). The class of DTPs is significantly more expressive than other problems previously studied in constraintbased temporal reasoning. In this paper we present a new algorithm for DTP solving, called Epilitis, which integrates strategies for efficient DTP solving from the previous literature, including conflictdirected backjumping, removal of subsumed variables, and semantic branching, and further adds nogood recording as a central technique. We discuss the theoretical and technical issues that arise in successfully integrating this range of strategies with one another and with nogood recording in the context of DTP solving. Using an implementation of Epilitis, we explore the effectiveness of various combinations of strategies for solving DTPs, and based on this analysis we demonstrate that Epilitis can achieve a nearly two orderofmagnitude speedup over the previously published algorithms on benchmark problems in the DTP literature.
Utilizing Constraint Satisfaction Techniques for Efficient Graph Pattern Matching
 IN 6TH INTERNATIONAL WORKSHOP ON THEORY AN APPLICATION OF GRAPH TRANSFORMATIONS (TAGT
, 1998
"... This paper presents a way to represent and solve the problem of graph matching  also known as the subgraph homomorphism problem  as a constraint satisfaction problem (CSP), opening up direct access to the large variety of research findings on optimized solution algorithms for CSPs. By decoupling ..."
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Cited by 25 (0 self)
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This paper presents a way to represent and solve the problem of graph matching  also known as the subgraph homomorphism problem  as a constraint satisfaction problem (CSP), opening up direct access to the large variety of research findings on optimized solution algorithms for CSPs. By decoupling the solution algorithm from the concrete graph model, the approach allows for variations of the model without affecting the algorithm. Furthermore, complementing the standard CSP definition, a query concept is introduced to allow abstract representation of concrete implementation properties for optimization purposes.
Distributed Constraint Satisfaction in a Wireless Sensor Tracking System
, 2001
"... This paper describes our ongoing work on an interesting distributed constraint satisfaction problem (DCSP), SensorCSP, that is based on a system of wireless sensors tracking multiple mobile nodes. We present some preliminary results showing that the source of combinatorial complexity in this problem ..."
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Cited by 16 (6 self)
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This paper describes our ongoing work on an interesting distributed constraint satisfaction problem (DCSP), SensorCSP, that is based on a system of wireless sensors tracking multiple mobile nodes. We present some preliminary results showing that the source of combinatorial complexity in this problem is closely linked to the level of communication in the system. This DCSP lends itself naturally to two models  one in which agents are associated with the sensors, and one in which agents are associated with the mobile nodes. We show that these models are duals of each other, and discuss how they di#er in the number of intra and interagent constraints and how this might a#ect the cost of finding a distributed solution. We also suggest that a careful distinction must be made between explicit and implicit interagent constraints in this problem domain as this might a#ect the communication costs and the scalability of a distributed solution. 1
Constraint Satisfaction
 In In the MIT Encyclopedia of the Cognitive Sciences (MITECS
, 1991
"... to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k ..."
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Cited by 15 (5 self)
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to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k colorability formulation, the graph to be colored is the constraint graph. In our SAT example the constraint graph has A connected to D and A; B and C are connected to each other. Constraintnetworks haveproven successful in modeling mundane cognitive tasks such as vision, language comprehension, default reasoning, and abduction, as well as in applications suchasscheduling, design, diagnosis, and temporal and spatial reasoning. In general, constraint satisfaction tasks are computationally intractable #NPhard# #see COMPUTATIONAL COMPLEXITY #. Techniques for pr
Predicatebased filtering of xpath expressions
, 2005
"... The XML/XPath filtering problem has found widespread interest. In this paper, we propose a novel algorithm for solving it. Our approach encodes XPath expressions (XPEs) as ordered sets of predicates and translates XML documents into sets of tuples, which are evaluated over these predicates. Predica ..."
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Cited by 13 (5 self)
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The XML/XPath filtering problem has found widespread interest. In this paper, we propose a novel algorithm for solving it. Our approach encodes XPath expressions (XPEs) as ordered sets of predicates and translates XML documents into sets of tuples, which are evaluated over these predicates. Predicates representing overlapping portions of XPEs are stored and processed once, thus fully exploiting potential overlap in XPEs. We experimentally evaluate the performance of our algorithm, demonstrating its scalability to millions of XPEs, with matching performance in the millisecond range. We show interesting tradeoffs to alternative approaches. 1
Distributed problem solving and the boundaries of selfconfiguration in multihop wireless networks
 In Hawaii International Conference on System Sciences (HICSS35
, 2002
"... In this paper we consider three distributed decision making tasks that arise in the design and configuration of multihop wireless networks: medium access scheduling, Hamiltonian cycle formation, and the partitioning of network nodes into coordinating cliques. We first model these tasks as distribut ..."
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Cited by 13 (7 self)
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In this paper we consider three distributed decision making tasks that arise in the design and configuration of multihop wireless networks: medium access scheduling, Hamiltonian cycle formation, and the partitioning of network nodes into coordinating cliques. We first model these tasks as distributed constraint satisfaction problems (DCSPs). We first show that the communication complexity of DCSPs can be related to the computational complexity of centralized constraint satisfaction problems. We then use centralized algorithms to obtain experimental results on the solvability and complexity of the three DCSPs. We show that these problems exhibit “phase transitions ” in solvability and complexity as the transmission power of the wireless nodes is varied. Based on these results, we argue that phase transition analysis provides a mechanism for quantifying the critical range of network resources needed for scalable, selfconfiguring multihop wireless networks. 1
On the Complexity of Distributed SelfConfiguration in Wireless Networks
 Journal of Telecommunication Systems
, 2003
"... We consider three distributed configuration tasks that arise in the setup and operation of multihop wireless networks: partition into coordinating cliques, Hamiltonian cycle formation and conflictfree channel allocation. We show that the probabilities of accomplishing these tasks undergo zeroone p ..."
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Cited by 11 (0 self)
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We consider three distributed configuration tasks that arise in the setup and operation of multihop wireless networks: partition into coordinating cliques, Hamiltonian cycle formation and conflictfree channel allocation. We show that the probabilities of accomplishing these tasks undergo zeroone phase transitions with respect to the transmission range of individual nodes. We model these tasks as distributed constraint satisfaction problems (DCSPs) and show that, even though they are NPhard in general, these problems can be solved efficiently on average when the network is operated sufficiently far from the transition region. Phase transition analysis is shown to be a useful mechanism for quantifying the critical range of energy and bandwidth resources needed for the scalable performance of selfconfiguring wireless networks. Keywords: selfconfiguration, wireless networks, distributed constraint satisfaction