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AND/OR multivalued decision diagrams (AOMDDs) for graphical models
, 2008
"... Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical model ..."
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Cited by 18 (3 self)
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Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR MultiValued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is searchbased, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inferencebased and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.
Interactive Cost Configuration Over Decision Diagrams
 Journal of Artificial Intelligence Research (JAIR
"... Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrackf ..."
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Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrackfree user interaction online. In particular, binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDDbased configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multivalued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is nonadditive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiplecost configuration is NPhard in the input MDD. However, for solving twocost configuration we develop a pseudopolynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over realworld configuration models and productcatalogue datasets. Response times are generally within a fraction of a second even for very large instances.
The weighted GRAMMAR constraint
, 2011
"... We introduce the WEIGHTEDGRAMMAR constraint and propose propagation algorithms based on the CYK parser and the Earley parser. We show that the traces of these algorithms can be encoded as a weighted negation normal form (WNNF), a generalization of NNF that allows nodes to carry weights. Based on thi ..."
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Cited by 2 (0 self)
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We introduce the WEIGHTEDGRAMMAR constraint and propose propagation algorithms based on the CYK parser and the Earley parser. We show that the traces of these algorithms can be encoded as a weighted negation normal form (WNNF), a generalization of NNF that allows nodes to carry weights. Based on this connection, we prove the correctness and complexity of these algorithms. Specifically, these algorithms enforce domain consistency on the WEIGHTEDGRAMMAR constraint in time O(n 3). Further, we propose that the WNNF constraint can be decomposed into a set of primitive arithmetic constraint without hindering propagation.
Explaining Propagators for sDNNF Circuits
"... Abstract. Smooth decomposable negation normal form (sDNNF) circuits are a compact form of representing many Boolean functions, that permit linear time satisfiability checking. Given a constraint defined by an sDNNF circuit, we can create a propagator for the constraint by decomposing the circuit u ..."
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Abstract. Smooth decomposable negation normal form (sDNNF) circuits are a compact form of representing many Boolean functions, that permit linear time satisfiability checking. Given a constraint defined by an sDNNF circuit, we can create a propagator for the constraint by decomposing the circuit using a Tseitin transformation. But this introduces many additional Boolean variables, and hides the structure of the original sDNNF. In this paper we show how we can build a propagator that works on the sDNNF circuit directly, and can be integrated into a lazyclause generationbased constraint solver. We show that the resulting propagator can efficiently solve problems where sDNNF circuits are the natural representation of the constraints of the problem, outperforming the decomposition based approach. 1
Knowledge Compilation: A Sightseeing Tour
 (TUTORIAL NOTES – ECAI’08)
, 2008
"... Pioneered two decades ago, knowledge compilation (KC) has been for a few years acknowledged as an important research topic in AI. KC is concerned with the preprocessing of pieces of available information for improving the computational efficiency of some tasks based on them. In AI such tasks typical ..."
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Pioneered two decades ago, knowledge compilation (KC) has been for a few years acknowledged as an important research topic in AI. KC is concerned with the preprocessing of pieces of available information for improving the computational efficiency of some tasks based on them. In AI such tasks typically amount to inference or decision making. KC gathers a number of research lines focusing on different problems, ranging from theoretical ones (where the key issue is the compilability one, i.e., determining whether computational improvements can be guaranteed via preprocessing) to more practical ones (mainly the design of compilation algorithms for some specific tasks, like clausal entailment). The (multicriteria) choice of a target language for KC is another major issue. In these tutorial notes, I review a number of the most common results of the literature on KC in the propositional case. The tour includes some attractions, especially algorithms for improving clausal entailment and other forms of inference; a visit of the compilability district and a promenade following the KC map are also included.
Algebraic model counting
, 2012
"... Abstract Weighted model counting (WMC) is a wellknown inference task on knowledge bases, used for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure. We show that AMC generalizes many wellknown tasks in a varie ..."
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Abstract Weighted model counting (WMC) is a wellknown inference task on knowledge bases, used for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure. We show that AMC generalizes many wellknown tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sdDNNF circuits. We identify further characteristics of AMC instances that allow for the use of even more succinct circuits.
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence Maintaining Alternative Values in ConstraintBased Configuration ∗
"... Constraint programming techniques are widely used to model and solve interactive decision problems, and especially configuration problems. In this type of application, the configurable product is described by means of a set of constraints bearing on the configuration variables. The user interactivel ..."
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Constraint programming techniques are widely used to model and solve interactive decision problems, and especially configuration problems. In this type of application, the configurable product is described by means of a set of constraints bearing on the configuration variables. The user interactively solves the CSP by assigning the variables according to her preferences. The system then has to keep the domains of the other variables consistent with these choices. Since maintaining the global inverse consistency of the domains is not tractable, the domains are instead filtered according to some level of local consistency, e.g. arcconsistency. The present paper aims at offering a more convenient interaction by providing the user with possible alternative values for the already assigned variables, i.e. values that could replace the current ones without leading to a constraint violation. We thus present the new concept of alternative domains in a (possibly) partially assigned CSP. We propose a propagation algorithm that computes all the alternative domains in a single step. Its worst case complexity is comparable to the one of the naive algorithm that would run a full propagation for each variable, but its experimental efficiency is better. 1