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21
Decomposable negation normal form
 Journal of the ACM
, 2001
"... Abstract. Knowledge compilation has been emerging recently as a new direction of research for dealing with the computational intractability of general propositional reasoning. According to this approach, the reasoning process is split into two phases: an offline compilation phase and an online quer ..."
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Cited by 117 (19 self)
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Abstract. Knowledge compilation has been emerging recently as a new direction of research for dealing with the computational intractability of general propositional reasoning. According to this approach, the reasoning process is split into two phases: an offline compilation phase and an online queryanswering phase. In the offline phase, the propositional theory is compiled into some target language, which is typically a tractable one. In the online phase, the compiled target is used to efficiently answer a (potentially) exponential number of queries. The main motivation behind knowledge compilation is to push as much of the computational overhead as possible into the offline phase, in order to amortize that overhead over all online queries. Another motivation behind compilation is to produce very simple online reasoning systems, which can be embedded costeffectively into primitive computational platforms, such as those found in consumer electronics. One of the key aspects of any compilation approach is the target language into which the propositional theory is compiled. Previous target languages included Horn theories, prime implicates/implicants and ordered binary decision diagrams (OBDDs). We propose in this paper a new target compilation language, known as decomposable negation normal form (DNNF), and present a number of its properties that make it of interest to the broad community. Specifically, we
Treewidth: Computational Experiments
, 2001
"... Many NPhard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost ..."
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Cited by 44 (10 self)
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Many NPhard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Although for fixed k, linear time algorithms exist to solve the decision problem “treewidth < k”, their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on wellknown algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary.
kNLC Graphs and Polynomial Algorithms
"... We introduce the class of knode label controlled (kNLC) graphs and the class of kNLC trees. Each kNLC graph is an undirected treestructured graph, where k is a positive integer. The class of kNLC trees is a proper subset of the class of kNLC graphs. Both classes include many interesting gr ..."
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Cited by 37 (2 self)
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We introduce the class of knode label controlled (kNLC) graphs and the class of kNLC trees. Each kNLC graph is an undirected treestructured graph, where k is a positive integer. The class of kNLC trees is a proper subset of the class of kNLC graphs. Both classes include many interesting graph families. For instance, each partial ktree is a (2 k+1 1)NLC tree and each cograph is a 1NLC graph. Furthermore, we introduce a very general method for the design of polynomial algorithms for NPcomplete graph problems, where the input graphs are restricted to treestructured graphs. We exemplify our method with the simple maxcut problem and the Hamiltonian circuit property on kNLC graphs.
dHugin: A computational system for dynamic timesliced Bayesian networks
, 1995
"... A computational system for reasoning about dynamic timesliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete timeseries analysis in the sense that it allows description of nonlinear, discret ..."
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Cited by 15 (0 self)
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A computational system for reasoning about dynamic timesliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete timeseries analysis in the sense that it allows description of nonlinear, discrete multivariate dynamic systems with complex conditional independence structures. The paper introduces the notions of dynamic timesliced Bayesian networks, a dynamic time window, and common operations on the time window. Inference, pertaining to the time window and time slices preceding it, are formulated in terms of the wellknown message passing scheme in junction trees [Jensen et al. (1990)]. Backward smoothing, for example, are performed efficiently through intertree message passing. Further, the system provides an ecient MonteCarlo algorithm for forecasting; i.e., inference pertaining to time slices succeeding the time window. The system has been implemented on top of the Hugin shell [Andersen et al. (1989)].
Safe Reduction Rules For Weighted Treewidth
, 2002
"... Several sets of reductions rules are known for preprocessing a graph when computing its treewidth. In this paper, we give reduction rules for a weighted variant of treewidth, motivated by the analysis of algorithms for probabilistic networks. We present two general reduction rules that are safe for ..."
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Cited by 12 (6 self)
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Several sets of reductions rules are known for preprocessing a graph when computing its treewidth. In this paper, we give reduction rules for a weighted variant of treewidth, motivated by the analysis of algorithms for probabilistic networks. We present two general reduction rules that are safe for weighted treewidth. They generalise many of the existing reduction rules for treewidth. Experimental results show that these reduction rules can significantly reduce the problem size for several instances of reallife probabilistic networks.
Make it Practical: A Generic LinearTime Algorithm for Solving MaximumWeightsum Problems
 In Proceedings of the 5th ACM SIGPLAN International Conference on Functional Programming (ICFP'00
, 2000
"... In this paper we propose a new method for deriving a practical lineartime algorithm from the specification of a maximumweight sum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for aut ..."
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Cited by 12 (8 self)
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In this paper we propose a new method for deriving a practical lineartime algorithm from the specification of a maximumweight sum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for automatically generating lineartime algorithms are theoretically appealing, but the algorithms generated are hardly useful in practice due to a huge constant factor for space and time. The key points of our approach are to express the property p by a recursive boolean function over the structure x rather than a usual logical predicate and to apply program transformation techniques to reduce the constant factor. We present an optimization theorem, give a calculational strategy for applying the theorem, and demonstrate the effectiveness of our approach through several nontrivial examples which would be difficult to deal with when using the methods previously available.
Counting HColorings of Partial kTrees
"... The problem of counting all Hcolorings of a graph G with n vertices is considered. While the problem is, in general, #Pcomplete, we give linear time algorithms that solve the main variants of this problem when the input graph G is a ktree or, in the case where G is directed, when the underlying g ..."
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Cited by 11 (3 self)
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The problem of counting all Hcolorings of a graph G with n vertices is considered. While the problem is, in general, #Pcomplete, we give linear time algorithms that solve the main variants of this problem when the input graph G is a ktree or, in the case where G is directed, when the underlying graph of G is a ktree. Our algorithms remain polynomial even in the case where k = O(log n) or in the case where the size of H is O(n). Our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial ktrees such as core checking and chromatic polynomial computation.
Treewidth and Minimum Fillin on DTrapezoid Graphs
, 1998
"... We show that the minimum llin and the minimum interval graph completion of a dtrapezoid graph can be computed in time O(n d). We also show that the treewidth and the pathwidth of a dtrapezoid graph can be computed in time O(n tw(G)^{d1}). In both cases, d is supposed to be a fixed positive integ ..."
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Cited by 9 (3 self)
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We show that the minimum llin and the minimum interval graph completion of a dtrapezoid graph can be computed in time O(n d). We also show that the treewidth and the pathwidth of a dtrapezoid graph can be computed in time O(n tw(G)^{d1}). In both cases, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given dtrapezoid graph is part of the input. As a consequence, each of the four graph parameters can be computed in time O(n^2) for trapezoid graphs and thus for permutation graphs even if no intersection model is part of the input.
Descriptive and Parameterized Complexity
 In Proc. CSL’99, volume 1683 of LNCS
, 1999
"... . Descriptive Complexity Theory studies the complexity of problems of the following type: Given a nite structure A and a sentence ' of some logic L, decide if A satises '? In this survey we discuss the parameterized complexity of such problems. Basically, this means that we ask under ..."
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Cited by 7 (1 self)
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. Descriptive Complexity Theory studies the complexity of problems of the following type: Given a nite structure A and a sentence ' of some logic L, decide if A satises '? In this survey we discuss the parameterized complexity of such problems. Basically, this means that we ask under which circumstances we have an algorithm solving the problem in time f(j'j)jjAjj c , where f is a computable function and c > 0 a constant. We argue that the parameterized perspective is most appropriate for analyzing typical practical problems of the above form, which appear for example in database theory, automated verication, and articial intelligence. 1 Introduction One of the main themes in descriptive complexity theory is to study the complexity of problems of the following type: Given a nite structure A and a sentence ' of some logic L, decide if A satises '? This problem, let us call it the modelchecking problem for L, has several natural variants. For example, given a struc...
Tree Decomposition With Small Cost
 IN PROCEEDINGS 8TH SWAT, LNCS
, 2002
"... The fcost of a tree decomposition (fX i j i 2 Ig; T = (I; F )) for a function f : N ! R is defined as f(jX i j). This measure associates with the running time or memory use of some algorithms that use the tree decomposition. In this paper we investigate the problem to find tree decompositions of mi ..."
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Cited by 6 (2 self)
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The fcost of a tree decomposition (fX i j i 2 Ig; T = (I; F )) for a function f : N ! R is defined as f(jX i j). This measure associates with the running time or memory use of some algorithms that use the tree decomposition. In this paper we investigate the problem to find tree decompositions of minimum fcost. A function