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158
Learning Bayesian networks: The combination of knowledge and statistical data
 Machine Learning
, 1995
"... We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simpl ..."
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Cited by 901 (35 self)
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We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user’s prior knowledge. In particular, a user can express his knowledge—for the most part—as a single prior Bayesian network for the domain. 1
Minimizing Conflicts: A Heuristic Repair Method for ConstraintSatisfaction and Scheduling Problems
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 1993
"... This paper describes a simple heuristic approach to solving largescale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a valueorder ..."
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Cited by 397 (6 self)
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This paper describes a simple heuristic approach to solving largescale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a valueordering heuristic, the minconflicts heuristic, that attempts to minimize the number of constraint violations after each step. The heuristic can be used with a variety of different search strategies. We demonstrate empirically that on the nqueens problem, a technique based on this approach performs orders of magnitude better than traditional backtracking techniques. We also describe a scheduling application where the approach has been used successfully. A theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective.
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 315 (3 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes are in � d, the running time increases to O(n(log n) (O(�dc))d�1). For every fixed c, d the running time is n � poly(log n), that is nearly linear in n. The algorithm can be derandomized, but this increases the running time by a factor O(n d). The previous best approximation algorithm for the problem (due to Christofides) achieves a 3/2approximation in polynomial time. We also give similar approximation schemes for some other NPhard Euclidean problems: Minimum Steiner Tree, kTSP, and kMST. (The running times of the algorithm for kTSP and kMST involve an additional multiplicative factor k.) The previous best approximation algorithms for all these problems achieved a constantfactor approximation. We also give efficient approximation schemes for Euclidean MinCost Matching, a problem that can be solved exactly in polynomial time. All our algorithms also work, with almost no modification, when distance is measured using any geometric norm (such as �p for p � 1 or other Minkowski norms). They also have simple parallel (i.e., NC) implementations.
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 246 (12 self)
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This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feedforward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...
The complexity of computing a Nash equilibrium
, 2006
"... We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability of n ..."
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Cited by 221 (14 self)
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We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability of normalform games and graphical games, and shows that these kinds of games can implement arbitrary members of a PPADcomplete class of Brouwer functions. 1
Static Scheduling Algorithms for Allocating Directed Task Graphs to Multiprocessors
, 1999
"... Devices]: Modes of ComputationParallelism and concurrency General Terms: Algorithms, Design, Performance, Theory Additional Key Words and Phrases: Automatic parallelization, DAG, multiprocessors, parallel processing, software tools, static scheduling, task graphs This research was supported ..."
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Cited by 202 (4 self)
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Devices]: Modes of ComputationParallelism and concurrency General Terms: Algorithms, Design, Performance, Theory Additional Key Words and Phrases: Automatic parallelization, DAG, multiprocessors, parallel processing, software tools, static scheduling, task graphs This research was supported by the Hong Kong Research Grants Council under contract numbers HKUST 734/96E, HKUST 6076/97E, and HKU 7124/99E. Authors' addresses: Y.K. Kwok, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong; email: ykwok@eee.hku.hk; I. Ahmad, Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong. Permission to make digital / hard copy of part or all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and / or a fee. 2000 ACM 03600300/99/12000406 $5.00 ACM Computing Surveys, Vol. 31, No. 4, December 1999 1.
On the complexity of the parity argument and other inefficient proofs of existence
 JCSS
, 1994
"... We define several new complexity classes of search problems, "between " the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is defined in terms ..."
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Cited by 153 (8 self)
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We define several new complexity classes of search problems, "between " the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph. The existence of the solution sought is established via a simple graphtheoretic argument with an inefficiently constructive proof; for example, PLS can be thought of as corresponding to the lemma "every dag has a sink. " The new classes are based on lemmata such as "every graph has an even number of odddegree nodes. " They contain several important problems for which no polynomial time algorithm is presently known, including the computational versions of Sperner's lemma, Brouwer's fixpoint theorem, Chfvalley's theorem, and the BorsukUlam theorem, the linear complementarity problem for Pmatrices, finding a mixed equilibrium in a nonzero sum game, finding a second Hamilton circuit in a Hamiltonian cubic graph, a second Hamiltonian decomposition in a quartic graph, and others. Some of these problems are shown to be complete. © 1994 Academic Press, Inc. 1.
The Complexity of Pure Nash Equilibria
, 2004
"... We investigate from the computational viewpoint multiplayer games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLScomplete in general. ..."
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Cited by 140 (6 self)
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We investigate from the computational viewpoint multiplayer games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLScomplete in general. We discuss implications to nonatomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.
PseudoBoolean Optimization
 DISCRETE APPLIED MATHEMATICS
, 2001
"... This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of ..."
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Cited by 107 (4 self)
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This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of quadratic pseudoBoolean optimization (to which every pseudoBoolean optimization can be reduced), several other important special classes, and approximation algorithms.