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Branch and Bound Algorithm Selection by Performance Prediction
 In AAAI
, 1998
"... We propose a method called Selection by Performance Prediction (SPP) which allows one, when faced with a particular problem instance, to select a Branch and Bound algorithm from among several promising ones. This method is based on Knuth's sampling method which estimates the efficiency of a bac ..."
Abstract

Cited by 27 (1 self)
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We propose a method called Selection by Performance Prediction (SPP) which allows one, when faced with a particular problem instance, to select a Branch and Bound algorithm from among several promising ones. This method is based on Knuth's sampling method which estimates the efficiency of a backtrack program on a particular instance by iteratively generating random paths in the search tree. We present a simple adaptation of this estimator in the field of combinatorial optimization problems, more precisely for an extension of the maximal constraint satisfaction framework. Experiments both on random and strongly structured instances show that, in most cases, the proposed method is able to select, from a candidate list, the best algorithm for solving a given instance. Introduction The Branch and Bound search is a wellknown algorithmic schema, widely used for solving combinatorial optimization problems. A lot of specific algorithms can be derived from this general schema. ...
Local search for statistical counting
 In Proceedings of the Fifteenth National Conference on Arti Intelligence
, 1998
"... In this paper, statistical counting is introduced in the context of stochastic local search. From a sample of trajectories by independent local search computations, it is shown that interesting statistical information can be actually extracted about the search space, most notably an unbiased estimat ..."
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Cited by 2 (0 self)
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In this paper, statistical counting is introduced in the context of stochastic local search. From a sample of trajectories by independent local search computations, it is shown that interesting statistical information can be actually extracted about the search space, most notably an unbiased estimate of the number of solutions. Computational results for random #SAT instances are provided.
c ○ 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. Phase Transitions in Relational Learning
"... Abstract. One of the major limitations of relational learning is due to the complexity of verifying hypotheses on examples. In this paper we investigate this task in light of recent published results, which show that many hard problems exhibit a narrow “phase transition ” with respect to some order ..."
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Abstract. One of the major limitations of relational learning is due to the complexity of verifying hypotheses on examples. In this paper we investigate this task in light of recent published results, which show that many hard problems exhibit a narrow “phase transition ” with respect to some order parameter, coupled with a large increase in computational complexity. First we show that matching a class of artificially generated Horn clauses on ground instances presents a typical phase transition in solvability with respect to both the number of literals in the clause and the number of constants occurring in the instance to match. Then, we demonstrate that phase transitions also appear in realworld learning problems, and that learners tend to generate inductive hypotheses lying exactly on the phase transition. On the other hand, an extensive experimenting revealed that not every matching problem inside the phase transition region is intractable. However, unfortunately, identifying those that are feasible cannot be done solely on the basis of the order parameters. To face this problem, we propose a method, based on a Monte Carlo algorithm, to estimate online the likelihood that the current matching problem will exceed a given amount of computational resources. The impact of the above findings on relational learning is discussed. Keywords: complexity, phase transitions, relational learning, matching problem