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Bayesian Optimization Algorithm: From Single Level to Hierarchy
, 2002
"... There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decompositi ..."
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Cited by 90 (18 self)
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There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decomposition as opposed to decomposition on only a single level. Third, design a class of difficult hierarchical problems that can be used to test the algorithms that attempt to exploit hierarchical decomposition. Fourth, test the developed algorithms on the designed class of problems and several realworld applications. The dissertation proposes the Bayesian optimization algorithm (BOA), which uses Bayesian networks to model the promising solutions found so far and sample new candidate solutions. BOA is theoretically and empirically shown to be capable of both learning a proper decomposition of the problem and exploiting the learned decomposition to ensure robust and scalable search for the optimum across a wide range of problems. The dissertation then identifies important features that must be incorporated into the basic BOA to solve problems that are not decomposable on a single level, but that can still be solved by decomposition over multiple levels of difficulty. Hierarchical
Visibilitybased pursuitevasion with limited field of view
 International Journal of Robotics Research
, 2004
"... We study a form of the pursuitevasion problem, in which one or more searchers must move through a given environment so as to guarantee detection of any and all evaders, which can move arbitrarily fast. Our goal is to develop techniques for coordinating teams of robots to execute this task in ap ..."
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Cited by 69 (2 self)
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We study a form of the pursuitevasion problem, in which one or more searchers must move through a given environment so as to guarantee detection of any and all evaders, which can move arbitrarily fast. Our goal is to develop techniques for coordinating teams of robots to execute this task in application domains such as clearing a building, for reasons of security or safety. To this end, we introduce a new class of searcher, the #searcher, which can be readily instantiated as a physical mobile robot. We present a detailed analysis of the pursuitevasion problem using #searchers. We show that computing the minimum number of #searchers required to search a given environment is NPhard, and present the first complete search algorithm for a single #searcher. We show how this algorithm can be extended to handle multiple searchers, and give examples of computed trajectories.
Four Strikes against Physical Mapping of DNA
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 1993
"... Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NPcomplete ..."
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Cited by 59 (8 self)
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Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NPcomplete decision problems: Colored unit interval graph completion, the maximum interval (or unit interval) subgraph, the pathwidth of a bipartite graph, and the kconsecutive ones problem for k >= 2. These models have been chosen to reflect various features typical in biological data, including false negative and positive errors, small width of the map and chimericism.
Dynamic Programming On Graphs With Bounded Treewidth
, 1987
"... In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth _< k, (or equivalently, the class of partial ktrees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses CLCC, and CECC. We show that ea ..."
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Cited by 55 (1 self)
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In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth _< k, (or equivalently, the class of partial ktrees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses CLCC, and CECC. We show that each problem in LCC (or CLCC) is solvable in polynomial (O(nc)) time, when restricted to graphs with fixed up perbounds on the treewidth and degree; and that each problem in ECC (or CECC) is solvable in polynomial (O(nc)) time, when re stricted to graphs with a fixed upperbound on the treewidth (with given corresponding treedecomposition). Also, problems in CLCC and CECC are solvable in polynomial time for graphs with a logarithmic treewidth, and given corresponding treedecomposition, and in the case of CLCCproblems, a fixed upperbound on the degree of the graph. Also, we show
Hierarchical BOA Solves Ising Spin Glasses and MAXSAT
 In Proc. of the Genetic and Evolutionary Computation Conference (GECCO 2003), number 2724 in LNCS
, 2003
"... Theoretical and empirical evidence exists that the hierarchical Bayesian optimization algorithm (hBOA) can solve challenging hierarchical problems and anything easier. This paper applies hBOA to two important classes of realworld problems: Ising spinglass systems and maximum satis ability (MAX ..."
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Cited by 47 (18 self)
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Theoretical and empirical evidence exists that the hierarchical Bayesian optimization algorithm (hBOA) can solve challenging hierarchical problems and anything easier. This paper applies hBOA to two important classes of realworld problems: Ising spinglass systems and maximum satis ability (MAXSAT). The paper shows how easy it is to apply hBOA to realworld optimization problems. The results indicate that hBOA is capable of solving enormously dicult problems that cannot be solved by other optimizers and still provide competitive or better performance than problemspeci c approaches on other problems. The results thus con rm that hBOA is a practical, robust, and scalable technique for solving challenging realworld problems.
Pathwidth, Bandwidth and Completion Problems to Proper Interval Graphs with Small Cliques
 SIAM Journal on Computing
, 1996
"... We study two related problems motivated by molecular biology: ffl Given a graph G and a constant k, does there exist a supergraph G of G which is a unit interval graph and has clique size at most k? ffl Given a graph G and a proper kcoloring c of G, does there exist a supergraph We show th ..."
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Cited by 30 (6 self)
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We study two related problems motivated by molecular biology: ffl Given a graph G and a constant k, does there exist a supergraph G of G which is a unit interval graph and has clique size at most k? ffl Given a graph G and a proper kcoloring c of G, does there exist a supergraph We show that those problems are polynomial for fixed k. On the other hand we prove that the first problem is equivalent to deciding if the bandwidth of G is at most k \Gamma 1. Hence, it is NPhard, and W [t]hard for all t. We also show that the second problem is W [1]hard. This implies that for fixed k, both of the problems are unlikely to have an O(n ) algorithm, where ff is a constant independent of k.
Computing Optimal Linear Layouts of Trees in Linear Time
 Proc. ESA 2000, number 1879
, 1999
"... We present a linear time algorithm which, given a tree, computes a linear layout optimal with respect to vertex separation. As a consequence optimal edge search strategies, optimal node search strategies, and optimal interval augmentations can be computed also in O(n) for trees. This improves the ru ..."
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Cited by 14 (0 self)
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We present a linear time algorithm which, given a tree, computes a linear layout optimal with respect to vertex separation. As a consequence optimal edge search strategies, optimal node search strategies, and optimal interval augmentations can be computed also in O(n) for trees. This improves the running time of former algorithms from O(n log n) to O(n) and answers two related open questions raised in [7] and [15].
DECONTAMINATING CHORDAL RINGS AND TORI USING MOBILE AGENTS
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
"... In this paper we consider a network where an intruder is moving “contaminating ” the nodes it passes by, and we focus on the problem of decontaminating such a network by a team of mobile agents. The contamination/decontamination process has the following asynchronous dynamics: when the team is depl ..."
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Cited by 10 (5 self)
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In this paper we consider a network where an intruder is moving “contaminating ” the nodes it passes by, and we focus on the problem of decontaminating such a network by a team of mobile agents. The contamination/decontamination process has the following asynchronous dynamics: when the team is deployed all nodes are assumed to be contaminated, when an agent transits on a node, it will clean the node, when the node is left with no agent, the node will be recontaminated as soon as at least one of its neighbours is contaminated. We study the problem in asynchronous chordal ring networks and in tori. We consider two variations of the model: one where agents have only local knowledge, the other in which they have “visibility”, i.e., they can “see ” the state of their neighbouring nodes. We first derive lower bounds on the minimum number of agents necessary for the decontamination. In the case of chordal rings we show that the number of agents necessary to perform the cleaning does not depend on the size of the network; in fact it is linear in the length of the longest chord (provided that it is not too long). In the case of a torus, the minimum number of agents is equal to 2 · h, where h is the smallest dimension. We then propose optimal strategies for decontamination and we analyse the number of moves and the time complexity of the decontamination algorithms, showing that the visibility assumption allows us to decrease substantially both complexity measures. Another advantage of the “visibility model ” is that agents move independently and autonomously without requiring any coordination.
A Constructive Linear Time Algorithm for Small Cutwidth
 PROC. 11TH INTERNATINAL CONFERENCE ISAAC 2000, NUMBER 1969
, 2000
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