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11
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 55 (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.
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 29 (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.
Linear Gate Assignment: a Fast Statistical Mechanics Approach
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGNED OF INTEGRATED CIRCUITS AND SYSTEMS
, 1999
"... This paper deals with the problem of linear gate assignment in two layout styles: onedimensional logic array, and gate matrix layout. The goal is to find the optimal sequencing of gates in order to minimize the required number of tracks, and thus to reduce the overall circuit layout area. This is kn ..."
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Cited by 6 (1 self)
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This paper deals with the problem of linear gate assignment in two layout styles: onedimensional logic array, and gate matrix layout. The goal is to find the optimal sequencing of gates in order to minimize the required number of tracks, and thus to reduce the overall circuit layout area. This is known to be an NPHard optimization problem, for whose solution no absolute approximation algorithm exists. Here we report the use of a new optimization heuristic derived from statistical mechanics  the microcanonical optimization algorithm, µO  to solve the linear gate assignment problem. Our numerical results show that µO compares favorably with at least five previously employed heuristics: simulated annealing, the unidirectional and the bidirectional Hong construction methods, and the artificial intelligence heuristics GM_Plan and GM_Learn. Moreover, in a massive set of experiments with circuits whose optimal layout is not known, our algorithm has been able to match and even to improve, b...
Industrial Pattern Sequencing Problems: some complexity results and new local search models
, 2001
"... In this thesis we explore some industrial pattern sequencing problems arising in settings as distinct as the scheduling of flexible machines, the design of VLSI circuits, and the sequencing of cutting patterns. This latter setting presents us the minimization of open stacks problem, which is the mai ..."
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Cited by 5 (0 self)
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In this thesis we explore some industrial pattern sequencing problems arising in settings as distinct as the scheduling of flexible machines, the design of VLSI circuits, and the sequencing of cutting patterns. This latter setting presents us the minimization of open stacks problem, which is the main focus of our study. Some complexity results are presented for these sequencing problems, establishing a surprising connection between previously unrelated fields. New local search methods are also presented to deal with these problems, and their effectiveness is evaluated by comparisons with results previously obtained in the literature. The first method is derived from the simulated annealing algorithm, bringing new ideas from statistical physics. The second method advances these ideas, by proposing a collective search model based on two themes: (i) to explore the search space while simultaneously exhibiting search intensity and search diversity, and (ii) to explore the search space in proportion to the perceived quality of each region. Some preliminaries, given by coordination policies (to guide the search processes) and distance metrics, are introduced to support the model.
Hybrid evolutionary algorithms and clustering search
 IN: CRINA GROSAN,AJITH ABRAHAM AND HISAO ISHIBUCHI (EDS) HYBRID EVOLUTIONARY SYSTEMS  STUDIES IN COMPUTATIONAL INTELLIGENCE  SPRINGER SCI SERIES. 75 (2007) 81–102
"... A challenge in hybrid evolutionary algorithms is to employ efficient strategies to cover all the search space, applying local search only in actually promising search areas. The inspiration in nature has been pursued to design flexible, coherent and efficient computational models. In this chapter, ..."
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Cited by 5 (1 self)
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A challenge in hybrid evolutionary algorithms is to employ efficient strategies to cover all the search space, applying local search only in actually promising search areas. The inspiration in nature has been pursued to design flexible, coherent and efficient computational models. In this chapter, the Clustering Search (*CS) is proposed as a generic way of combining search metaheuristics with clustering to detect promising search areas before applying local search procedures. The clustering process aims to gather similar information about the search space into groups, maintaining a representative solution associated to this information. Two applications are examined for combinatorial and continuous optimization problems, presenting how to develop hybrid evolutionary algorithms based on *CS.
Synthesizing a Predatory Search Strategy for VLSI Layouts
 IEEE Transactions on Evolutionary Computation
, 1998
"... When searching for prey, many predator species exhibit a remarkable behavior: after prey capture, the predators promptly engage in `arearestricted search', probing for consecutive captures nearby. Biologists have been surprised with the efficiency and adaptability of this search strategy to a great ..."
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Cited by 4 (0 self)
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When searching for prey, many predator species exhibit a remarkable behavior: after prey capture, the predators promptly engage in `arearestricted search', probing for consecutive captures nearby. Biologists have been surprised with the efficiency and adaptability of this search strategy to a great number of habitats and prey distributions. We propose to synthesize a similar search strategy for the massively multimodal problems of combinatorial optimization. The predatory search strategy restricts the search to a small area after each new improving solution is found. Subsequent improvements are often found during arearestricted search. Results of this approach to Gate Matrix Layout, an important problem arising in VLSI architectures, are presented. Compared to established methods over a set of benchmark circuits, predatory search is able to either match or outperform the best known layouts. Additional remarks address the relation of predatory search to the `bigvalley' hypothesis and...
Population training heuristics
 Lecture Notes in Computer Science
, 2005
"... Abstract. This work describes a new way of employing problemspecific heuristics to improve evolutionary algorithms: the Population Training Heuristic (PTH). The PTH employs heuristics in fitness definition, guiding the population to settle down in search areas where the individuals can not be impro ..."
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Cited by 4 (0 self)
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Abstract. This work describes a new way of employing problemspecific heuristics to improve evolutionary algorithms: the Population Training Heuristic (PTH). The PTH employs heuristics in fitness definition, guiding the population to settle down in search areas where the individuals can not be improved by such heuristics. Some new theoretical improvements not present in early algorithms are now introduced. An application for pattern sequencing problems is examined with new improved computational results. The method is also compared against other approaches, using benchmark instances taken from the literature. Keywords: Hybrid evolutionary algorithms; population training; MOSP; GMLP. 1
Narrowness, Pathwidth, and their Application in Natural Language Processing
, 1992
"... In the syntactic theory of Tesni`ere (1959) the structural description of sentences are given as graphs. We discuss how the graphtheoretic concept of pathwidth is relevant in this approach. In particular, we point out the importance of graphs with pathwidth 6 in connection with natural language ..."
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Cited by 3 (0 self)
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In the syntactic theory of Tesni`ere (1959) the structural description of sentences are given as graphs. We discuss how the graphtheoretic concept of pathwidth is relevant in this approach. In particular, we point out the importance of graphs with pathwidth 6 in connection with natural language processing, and give a short proof of the characterization theorem of trees with pathwidth k. 1 The linguistic background Following the pioneering work of Tesni`ere [Te], the field of dependency grammar evolved at a steady pace. For results and references, see [Ma] and [Me]. In the present note we concentrate on one particular dependency model, put forth by K'alm'an and Kornai [KK], although our observations are applicable for a wider range of dependency formalisms where the syntactic description of a sentence is given as an ordered graph (with vertices corresponding to words and arcs corresponding to dependencies). In this model a grammatical derivation starts with a dependency graph wh...
Constructive Algorithms Based on Graph Minors
, 1997
"... We consider the development of practical algorithms based on the theory of graph minors. Although an exact decision algorithm using this approach would generally require testing to ensure the absence of a prohibitively large number of obstructions, approximate algorithms can be designed that test fo ..."
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We consider the development of practical algorithms based on the theory of graph minors. Although an exact decision algorithm using this approach would generally require testing to ensure the absence of a prohibitively large number of obstructions, approximate algorithms can be designed that test for only a few obstructions. Efficient selfreduction strategies can then be incorporated to approximate a solution to the problem at hand. In this paper, we investigate a prototypical problem, that of finding a threetrack gate matrix layout for VLSI circuits. We design a streamlined test for a half dozen of the densest obstructions, thereby approximating an exact algorithm that would require over one hundred such tests, many of which appear very difficult. In this effort, we have also built a software package to automate the use of our tools. Experimental results obtained using this package demonstrate that it is extremely fast and suggest that, despite its theoretical limitations, its resul...