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 NP-complete decision problems: Colored unit interval graph completion, the maximum interval (or unit interval) subgraph, the pathwidth of a bipartite graph, and the k-consecutive 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.

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 k-coloring 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 NP-hard, 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.

Abstract not found

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 NP-Hard 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...

When searching for prey, many predator species exhibit a remarkable behavior: after prey capture, the predators promptly engage in `area-restricted 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 area-restricted 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 `big-valley' hypothesis and...

Abstract. This work describes a new way of employing problem-specific 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

Summary. 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.

In the syntactic theory of Tesni`ere (1959) the structural description of sentences are given as graphs. We discuss how the graph-theoretic concept of path-width is relevant in this approach. In particular, we point out the importance of graphs with path-width 6 in connection with natural language processing, and give a short proof of the characterization theorem of trees with path-width 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...

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 self-reduction 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 three-track 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...

This paper describes an application of a Constructive Genetic Algorithm (CGA) to the Minimization Open Stack Problem (MOSP). The MOSP happens in a production system scenario, and consists of determining a sequence of cut patterns that minimizes the maximum number of opened stacks during the cutting process. The CGA has a number of new features compared to a traditional genetic algorithm, as a population of dynamic size composed of schemat a and structures that is trained with respect to some problem specific heuristic. The application of CGA to MOSP uses a 2-Opt like heuristic to define the fitness functions and the mutation operator. Computational tests are presented using available instances taken from the literature.