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Combinatorial Optimization on Graphs of Bounded Treewidth

Bodlaender, H. L., Koster, A. M. C. A. — 2008-04-29

There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixed-parameter tractable algorithms. Starting from trees and series-parallel graphs, we introduce the concepts of treewidth and tree decompositions, and illustrate the technique with the Weighted Independent Set problem as an example. The paper surveys some of the latest developments, putting an emphasis on applicability, on algorithms that exploit tree decompositions, and on algorithms that determine or approximate treewidth and find tree decompositions with optimal or close to optimal treewidth. Directions for further research and suggestions for further reading are also given.

Parameterized Complexity and Biopolymer Sequence Comparison

Cai, L., Huang, X., Liu, C., Rosamond, F., Song, Y. — 2008-04-29

The paper surveys parameterized algorithms and complexities for computational tasks on biopolymer sequences, including the problems of longest common subsequence, shortest common supersequence, pairwise sequence alignment, multiple sequencing alignment, structure–sequence alignment and structure–structure alignment. Algorithm techniques, built on the structural-unit level as well as on the residue level, are discussed.

The Bidimensionality Theory and Its Algorithmic Applications

Demaine, E. D., Hajiaghayi, M. — 2008-04-29

This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixed-parameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the Graph Minor Theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. Here, we summarize the known combinatorial and algorithmic results of bidimensionality theory with the high-level ideas involved in their proof; we describe the previous work on which the theory is based and/or extends; and we mention several remaining open problems.

Fixed-Parameter Algorithms For Artificial Intelligence, Constraint Satisfaction and Database Problems

Gottlob, G., Szeider, S. — 2008-04-29

We survey the parameterized complexity of problems that arise in artificial intelligence, database theory and automated reasoning. In particular, we consider various parameterizations of the constraint satisfaction problem, the evaluation problem of Boolean conjunctive database queries and the propositional satisfiability problem. Furthermore, we survey parameterized algorithms for problems arising in the context of the stable model semantics of logic programs, for a number of other problems of non-monotonic reasoning, and for the computation of cores in data exchange.

Width Parameters Beyond Tree-width and their Applications

Hlineny, P., Oum, S.-i., Seese, D., Gottlob, G. — 2008-04-29

Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width’ parameters in combinatorial structures delivers—besides traditional tree-width and derived dynamic programming schemes—also a number of other useful parameters like branch-width, rank-width (clique-width) or hypertree-width. In this contribution, we demonstrate how ‘width’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.

Some Parameterized Problems On Digraphs

Gutin, G., Yeo, A. — 2008-04-29

We survey results and open questions on complexity of parameterized problems on digraphs. The problems include the feedback vertex and arc set problems, induced subdigraph problems and directed k-leaf problems. We also prove some new results on the topic. Most of these new results are on parameterizations of the backward paired comparison problem.

Parameterized Complexity of Geometric Problems

Giannopoulos, P., Knauer, C., Whitesides, S. — 2008-04-29

This paper surveys parameterized complexity results for hard geometric algorithmic problems. It includes fixed-parameter tractable problems in graph drawing, geometric graphs, geometric covering and several other areas, together with an overview of the algorithmic techniques used. Fixed-parameter intractability results are surveyed as well. Finally, we give some directions for future research.

Parameterized Complexity in Cognitive Modeling: Foundations, Applications and Opportunities

van Rooij, I., Wareham, T. — 2008-04-29

In cognitive science, natural cognitive processes are generally conceptualized as computational processes: they serve to transform sensory and mental inputs into mental and action outputs. At the highest level of abstraction, computational models of cognitive processes aim at specifying the computational problem computed by the process under study. Because computational problems are realistic cognitive models only insofar as they can plausibly be computed by the human brain given its limited resources for computation, computational tractability provides a useful constraint on cognitive models. In this paper, we consider the particular benefits of the parameterized complexity framework for identifying sources of intractability in cognitive models. We review existing applications of the parameterized framework to this end in the domains of perception, action and higher cognition. We further identify important opportunities and challenges for future research. These include the development of new methods for complexity analyses specifically tailored to the reverse engineering perspective underlying cognitive science.