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Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
Finding Common Structured Patterns in Linear Graphs
, 2009
"... A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a nonempty subset R ⊆ {<, ⊏, ≬}, we are interested in the Maximum Common Structured ..."
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A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a nonempty subset R ⊆ {<, ⊏, ≬}, we are interested in the Maximum Common Structured Pattern (MCSP) problem: find a maximum size edgedisjoint graph, with edgepairs all comparable by one of the relations in R, that occurs as a subgraph in each of the linear graphs of the family. The MCSP problem generalizes many structurecomparison and structureprediction problems that arise in computational molecular biology. We give tight hardness results for the MCSP problem for {<, ≬}structured patterns and {⊏, ≬}structured patterns. Furthermore, we prove that the problem is approximable within ratios: (i) 2H (k) for {<, ≬}structured patterns, (ii) k1/2 for {⊏, ≬}structured patterns, and (iii) O ( √ k log k) for {<, ⊏, ≬}structured patterns, where k is the size of the optimal solution and H (k) = ∑k i=1