Parameterized Complexity of Edge Interdiction Problems

We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who compete on an objective with opposing interests. In edge interdiction problems, every edge of the input graph has an interdiction cost associated with it and the interdictor interdicts the graph by modifying the edges in the graph, and the number of such modifications is constrained by the interdictor's budget. The evader then solves the given optimization problem on the modified graph. The action of the interdictor must impede the evader as much as possible. We focus on edge interdiction problems related to minimum spanning tree, maximum matching and shortest paths. These problems arise in different real world scenarios. We derive several fixed-parameter tractability and W[1]-hardness results for these interdiction problems with respect to various parameters. Next, we show close relation between interdiction problems and partial cover problems on bipartite graphs where the goal is not to cover all elements but to minimize/maximize the number of covered elements with specific number of sets. Hereby, we investigate the parameterized complexity of several partial cover problems on bipartite graphs

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context

Algorithm design techniques for parameterized graph modification problems

Diese Arbeit beschaeftigt sich mit dem Entwurf parametrisierter Algorithmen fuer Graphmodifikationsprobleme wie Feedback Vertex Set, Multicut in Trees, Cluster Editing und Closest 3-Leaf Powers. Anbei wird die Anwendbarkeit von vier Technicken zur Entwicklung parametrisierter Algorithmen, naemlich, Datenreduktion, Suchbaum, Iterative Kompression und Dynamische Programmierung, fuer solche Graphmodifikationsprobleme untersucht

GEDEVO: An Evolutionary Graph Edit Distance Algorithm for Biological Network Alignment

Introduction: With the so-called OMICS technology the scientific community has generated huge amounts of data that allow us to reconstruct the interplay of all kinds of biological entities. The emerging interaction networks are usually modeled as graphs with thousands of nodes and tens of thousands of edges between them. In addition to sequence alignment, the comparison of biological networks has proven great potential to infer the biological function of proteins and genes. However, the corresponding network alignment problem is computationally hard and theoretically intractable for real world instances. Results: We therefore developed GEDEVO, a novel tool for efficient graph comparison dedicated to real-world size biological networks. Underlying our approach is the so-called Graph Edit Distance (GED) model, where one graph is to be transferred into another one, with a minimal number of (or more general: minimal costs for) edge insertions and deletions. We present a novel evolutionary algorithm aiming to minimize the GED, and we compare our implementation against state of the art tools: SPINAL, GHOST, CGRAAL, and MIGRAAL. On a set of protein-protein interaction networks from different organisms we demonstrate that GEDEVO outperforms the current methods. It thus refines the previously suggested alignments based on topological information only. Conclusion: With GEDEVO, we account for the constantly exploding number and size of available biological networks. The software as well as all used data sets are publicly available at http://gedevo.mpi-inf.mpg.de