Publications (58) View all
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Article: Fixed-Parameter Algorithms for Cluster Vertex Deletion
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ABSTRACT: We initiate the first systematic study of the NP-hard Cluster Vertex Deletion (CVD) problem (unweighted and weighted) in terms of fixed-parameter algorithmics. In the unweighted case, one searches for a minimum number of vertex deletions to transform a graph into a collection of disjoint cliques. The parameter is the number of vertex deletions. We present efficient fixed-parameter algorithms for CVD applying the fairly new iterative compression technique. Moreover, we study the variant of CVD where the maximum number of cliques to be generated is prespecified. Here, we exploit connections to fixed-parameter algorithms for (weighted) Vertex Cover. KeywordsParameterized complexity-Iterative compression-NP-hard problems-Graph algorithms-ClusteringTheory of Computing Systems 04/2012; 47(1):196-217. · 0.44 Impact Factor -
Conference Proceeding: Confluence in Data Reduction: Bridging Graph Transformation and Kernelization
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ABSTRACT: Kernelization is a core tool of parameterized algorithmics for coping with computationally intractable problems. A emphkernelization reduces in polynomial time an input instance to an equivalent instance whose size is bounded by a function only depending on some problem-specific parameter~$k$; this new instance is called problem kernel. Typically, problem kernels are achieved by performing efficient data reduction rules. So far, there was little study in the literature concerning the mutual interaction of data reduction rules, in particular whether data reduction rules for a specific problem always lead to the same reduced instance, no matter in which order the rules are applied. This corresponds to the concept of confluence from the theory of rewriting systems. We argue that it is valuable to study whether a kernelization is confluent, using the NP-hard graph problems textsc(Edge) Clique Cover and textscPartial Clique Cover as running examples. We apply the concept of critical pair analysis from graph transformation theory, supported by the AGG software tool. These results support the main goal of our work, namely, to establish a fruitful link between (parameterized) algorithmics and graph transformation theory, two so far unrelated fields.Proc. of Int. Conf. on Computability in Europe (CiE'12); 01/2012 -
Article: Exploiting bounded signal flow for graph orientation based on cause-effect pairs.
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ABSTRACT: ABSTRACT: We consider the following problem: Given an undirected network and a set of sender-receiver pairs, direct all edges such that the maximum number of "signal flows" defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases. We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances. Several biologically relevant special cases of the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies.Algorithms for Molecular Biology 08/2011; 6:21. · 1.35 Impact Factor -
Conference Proceeding: Exploiting Bounded Signal Flow for Graph Orientation Based on Cause-Effect Pairs.
Theory and Practice of Algorithms in (Computer) Systems - First International ICST Conference, TAPAS 2011, Rome, Italy, April 18-20, 2011. Proceedings; 01/2011 -
Article: Balanced Interval Coloring
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ABSTRACT: We consider the discrepancy problem of coloring $n$ intervals with $k$ colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal. Somewhat surprisingly, a coloring with maximal difference at most one always exists. Furthermore, we give an algorithm with running time $O(n \log n + kn \log k)$ for its construction. This is in particular interesting because many known results for discrepancy problems are non-constructive. This problem naturally models a load balancing scenario, where $n$ tasks with given start- and endtimes have to be distributed among $k$ servers. Our results imply that this can be done ideally balanced. When generalizing to $d$-dimensional boxes (instead of intervals), a solution with difference at most one is not always possible. We show that for any $d \ge 2$ and any $k \ge 2$ it is NP-complete to decide if such a solution exists, which implies also NP-hardness of the respective minimization problem. In an online scenario, where intervals arrive over time and the color has to be decided upon arrival, the maximal difference in the size of color classes can become arbitrarily high for any online algorithm. Comment: Accepted at STACS 201112/2010;
