A popular model for protecting privacy when person-specific data is released is k -anonymity. A dataset is k-anonymous if each record is identical to at least (k-1) other records in the dataset. The basic k-anonymizat...
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A popular model for protecting privacy when person-specific data is released is k -anonymity. A dataset is k-anonymous if each record is identical to at least (k-1) other records in the dataset. The basic k-anonymization problem, which minimizes the number of dataset entries that must be suppressed to achieve k-anonymity, is NP-hard and hence not solvable both quickly and optimally in general. We apply parameterized complexity analysis to explore algorithmic options for restricted versions of this problem that occur in practice. We present the first fixed-parameter algorithms for this problem and identify key techniques that can be applied to this and other k-anonymization problems.
In an undirected graph G = (V, E), a set of k vertices is called c-isolated if it has less than c . k outgoing edges. Ito and Iwama [H. Ito, K. Iwama, Enumeration of isolated cliques and pseudo-cliques, ACM Transactio...
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In an undirected graph G = (V, E), a set of k vertices is called c-isolated if it has less than c . k outgoing edges. Ito and Iwama [H. Ito, K. Iwama, Enumeration of isolated cliques and pseudo-cliques, ACM Transactions on Algorithms (2008) (in press)] gave an algorithm to enumerate all c-isolated maximal cliques in O(4(c) . c(4). vertical bar E vertical bar) time. We extend this to enumerating all maximal c-isolated cliques (which are a superset) and improve the running time bound to O(2.89(c). c(2) . vertical bar E vertical bar), using modifications which also facilitate parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to s-plexes (a relaxation of the clique notion), providing a W[1]-hardness result when the size of the s-plex is the parameter and a fixed-parameter algorithm for enumerating isolated s-plexes when the parameter describes the degree of isolation. (C) 2009 Elsevier B.V. All rights reserved.
We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas (QBF). This allows us to obtain hierarchies of tractable classes of quantified Boolean formulas with the classes of ...
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We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas (QBF). This allows us to obtain hierarchies of tractable classes of quantified Boolean formulas with the classes of quantified Horn and quantified 2CNF formulas, respectively, at their first level, thus gradually generalizing these two important tractable classes. In contrast to known tractable classes based on bounded treewidth, the number of quantifier alternations of our classes is unbounded. As a side product of our considerations we develop a theory of variable dependency which is of independent interest.
The multiple knapsack problem (MKP) is a well-known generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins ( knapsacks) such that each item a is an element of A has a siz...
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The multiple knapsack problem (MKP) is a well-known generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins ( knapsacks) such that each item a is an element of A has a size size( a) and a profit value profit( a), and each bin b is an element of B has a capacity c( b). The goal is to find a subset U subset of A of maximum total profit such that U can be packed into B without exceeding the capacities. The decision version of MKP is strongly NP-complete, since it is a generalization of the classical knapsack and bin packing problem. Furthermore, MKP does not admit a fully time polynomial time approximation scheme (FPTAS) even if the number m of bins is two. Kellerer gave a polynomial time approximation scheme (PTAS) for MKP with identical capacities and Chekuri and Khanna presented a PTAS for MKP with general capacities with running time n(O)(log(1/epsilon)/epsilon(8)). In this paper we propose an efficient PTAS (EPTAS) with parameterized running time 2(O)(log(1/epsilon)/epsilon(5)) . poly(n) + O(m) for MKP. This also solves an open question by Chekuri and Khanna.
In the context of comparative analysis of protein-protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex G in the protein-protein interaction graph H of anothe...
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In the context of comparative analysis of protein-protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex G in the protein-protein interaction graph H of another species with respect to (w. r. t.) orthologous proteins. Two problems are considered: the Exact-(mu(G), mu(H))-Matching problem and the Max-(mu(G), mu(H))-Matching problems, where mu(G) (resp. mu(H)) denotes in both problems the maximum number of orthologous proteins in H (resp. G) of a protein in G (resp. H). Following [I. Fagnot, G. Lelandais, S. Vialette, Bounded list injective homomorphism for comparative analysis of protein-protein interaction graphs, Journal of Discrete Algorithms 6 (2) (2008) 178-191], the Exact-(mu(G), mu(H))-Matching problem asks for an injective homomorphism of G to H w. r. t. orthologous proteins. The optimization version is called the Max-(mu(G), mu(H))-Matching problem and is concerned with finding an injective mapping of a graph G to a graph H w. r. t. orthologous proteins that matches as many edges of G as possible. For both problems, we essentially focus on bounded degree graphs and extremal small values of parameters mu(G) and mu(H). (C) 2008 Elsevier B.V. All rights reserved.
In this paper we propose an O(1.0892(n))algorithm solving the Maximum Independent Set problem for graphs with maximum degree 3 improving the previously best upper bound of O(1.0977(n)). A useful secondary effect of th...
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In this paper we propose an O(1.0892(n))algorithm solving the Maximum Independent Set problem for graphs with maximum degree 3 improving the previously best upper bound of O(1.0977(n)). A useful secondary effect of the proposed algorithm is that being applied to 2k kernel, it improves the upper bound on the parameterized complexity of the Vertex Cover problem for graphs with maximum degree 3 (VC-3). In particular, the new upper bound for the VC-3 problem is O(1.1864(k) + n), improving the previously best upper bound of O(k(2) * 1.194(k) + n). The presented results have a methodological interest because, to the best of our knowledge, this is the first time when a new parameterized upper bound is obtained through design and analysis of an exact exponential algorithm. (C) 2008 Elsevier B.V. All rights reserved.
Many real-world problems are NP-hard;to solve them, usually heuristics are used. parameterized complexity is a recent approach that tries to exploit structures of real-world problem instances. The aim of the work was ...
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Many real-world problems are NP-hard;to solve them, usually heuristics are used. parameterized complexity is a recent approach that tries to exploit structures of real-world problem instances. The aim of the work was to establish that parameterized complexity, and in particular novel algorithmic techniques whose development was driven by this concept, can actually lead to practically useful programs for exactly solving real-world problem instances. We show this here using the example of Clique Cover und Minimum-Weight Path, which have applications in computational biology and other areas.
We prove a parameterized analog of Schaefer's Dichotomy Theorem: we show that for every finite boolean constraint family F, deciding whether a formula containing constraints from F has a satisfying assignment of w...
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We prove a parameterized analog of Schaefer's Dichotomy Theorem: we show that for every finite boolean constraint family F, deciding whether a formula containing constraints from F has a satisfying assignment of weight exactly k is either fixed-parameter tractable (FPT) or W[1]-complete. We give a simple characterization of those constraints that make the problem fixed-parameter tractable. The special cases when the formula is restricted to be bounded occurrence, bounded treewidth, or planar are also considered: it turns out that in these cases the problem is in FPT for every constraint family F.
We present efficient algorithms to solve the Line Cover Problem exactly. In this NP-complete problem, the inputs are n points in the plane and a positive integer k, and we are asked to answer if we can cover these n p...
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We present efficient algorithms to solve the Line Cover Problem exactly. In this NP-complete problem, the inputs are n points in the plane and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines. Our approach is based on fixed-parameter tractability and, in particular, kernelization. We propose several reduction rules to transform instances of Line Cover into equivalent smaller instances. Once instances are no longer susceptible to these reduction rules, we obtain a problem kernel whose size is bounded by a polynomial function of the parameter k and does not depend on the size n of the input. Our algorithms provide exact solutions and are easy to implement. We also describe the design of algorithms to solve the corresponding optimization problem exactly. We experimentally evaluated ten variants of the algorithms to determine the impact and trade-offs of several reduction rules. We show that our approach provides tractability for a larger range of values of the parameter and larger inputs, improving the execution time by several orders of magnitude with respect to earlier algorithms that use less rules.
We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered wit...
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ISBN:
(纸本)9783540770497
We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques;the biclique partition problem is defined similarly with the additional condition that the bicliques are required to be mutually edge-disjoint. The biclique vertex-cover problem asks whether the vertex-set of the given graph can be covered with at most k bicliques, the biclique vertex-partition problem is defined similarly with the additional condition that the bicliques are required to be mutually vertex-disjoint. All these four problems are known to be NP-complete even if the given graph is bipartite. In this paper, we investigate them in the framework of parameterized complexity: do the problems become easier if k is assumed to be small? We show that, considering k as the parameter, the first two problems are fixed-parameter tractable, while the latter two problems are not fixed-parameter tractable unless P = NP. (C) 2008 Elsevier B.V. All rights reserved.
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