In this paper, the parameter which is the source of the complexity of disjunctionfree default reasoning is determined. It is shown that when the value of this parameter is fixed, the disjunction-free default reasoning...
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In this paper, the parameter which is the source of the complexity of disjunctionfree default reasoning is determined. It is shown that when the value of this parameter is fixed, the disjunction-free default reasoning can be solved in time bounded by a polynomial whose degree does not depend on the parameter. Consequently, disjunction-free default reasoning is fixedparameter tractable.
We provide first-time fixed-parameter tractability results for the NP-hard problems MAXIMUM FULL-DEGREE SPANNING TREE (FDST) and MINIMUM-VERTEX FEEDBACK EDGE SET. These problems are dual to each other. In MAXIMUM FDST...
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We provide first-time fixed-parameter tractability results for the NP-hard problems MAXIMUM FULL-DEGREE SPANNING TREE (FDST) and MINIMUM-VERTEX FEEDBACK EDGE SET. These problems are dual to each other. In MAXIMUM FDST, the task is to find a spanning tree for a given graph that maximizes the number of vertices that preserve their degree. For MINIMUM-VERTEX FEEDBACK EDGE SET, the task is to minimize the number of vertices that end up with a reduced degree. parameterized by the solution size, we exhibit that MINIMUM-VERTEX FEEDBACK EDGE SET is fixed-parameter tractable and has a problem kernel with the number of vertices linearly depending on the parameter k. Our main contribution for MAXIMUM FULL-DEGREE SPANNING TREE, which is W[1]-hard, is a linear-size problem kernel when restricted to planar graphs. Moreover, we present a dynamic programing algorithm for graphs of bounded treewidth. (C) 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 56(2), 116-130 2010
Computational biology is mainly concerned with discovering an object from a given set of observations that are supposed to be good approximations of the real object. Two important steps here are to define a way to mea...
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Computational biology is mainly concerned with discovering an object from a given set of observations that are supposed to be good approximations of the real object. Two important steps here are to define a way to measure the distance between different objects and to calculate the distance between two given objects. The main problem is then to find an object that has the minimum total distance to the given observations. We study two NP-hard problems formulated in computational biology. The minimum tree cut/paste distance problem asks for the minimum number of cut/paste operations we need to transform a tree to another tree. The minimum common integer partition problem asks for a minimum-cardinality integer partition of a number that refines two given integer partitions of the same number. We give parameterized algorithms for both problems. (C) 2019 Elsevier B.V. All rights reserved.
We study an NP-complete (and MaxSNP-hard) communication problem on tree networks, the so-called MULTICUT IN TREES: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at mo...
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We study an NP-complete (and MaxSNP-hard) communication problem on tree networks, the so-called MULTICUT IN TREES: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at most k tree edges whose removal separates all given pairs of nodes. MULTICUT has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomial time approximation algorithms. By way of contrast, we provide a simple fixed-parameter algorithm for MULTICUT IN TREES showing fixed-parameter tractability with respect to parameter k. Moreover, based on some polynomial time data reduction rules, which appear to be of particular interest from an applied point of view, we show a problem kernel for MULTICUT IN TREES by an intricate mathematical analysis. (c) 2005 Wiley Periodicals, Inc.
We study the following general stabbing problem from a parameterized complexity point of view: Given a set S of n translates of an object in R-d, find a set of k lines with the property that every object in S is "...
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We study the following general stabbing problem from a parameterized complexity point of view: Given a set S of n translates of an object in R-d, find a set of k lines with the property that every object in S is "stabbed" (intersected) by at least one line. We show that when S consists of axis-parallel unit squares in R-2 the (decision) problem of stabbing S with axis-parallel lines is W[1]-hard with respect to k (and thus, not fixed-parameter tractable unless FPT = W[1]) while it becomes fixed-parameter tractable when the squares are disjoint. We also show that the problem of stabbing a set of disjoint unit squares in R-2 with lines of arbitrary directions is W[1]-hard with respect to k. Several generalizations to other types of objects and lines with arbitrary directions are also presented. Finally, we show that deciding whether a set of unit balls in R-d can be stabbed by one line is W[1]-hard with respect to the dimension d. (C) 2011 Elsevier B.V. All rights reserved.
We investigate the effect of crossover in the context of parameterized complexity on a well-known fixed-parameter tractable combinatorial optimization problem known as the closest string problem. We prove that a multi...
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We investigate the effect of crossover in the context of parameterized complexity on a well-known fixed-parameter tractable combinatorial optimization problem known as the closest string problem. We prove that a multi-start (mu+1) GA solves arbitrary length-n instances of closest string in 2(O(d2+dlogk)) center dot t(n) steps in expectation. Here, k is the number of strings in the input set, d is the value of the optimal solution, and n <= t(n) <= poly(n) is the number of iterations allocated to the (mu+1) GA before a restart, which can be an arbitrary polynomial in n. This confirms that the multi-start (mu+1) GA runs in randomized fixed-parameter tractable (FPT) time with respect to the above parameterization. On the other hand, if the crossover operation is disabled, we show there exist instances that require n(Omega(log(d+k))) steps in expectation. The lower bound asserts that crossover is a necessary component in the FPT running time.
The MULTICUT problem, given a graph G, a set of terminal pairs T = {(s(i), t(i)) \ 1 <= i <= r}, and an integer p, asks whether one can find a cutset consisting of at most p nonterminal vertices that separates a...
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The MULTICUT problem, given a graph G, a set of terminal pairs T = {(s(i), t(i)) \ 1 <= i <= r}, and an integer p, asks whether one can find a cutset consisting of at most p nonterminal vertices that separates all the terminal pairs, i.e., after removing the cutset, ti is not reachable from si for each 1 <= i <= r. The fixed-parameter tractability of MULTICUT in undirected graphs, parameterized by the size of the cutset only, has been recently proved by Marx and Razgon [SIAM J. Comput., 43 (2014), pp. 355-388] and, independently, by Bousquet, Daligault, and Thomasse [Proceedings of STOC, ACM, 2011, pp. 459-468], after resisting attacks as a long-standing open problem. In this paper we prove that MULTICUT is fixed-parameter tractable on directed acyclic graphs when parameterized both by the size of the cutset and the number of terminal pairs. We complement this result by showing that this is implausible for parameterization by the size of the cutset only, as this version of the problem remains W[1]-hard.
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.
Complementing recent progress on classical complexity and polynomial-time approximability of feedback set problems in (bipartite) tournaments, we extend and improve fixed-parameter tractability results for these probl...
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Complementing recent progress on classical complexity and polynomial-time approximability of feedback set problems in (bipartite) tournaments, we extend and improve fixed-parameter tractability results for these problems. We show that Feedback Vertex Set in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depth-bounded search tree for Feedback Arc Set in bipartite tournaments based on a new forbidden subgraph characterization. Moreover, we apply the iterative compression technique to d-Hitting Set, which generalizes Feedback Vertex Set in tournaments, and obtain improved upper bounds for the time needed to solve 4-HITTING Set and 5-HITTING Set. Using our parameterized algorithm for Feedback Vertex Set in tournaments, we also give an exact (not parameterized) algorithm for it running in O(1.709(n)) time, where n is the number of input graph vertices, answering a question of Woeginger [G.J. Woeginger, Open problems around exact algorithms, Discrete Appl. Math. 156 (3) (2008) 397-405]. (C) 2009 Elsevier B.V. All rights reserved.
This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, a...
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This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, and adding at most k edges, where i,j, k are fixed integers. It is shown that this problem is fixed-parameter tractable whenever the hereditary property can be characterized by a finite set of forbidden induced subgraphs. Furthermore, the problem of deciding whether a graph can be made into a chordal graph by adding a fixed number k of edges is shown to be solvable in O(4(k)(k + 1)(-3/2)(m + n)) time, and is thus fixed-parameter tractable.
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