In order to increase the potential kidney transplants between patients and their incompatible donors, kidney exchange programs have been created in many countries. In the programs, designing algorithms for the kidney ...
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In order to increase the potential kidney transplants between patients and their incompatible donors, kidney exchange programs have been created in many countries. In the programs, designing algorithms for the kidney exchange problem plays a critical role. The graph theory model of the kidney exchange problem is to find a maximum weight packing of vertex-disjoint cycles and chains for a given weighted digraph. In general, the length of cycles is not more than a given constant L (typically 2 <= L <= 5), and the objective function corresponds to maximizing the number of possible kidney transplants. In this paper, we study the parameterized complexity and randomized algorithms for the kidney exchange problem without chains from theory. We construct two different parameterized models of the kidney exchange problem for two cases L = 3 and L >= 3, and propose two randomized parameterized algorithms based on the random partitioning technique and the randomized algebraic technique, respectively.
Coloring of mixed graphs that contain both directed arcs and undirected edges is relevant for scheduling of unit-length jobs with precedence constraints and conflicts. The classic GHRV theorem (attributed to Gallai, H...
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Coloring of mixed graphs that contain both directed arcs and undirected edges is relevant for scheduling of unit-length jobs with precedence constraints and conflicts. The classic GHRV theorem (attributed to Gallai, Hasse, Roy, and Vitaver) relates graph coloring to longest paths. It can be extended to mixed graphs. In the present paper we further extend the GHRV theorem to weighted mixed graphs. As a byproduct this yields a kernel and a parameterized algorithm (with the number of undirected edges as parameter) that is slightly faster than the brute-force algorithm. The parameter is natural since the directed version is polynomial whereas the undirected version is NP-complete. Furthermore we point out a new polynomial case where the edges form a clique.
Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facilit...
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Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the problems of balanced k-means and k-median are W[2]-hard if parameterized by k, implying that the existences of FPT(k )-time exact algorithms for these problems are unlikely. In this paper, we give FPT(k)-time (9 + is an element of )-approximation and (3 + is an element of )-approximation algorithms for balanced k-means and k-median respectively, improving upon the previous best approximation ratios of 86.9 + is an element of and 7.2 + is an element of obtained in the same time. Our main technical contribution and the crucial step in getting the improved ratios is a different random sampling method for selecting opened facilities.
We study the MULTICUT ON TREES and the GENERALIZED MULTIWAY CUT ON TREES problems. For the MULTICUT ON TREES problem, we present a parameterized algorithm that runs in time O*(rho(k)), where rho = root root 2 + 1 <...
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We study the MULTICUT ON TREES and the GENERALIZED MULTIWAY CUT ON TREES problems. For the MULTICUT ON TREES problem, we present a parameterized algorithm that runs in time O*(rho(k)), where rho = root root 2 + 1 < 1.554 is the positive root of the polynomial x(4) - 2x(2) - 1. This improves the current-best algorithm of Chen et al. that runs in time O*(1.619(k)). For the GENERALIZED MULTIWAY CUT ON TREES problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed;this answers an open question posed in a recent paper by Liu and Zhang. By reducing the GENERALIZED MULTIWAY CUT ON TREES problem to the MULTICUT ON TREES problem, our results give a parameterized algorithm that solves the GENERALIZED MULTIWAY CUT ON TREES problem in time O*(rho(k)). (C) 2015 Elsevier B.V. All rights reserved.
This article studies the parameterized complexity of the unification problem with associative, commutative, or associative-commutative functions with respect to the parameter "number of variables". It is sho...
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This article studies the parameterized complexity of the unification problem with associative, commutative, or associative-commutative functions with respect to the parameter "number of variables". It is shown that if every variable occurs only once then both of the associative and associative-commutative unification problems can be solved in polynomial time, but that in the general case, both problems are W [1]-hard even when one of the two input terms is variable-free. For commutative unification, an algorithm whose time complexity depends exponentially on the number of variables is presented;moreover, if a certain conjecture is true then the special case where one input term is variable-free belongs to FPT. Some related results are also derived for a natural generalization of the classic string and tree edit distance problems that allows variables. (C) 2016 The Author(s). Published by Elsevier B.V.
A vertex cover of an n-vertex graph with perfect matching contains at least n/2 *** this paper,we study the parameterized complexity of the problem vc-pm*that decides if a given graph with perfect matching has a verte...
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A vertex cover of an n-vertex graph with perfect matching contains at least n/2 *** this paper,we study the parameterized complexity of the problem vc-pm*that decides if a given graph with perfect matching has a vertex cover of size bounded by n/2+*** first present an algorithm of running time O*(4k)for a variation of the vertex cover problem on K¨onig graphs with perfect *** algorithm combined with the iterative compression technique leads to an algorithm of running time O*(9k)for the problem vc-pm*.Our result improves the previous best algorithm of running time O*(15k)for the vc-pm*problem,which reduces the problem to the almost 2-sat problem and solves the latter by Razgon and O’Sullivan’s recent algorithm.
The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorit...
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The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it inefficient. Therefore, we suggest studying the parameterized complexity of maximization problems with respect to the size of the optimal solutions to their minimization versions. We examine this suggestion by considering the Maximum Minimal Vertex Cover (MMVC) problem, which has applications to wireless ad hoc networks and whose minimization version, Vertex Cover, is one of the most studied problems in the field of parameterized complexity. We first present tight conditional lower bounds for the running time of any algorithm for MMVC or its weighted variant. Next, we develop a parameterized approximation algorithm for MMVC and its weighted variant. The approximation ratio of this algorithm cannot be achieved by polynomial-time algorithms unless P = NP, and its running time cannot be matched by exact parameterized algorithms unless the strong exponential time hypothesis fails. In particular, the algorithm de fines a user-controlled parameter that corresponds to a trade-off between time and approximation ratio.
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution S is a subset of the input data. We introduce the notion of intersective approximability that...
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We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution S is a subset of the input data. We introduce the notion of intersective approximability that generalizes the one of safe approximability introduced in Guo et al. (2011) and show strong parameterized inapproximability results for many of the subset problems handled. (C) 2014 Elsevier B.V. All rights reserved.
In this paper, we present an O*(2.1479(k))-time algorithm to decide whether a graph of maximum degree 3 has an edge dominating set of size at most k or not, which is based on enumeration of vertex covers and improves ...
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In this paper, we present an O*(2.1479(k))-time algorithm to decide whether a graph of maximum degree 3 has an edge dominating set of size at most k or not, which is based on enumeration of vertex covers and improves all previous results on this problem. We first enumerate partial vertex covers of size at most 2k and then construct an edge dominating set based on each vertex cover to find a required edge dominating set. To effectively enumerate vertex covers, we adopt a branch-and-reduce method, and use some techniques, such as 'pseudo-cliques' and 'amortized transfer of cliques,' to analyze the running time bound. (C) 2012 Elsevier B.V. All rights reserved.
We survey results and open questions on complexity of parameterized problems on digraphs. The problems include the feedback vertex and arc set problems, induced subdigraph problems and directed k-leaf problems. We als...
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We survey results and open questions on complexity of parameterized problems on digraphs. The problems include the feedback vertex and arc set problems, induced subdigraph problems and directed k-leaf problems. We also prove some new results on the topic. Most of these new results are on parameterizations of the backward paired comparison problem.
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