The set cover problem is that of computing a minimum weight subfamily F', given a family F of weighted subsets of a base set U, such that every element of U is covered by some subset in F'. The k-set cover pro...
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The set cover problem is that of computing a minimum weight subfamily F', given a family F of weighted subsets of a base set U, such that every element of U is covered by some subset in F'. The k-set cover problem is a variant in which every subset is of size at most k. It has been long known that the problem can be approximated within a factor of H(k) = Sigma(k)(i=1) (1/i) by the greedy heuristic, but no better bound has been shown except for the case of unweighted subsets. In this paper we consider approximation of a restricted version of the weighted 3-set cover problem, as a first step towards better approximation of general k-set cover problem, where any two distinct subset costs differ by a multiplicative factor of at least 2. It will be shown, via LP duality, that an improved approximation bound of H(3) - 1/6 can be attained, when the greedy heuristic is suitably modified for this case. A key to our algorithm design and analysis is the Gallai-Edmonds structure theorem for maximum matchings. (c) 2005 Elsevier B.V. All rights reserved.
Using a connected dominating set (CDS) to serve as the virtual backbone of a wireless network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to an accidental damage or en...
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Using a connected dominating set (CDS) to serve as the virtual backbone of a wireless network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to an accidental damage or energy depletion, it is desirable that the virtual backbone is fault tolerant. A node set is an m-fold connected dominating set (m-fold CDS) of graph if every node in has at least neighbors in and the subgraph of induced by is connected. In this paper, we will present a greedy algorithm to compute an -fold CDS in a general graph, which has size at most 2 + ln (Delta + m - 2) times that of a minimum m-fold CDS, where Delta is the maximum degree of the graph. This result improves on the previous best known performance ratio of 2H (Delta + m - 1) for this problem, where H (.) is the Harmonic number.
During laboratory automation of life science experiments, coordinating specialized instruments and human experimenters for various experimental procedures is important to minimize the execution time. In particular, th...
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During laboratory automation of life science experiments, coordinating specialized instruments and human experimenters for various experimental procedures is important to minimize the execution time. In particular, the scheduling of life science experiments requires the consideration of time constraints by mutual boundaries (TCMB) and can be formulated as the "scheduling for laboratory automation in biology " (S-LAB) problem. However, existing scheduling methods for the S-LAB problems have difficulties in obtaining a feasible solution for large-size scheduling problems at a time sufficient for real-time use. In this study, we proposed a fast schedule-finding method for S-LAB problems, SAGAS (Simulated annealing and greedy algorithm scheduler). SAGAS combines simulated annealing and the greedy algorithm to find a scheduling solution with the shortest possible execution time. We have performed scheduling on real experimental protocols and shown that SAGAS can search for feasible or optimal solutions in practicable computation time for various S-LAB problems. Furthermore, the reduced computation time by SAGAS enables us to systematically search for laboratory automation with minimum execution time by simulating scheduling for various laboratory configurations. This study provides a convenient scheduling method for life science automation laboratories and presents a new possibility for designing laboratory configurations.
algorithmic construction of software interaction test suites has focussed on pairwise coverage, less is known about the efficient construction of test suites for t-way interactions with t >= 3. This study extends a...
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algorithmic construction of software interaction test suites has focussed on pairwise coverage, less is known about the efficient construction of test suites for t-way interactions with t >= 3. This study extends an efficient density-based algorithm for pairwise coverage to generate t-way interaction test suites and shows that it guarantees a logarithmic upper bound on the size of the test suites as a function of the number of factors. To complement this theoretical guarantee, an implementation is outlined and some practical improvements are made. Computational comparisons with other published methods are reported. Many of the results improve upon those in the literature. However, limitations on the ability of one-test-at-a-time algorithms are also identified. Copyright (C) 2008 John Wiley & Sons, Ltd.
The classical greedy algorithm for discrete optimization problems where the optimal solution is a maximal independent subset of a finite ground set of weighted elements, can be defined in two ways which are dual to ea...
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The classical greedy algorithm for discrete optimization problems where the optimal solution is a maximal independent subset of a finite ground set of weighted elements, can be defined in two ways which are dual to each other. The greedy-In where a solution is constructed from the empty set by adding the next best element, one at a time, until we reach infeasibility, and the greedy-Out where starting from the ground set we delete the next worst element, one at a time, until feasibility is reached. It is known that while the former provides an approximation ratio for maximization problems, its worst case performance is not bounded for minimization problems, and vice-versa for the later. However the greedy-Out algorithm requires an oracle for checking the existence of a maximal independent subset which for most discrete optimization problems is a difficult task. In this work we present a greedy-Out algorithm for the quadratic assignment problem by providing a combinatorial characterization of its solutions.
In this paper, we propose an optimal greedy algorithm for the problem of run-time many-core scheduling. The previously best known centralized optimal algorithm proposed for the problem is based on dynamic programming....
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In this paper, we propose an optimal greedy algorithm for the problem of run-time many-core scheduling. The previously best known centralized optimal algorithm proposed for the problem is based on dynamic programming. A dynamic programming-based scheduler has high overheads which grow fast with increase in both the number of cores in the many-cores as well as number of tasks independently executing on them. We show in this paper that the inherent concavity of extractable instructions per cycle in tasks with increase in number of allocated cores allows for an alternative greedy algorithm. The proposed algorithm significantly reduces the run-time scheduling overheads, while maintaining theoretical optimality. In practice, it reduces the problem solving time 10 000x to provide near-optimal solutions.
We provide a counterexample to the performance guarantee obtained in the paper "Il'ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroi...
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We provide a counterexample to the performance guarantee obtained in the paper "Il'ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid", which was published in Volume 171 of the European Journal of Operational Research. We point out where this error originates from in the proof of the main theorem. (C) 2020 The Author(s). Published by Elsevier B.V.
The domain decomposition is a conventional approach to compute complex multidisciplinary simulations. The data transfer must be performed on their common interface due to the non-matching meshes for different domains....
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The domain decomposition is a conventional approach to compute complex multidisciplinary simulations. The data transfer must be performed on their common interface due to the non-matching meshes for different domains. The adaptive Kriging interpolation method is proposed based on the greedy algorithm. By introducing a learning function, the Kriging interpolation model is constructed by the source grid values. In this way, part of the total source points are selected and the Kriging model is of high precision for the data transfer between the interface. Four examples are investigated to demonstrate the efficiency and accuracy of the proposed method.
It is well known that the greedy algorithm solves matroid base problems for all linear cost functions and is, in fact, correct if and only if the underlying combinatorial structure of the problem is a matroid. Moreove...
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It is well known that the greedy algorithm solves matroid base problems for all linear cost functions and is, in fact, correct if and only if the underlying combinatorial structure of the problem is a matroid. Moreover, the algorithm can be applied to problems with sum, bottleneck, algebraic sum or k-sum objective functions. In this paper, we address matroid base problems with a more general - "universal" - objective function which contains the previous ones as special cases. This universal objective function is of the sum type and associates multiplicative weights with the ordered cost coefficients of the elements of matroid bases such that, by choosing appropriate weights, many different - classical and new - objectives can be modeled. We show that the greedy algorithm is applicable to a larger class of objective functions than commonly known and, as such, it solves universal matroid base problems with non-negative or non-positive weight coefficients. Based on problems with mixed weights and a single (-, +)- sign change in the universal weight vector, we give a characterization of uniform matroids. In case of multiple sign changes, we use partition matroids. For non-uniform matroids, single sign change problems can be reduced to problems in minors obtained by deletion and contraction. Finally, we discuss how special instances of universal bipartite matching and shortest path problems can be tackled by applying greedy algorithms to associated transversal matroids. (C) 2014 Elsevier B.V. All rights reserved.
The problems related to energy consumption and improvement of the network lifetime of WSN (wireless sensor network) have been considered. The base station (BS) location is the main concern in WSN. BSs are fixed, yet, ...
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The problems related to energy consumption and improvement of the network lifetime of WSN (wireless sensor network) have been considered. The base station (BS) location is the main concern in WSN. BSs are fixed, yet, they have the ability to move in some situations to collect the information from sensor nodes (SNs). Recently, introducing mobile sinks to WSNs has been proved to be an efficient way to extend the lifespan of the network. This paper proposes the assimilation of the fuzzy clustering approach and the Elephant Herding Optimization (EHO)-greedy algorithm for efficient routing in WSN. This work considers the separate sink nodes of a fixed sink and movable sink to decrease the utilization of energy. A fixed node is deployed randomly across the network, and the movable sink node moves to different locations across the network for collecting the data. Initially, the number of nodes is formed into the multiple clusters using the enhanced expectation maximization algorithm. After that, the cluster head (CH) selection done through a fuzzy approach by taking the account of three factors of residual energy, node centrality, and neighborhood overlap. A suitable collection of CH can extremely reduce the utilization of energy and also enhancing the lifespan. Finally, the routing protocol of the hybrid EHO-greedy algorithm is used for efficient data transmission. Simulation results display that the proposed technique is better to other existing approaches in regard to energy utilization and the system lifetime.
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