In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation...
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In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be NP-hard, while also proving NP-hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting.
Several versions of the graph approximation problem are under study. approximation algorithms for these problems are proposed, and performance guarantees of the algorithms are obtained. In particular, it is shown that...
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In this paper, we address the k-Chinese postman problem under interdiction budget constraints (the k-CPIBC problem, for short), which is a further generalization of the k-Chinese postman problem and has many practical...
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In this paper, we address the k-Chinese postman problem under interdiction budget constraints (the k-CPIBC problem, for short), which is a further generalization of the k-Chinese postman problem and has many practical applications in real life. Specifically, given a weighted graph G = (V, E;w, c;v(1)) equipped with a weight function w : E -> R+ that satisfies the triangle inequality, an interdiction cost function c : E -> Z(+), a fixed depot v(1) is an element of V, an integer k is an element of Z(+) and a budget B is an element of N, we are asked to find a subset S-k subset of E such that c(S-k) = Sigma(e is an element of Sk) c(e) <= B and that the subgraph G\S-k is connected, the objective is to minimize the value minC(E\Sk) max{w(C-i) vertical bar C-i is an element of C-E\Sk} among such all aforementioned subsets S-k, where C-E\S-k is a set of k-tours (of G\S-k) starting and ending at the depot v1, jointly traversing each edge in G\S-k at least once, and w(C-i) = Sigma(e is an element of Ci) w(e) for each tour C-i is an element of C-E\Sk. We obtain the following main results: (1) Given an alpha-approximation algorithm to solve theminimization knapsack problem, we design an (alpha + beta)-approximation algorithm to solve the k-CPIBC problem, where beta = 7/2 - 1/k - left perpendicular1/kRIGHT perpendicular. (2) We present a beta-approximation algorithm to solve the special version of the k-CPIBC problem, where c(e) = 1 for each edge e in G and beta is defined in (1).
Today is an era where multiprocessor technology plays a major role in designs of modern computer architecture. While multiprocessor systems offer extra computing power, it also opens a new range of opportunities to im...
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Today is an era where multiprocessor technology plays a major role in designs of modern computer architecture. While multiprocessor systems offer extra computing power, it also opens a new range of opportunities to improve fault-robustness. This paper focuses on a problem of achieving fault-tolerance using replications in real-time, multiprocessor systems. In the problem, multiple replicas, or copies, of a computing task are executed on distinct processors to resist potential processor failures and computing faults. Two greedy, approximation heuristics, named Worst Fit Increasing K-Replication and First Fit Increasing K-Replication, are studied to maximise the number of real-time tasks assigned on a system with identical processors, respecting to the tasks' replicating and timely requirements. Worst case performance is analysed by using an approximation ratio between the algorithms and an optimal solution. We mathematically prove that the ratios of using both algorithms are infinitely close to 2. Simulations are performed on a large set of testing cases which can be used to bring to light the average performance of using the algorithms in practice. The results show that both heuristic algorithms provide simple but fast and effective solutions to solve the problem. [GRAPHICS] Assigning real-time tasks to a multiprocessor system with replications.
We study budget constrained,network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted gra...
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We study budget constrained,network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V, E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function c(e)(t) that specifies the cost of upgrading the edge by an amount t. A reduction strategy specifies for each edge e the amount by which the length e(e) is to be reduced, In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v, For a given budget B, the goal is to find an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e,g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint. After providing a brief overview of the models and definitions of the various problems considered, we present several new results on the complexity and approximability of network improvement problems.
This paper considers problems of the following type: given an edge-weighted k-colored input graph with maximum color class size c, find a minimum or maximum c-way cut such that each color class is totally partitioned....
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This paper considers problems of the following type: given an edge-weighted k-colored input graph with maximum color class size c, find a minimum or maximum c-way cut such that each color class is totally partitioned. Equivalently, given a weighted complete k-partite graph, cover its vertices with a minimum number of disjoint cliques in such a way that the total weight of the cliques is maximized or minimized. Our study was motivated by some work called the index domain alignment problem [6], which shows its relevance to optimization of distributed computation. Solutions of these problems also have applications in logistics [3] and manufacturing systems [10]. In this paper, we design some approximation algorithms by extending the matching algorithms to these problems. Both theoretical and experimental results show that the algorithms we designed produce good approximations.
In this paper we study the problem of finding placement tours for pick-and-place robots, also known as the printed circuit board assembly problem with m positions on a board, n bins containing In components and n loca...
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In this paper we study the problem of finding placement tours for pick-and-place robots, also known as the printed circuit board assembly problem with m positions on a board, n bins containing In components and n locations for the bins. In the standard model where the working time of the robot is proportional to the distances travelled, the general problem appears as a combination of the travelling salesman problem and the matching problem, and for m = n we have an Euclidean, bipartite travelling salesman problem. We give a polynomial-time algorithm which achieves an approximation guarantee of 3 + epsilon. An important special instance of the problem is the case of a fixed assignment of bins to bin-locations. This appears as a special case of a bipartite TSP satisfying the quadrangle inequality and given some fixed matching arcs. We obtain a 1.8 factor approximation with the stacker crane algorithm of Frederikson, Hecht and Kim. For the general bipartite case we also show a 2.0 factor approximation algorithm which is based on a new insertion technique for bipartite TSPs with quadrangle inequality. Implementations and experiments on "real-world" as well as random point configurations conclude this paper.
In the Euclidean traveling salesman problem with discrete neighborhoods, we are given a set of points P in the plane and a set of n connected regions (neighborhoods), each containing at least one point of P. We seek t...
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In the Euclidean traveling salesman problem with discrete neighborhoods, we are given a set of points P in the plane and a set of n connected regions (neighborhoods), each containing at least one point of P. We seek to find a tour of minimum length which visits at least one point in each region. We give (i) an O(alpha)-approximation algorithm for the case when the regions are disjoint and alpha-fat, with possibly varying size;(ii) an O(alpha(3))-approximation algorithm for intersecting alpha-fat regions with comparable diameters. These results also apply to the case with continuous neighborhoods, where the sought TSP tour can hit each region at any point. We also give (iii) a simple O(log n)- approximation algorithm for continuous non-fat neighborhoods. The most distinguishing features of these algorithms are their simplicity and low running-time complexities.
Modem distributed telecommunication networks have widely extended the possibilities of the telecommunication industry for offering a wide variety of services, directly or indirectly by facilitating them for other serv...
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Modem distributed telecommunication networks have widely extended the possibilities of the telecommunication industry for offering a wide variety of services, directly or indirectly by facilitating them for other service providers. As new services are often processing based there is a need for a shift of focus in research from traditional transportation of information to processing of information. This paper considers the problem of installing software applications for services at the computing nodes of the distributed network, in order to maximize the service provider's profit when meeting demand. The service provision problem is formulated as an integer linear programming model and is shown to be NP-hard. We exploit similarities to the well-known (multiple) knapsack problem in devising approximation algorithms and analysing their performance from a worst-case point of view. Among others, a fully polynomial-time approximation scheme is presented for the case with one computing node. The other main results of the paper concern the derivation of upper bounds on the optimal solution via LP. (C) 2002 Elsevier Science B.V. All rights reserved.
Given a set P of n points in R-d and an integer k >= 1, let w* denote the minimum value so that P can be covered by k congruent cylinders of radius w*. We describe a randomized algorithm that, given P and an epsilo...
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Given a set P of n points in R-d and an integer k >= 1, let w* denote the minimum value so that P can be covered by k congruent cylinders of radius w*. We describe a randomized algorithm that, given P and an epsilon>0, computes k cylinders of radius (1+epsilon) w* that cover P. The expected running time of the algorithm is 0 (n log n), with the constant of proportionality depending on k, d, and epsilon. We first show that there exists a small "certificate" Q subset of P, whose size does not depend on n, such that for any k congruent cylinders that cover Q, an expansion of these cylinders by a factor of (1+epsilon) covers P. We then use a well-known scheme based on sampling and iterated re-weighting for computing the cylinders.
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