We consider the problem of finding edge search strategies of minimum cost. The cost of a search strategy is the sum of searchers used in the clearing steps of the search. One of the natural questions is whether it is ...
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We consider the problem of finding edge search strategies of minimum cost. The cost of a search strategy is the sum of searchers used in the clearing steps of the search. One of the natural questions is whether it is possible to find a search strategy that minimizes both the cost and the number of searchers used to clear a given graph G. We call such a strategy ideal. We prove, by an example, that ideal search strategies do not exist in general. On the other hand, we provide a formula for the cost of clearing complete graphs. From our construction it follows that an ideal search strategy of a complete graph does exist and can be calculated efficiently. For general graphs G we give a polynomial-time O (log n)-approximation algorithm for finding minimum cost search strategies. We also prove that recontamination does not help to obtain minimum cost edge search strategies. (C) 2013 Elsevier B.V. All rights reserved.
In this paper, we consider the scheduling problem in which the jobs are first processed on a single machine and then delivered in batches by a single vehicle with limited capacity to the respective customers located a...
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In this paper, we consider the scheduling problem in which the jobs are first processed on a single machine and then delivered in batches by a single vehicle with limited capacity to the respective customers located at the vertices of a star-shaped network. The goal is to minimize the makespan. We present a 3/2-approximation algorithm for the identical job size case and a 2-approximation algorithm for the non-identical job sizes case.
We consider a two-stage flexible flow shop problem with a single machine at one stage and m identical machines at the other stage, where the processing times of each job at both stages are identical. The objective is ...
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We consider a two-stage flexible flow shop problem with a single machine at one stage and m identical machines at the other stage, where the processing times of each job at both stages are identical. The objective is to minimize the makespan. We describe some optimality conditions and show that the problem is NP-hard when m is fixed. Finally, we present an approximation algorithm that has a worst-case performance ratio of for m=2 and for ma parts per thousand yen3.
For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balance...
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For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition (BCP2) problem looks for a way to bipartition a graph into two connected subgraphs with their weights as equal as possible. In this paper we present an algorithm in time O(NlogN) for finding a minimum weight non-separating path between two given nodes in a grid graph of N nodes with positive weight. This result leads to a 5/4-approximation algorithm for the BCP2 problem on grid graphs, which is the currently best ratio achieved in polynomial time. We also developed an exact algorithm for the BCP2 problem on grid graphs. Based on the exact algorithm and a rounding technique, we show an approximation scheme, which is a fully polynomial time approximation scheme for fixed number of rows.
We use the idea of the direct multiple shooting method (presented by Bock in Proceedings of the 9th IFAC World Congress Budapest, Pergamon Press, 1984, for solving optimal control problems) to introduce an algorithm f...
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We use the idea of the direct multiple shooting method (presented by Bock in Proceedings of the 9th IFAC World Congress Budapest, Pergamon Press, 1984, for solving optimal control problems) to introduce an algorithm for solving some approximate shortest path problems in motion planning. The algorithm is based on a direct multiple shooting discretization that includes a collinear condition (a continuity condition type in the direct multiple shooting method), multiple shooting structure, and approximation conditions. In the case of monotone polygons, it is implemented by a C code, and a numerical example shows that our algorithm significantly reduces the running time and memory usage of the system. (c) 2012 Elsevier B.V. All rights reserved.
Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as...
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Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as to minimize the number of edges shared among the paths. This is a generalization of the well-known disjoint paths problem. While disjoint paths can be computed efficiently, we show that finding paths with minimum shared edges is NP-hard. Moreover, we show that it is even hard to approximate the minimum number of shared edges within a factor of 2(log1-epsilon) n, for any constant epsilon > 0. On the positive side, we show that there exists a (k - 1)-approximation algorithm for the problem, using an adaption of a network flow algorithm. We design some heuristics to improve the quality of the output, and provide empirical results.
This paper studies an optimal monitoring problem for behavior-based detection in multi-channel multi-radio wireless mesh networks. In behavior-based detection, nodes overhear communications in their neighborhood to de...
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This paper studies an optimal monitoring problem for behavior-based detection in multi-channel multi-radio wireless mesh networks. In behavior-based detection, nodes overhear communications in their neighborhood to determine if the behaviors of their neighbors are legitimate. The objective of this work is to maximize the number of nodes being monitored by judiciously choosing a set of monitoring nodes and also channels for the chosen monitoring nodes. This problem is NP-hard, growing exponentially with the number of monitoring nodes. We develop three approximation algorithms, each of which achieves at least a constant factor of the optimum. Furthermore, one of our algorithms achieves the best possible approximation ratio among all polynomial-time algorithms, unless P = NP. We conduct simulations in random networks and scale-free networks to evaluate the coverage and the execution time of the three algorithms. (C) 2012 Elsevier B.V. All rights reserved.
In this note, we present a simple combinatorial factor 6 algorithm for approximating the minimum hitting set of a family R = {R-1, ..., R-n} of axis-parallel rectangles in the plane such that there exists an axis-mono...
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In this note, we present a simple combinatorial factor 6 algorithm for approximating the minimum hitting set of a family R = {R-1, ..., R-n} of axis-parallel rectangles in the plane such that there exists an axis-monotone curve gamma that intersects each rectangle in the family. The quality of the hitting set is shown by comparing it to the size of a packing (set of pairwise non-intersecting rectangles) that is constructed along, hence, we also obtain a factor 6 approximation for the maximum packing of R. In cases where the axis-monotone curve gamma intersects the same side (e.g. the bottom side) of each rectangle in the family the approximation factor for hitting set and packing is 3. (C) 2013 Elsevier B.V. All rights reserved.
We study the problem of computing correlation between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in three dimensions-polyhedral terrains-can be transformed ve...
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We study the problem of computing correlation between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in three dimensions-polyhedral terrains-can be transformed vertically by a linear transformation of the third coordinate (scaling and translation). We present a randomized algorithm that minimizes the maximum vertical distance between the graphs of the two functions, over all linear transformations of one of the terrains, in O(n(4/3) polylog n) expected time, where n is the total number of vertices in the graphs of the two functions. We also present approximation algorithms for minimizing the mean distance between the graphs of univariate and bivariate functions. For univariate functions we present a (1 + epsilon)-approximation algorithm that runs in O(n(1 + log(2)(1/epsilon))) expected time for any fixed epsilon > 0. The (1 + epsilon)-approximation algorithm for bivariate functions runs in O(n/epsilon) time, for any fixed epsilon > 0, provided the two functions are defined over the same triangulation of their domain.
Most prior theoretical research on real-time partitioning algorithms for multiprocessor platforms has focused on ensuring that the cumulative computing requirements of the tasks assigned to each processor does not exc...
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Most prior theoretical research on real-time partitioning algorithms for multiprocessor platforms has focused on ensuring that the cumulative computing requirements of the tasks assigned to each processor does not exceed the processor's processing power. However, computing capacity is often not the only limiting resource: on many multiprocessor platforms each individual computing unit may have limited amounts of multiple additional types of resources (such as local memory) in addition to having limited processing power. We present algorithms for partitioning a collection of sporadic tasks, each characterized by a WCET, a relative deadline, and a period, upon a multiprocessor platform in a manner that is cognizant of such additional constraints as well as the processing capacity constraints.
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