We study a set of problems related to efficient battery energy utilization for monitoring applications in a wireless sensor network with the goal to increase the sensor network lifetime. We study several generalizatio...
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We study a set of problems related to efficient battery energy utilization for monitoring applications in a wireless sensor network with the goal to increase the sensor network lifetime. We study several generalizations of a basic problem called Set k-Cover. The problem can be described as follows: we are given a set of sensors, and a set of targets to be monitored. Each target can be monitored by a subset of the sensors. To increase the lifetime of the sensor network, we would like to partition the sensors into k sets (or time-slots), and activate each set of sensors in a different time-slot, thus extending the battery life of the sensors by a factor of k. The goal is to find a partitioning that maximizes the total coverage of the targets for a given k. This problem is known to be NP-hard. We develop an improved approximation algorithm for this problem using a reduction to Max k-Cut. Moreover, we are able to demonstrate that this algorithm is efficient, and yields almost optimal solutions in practice. We also consider generalizations of this problem in several different directions. First, we allow each sensor to be active in alpha different sets (time-slots). This means that the battery life is extended by a factor of k/alpha, and allows for a richer space of solutions. We also consider different coverage requirements, such as requiring that all targets, or at least a certain number of targets, be covered in each time slot. In the Set k-Cover formulation, there is no requirement that a target be monitored at all, or in any number of time slots. We develop a randomized rounding algorithm for this problem. We also consider extensions where each sensor can monitor only a bounded number of targets in any time-slot, and not all the targets adjacent to it. This kind of problem may arise when a sensor has a directional camera, or some other physical constraint might prevent it from monitoring all adjacent targets even when it is active. We develop the first approximation
This paper addresses the problem of fault-tolerant many-to-one routing in static wireless networks with asymmetric links, which is important in both theoretical and practical aspects. The problem is to find a minimum ...
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This paper addresses the problem of fault-tolerant many-to-one routing in static wireless networks with asymmetric links, which is important in both theoretical and practical aspects. The problem is to find a minimum energy subgraph for a given subset and a destination node such that there are k node-disjoint paths from each node in the subset to the destination node in the subgraph. Firstly, we prove that the problem is NP-hard, and then propose two approximation algorithms: the minimum weight k node-disjoint paths based (MWkNDPB) algorithm and the minimum energy k node-disjoint paths based (MEkNDPB) algorithm. Extensive simulations have been conducted to show that proposed algorithms are efficient. (C) 2009 Elsevier B.V. All rights reserved.
Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in t...
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Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in this set. And the minimum-weighted connected dominating set (MWCDS) problem is to find a MWDS such that the graph induced by this subset is connected. In this paper, we study these two problems on a unit disk graph. A (4 +epsilon)-approximation algorithm for an MWDS based on a dynamic programming algorithm for a Min-Weight Chromatic Disk Cover is presented. Meanwhile, we also propose a (1 +epsilon)-approximation algorithm for the connecting part by showing a polynomial-time approximation scheme for a Node-Weighted Steiner Tree problem when the given terminal set is c-local and thus obtain a (5 +epsilon)-approximation algorithm for an MWCDS. (C) 2009 Elsevier B.V. All rights reserved.
Let f : 2(X) -> R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem max(S is an element of I)f(S). It is known that the greedy algorithm yields a 1/2-approximation [M. L. ...
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Let f : 2(X) -> R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem max(S is an element of I)f(S). It is known that the greedy algorithm yields a 1/2-approximation [M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey, Math. Programming Stud., no. 8 (1978), pp. 73-87] for this problem. For certain special cases, e. g., max(|S|<= k)f(S), the greedy algorithm yields a (1 - 1/e)-approximation. It is known that this is optimal both in the value oracle model (where the only access to f is through a black box returning f(S) for a given set S) [G. L. Nemhauser and L. A. Wolsey, Math. Oper. Res., 3 (1978), pp. 177-188] and for explicitly posed instances assuming P not equal NP [U. Feige, J. ACM, 45 (1998), pp. 634-652]. In this paper, we provide a randomized (1 - 1/e)-approximation for any monotone submodular function and an arbitrary matroid. The algorithm works in the value oracle model. Our main tools are a variant of the pipage rounding technique of Ageev and Sviridenko [J. Combin. Optim., 8 (2004), pp. 307-328], and a continuous greedy process that may be of independent interest. As a special case, our algorithm implies an optimal approximation for the submodular welfare problem in the value oracle model [J. Vondrak, Proceedings of the 38th ACM Symposium on Theory of Computing, 2008, pp. 67-74]. As a second application, we show that the generalized assignment problem (GAP) is also a special case;although the reduction requires |X| to be exponential in the original problem size, we are able to achieve a (1 - 1/e - o(1))-approximation for GAP, simplifying previously known algorithms. Additionally, the reduction enables us to obtain approximation algorithms for variants of GAP with more general constraints.
A method is proposed for estimating the parameters of motion of a moving sound source on the basis of digital processing of Doppler-shifted underwater acoustic signals received by a set of hydrophones. A two-step appr...
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A method is proposed for estimating the parameters of motion of a moving sound source on the basis of digital processing of Doppler-shifted underwater acoustic signals received by a set of hydrophones. A two-step approximation algorithm is used. An example of implementing the method of estimating the parameters of motion is presented for a two-hydrophone receiving system. Errors in estimating the parameters by means of the proposed method are considered.
In the multicast k-tree routing problem, a data copy is sent from the source node to at most k destination nodes in every transmission. The goal is to minimize the total cost of sending data to all destination nodes, ...
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In the multicast k-tree routing problem, a data copy is sent from the source node to at most k destination nodes in every transmission. The goal is to minimize the total cost of sending data to all destination nodes, which is measured as the sum of the costs of all routing trees. This problem was formulated out of optical networking and has applications in general multicasting. Several approximation algorithms, with increasing performance, have been proposed in the last several years;the most recent ones rely heavily on a tree partitioning technique. In this paper, we present a further improved approximation algorithm along the line. The algorithm has a worst-case performance ratio of 5/4 rho + 3/2, where rho denotes the best approximation ratio for the Steiner minimum tree problem. The proofs of the technical routing lemmas also provide some insights into why such a performance ratio could be the best possible that one can get using this tree partitioning technique. (C) 2009 Elsevier B.V. All rights reserved.
We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second mac...
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We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a 3/2-approximation algorithm that outputs a two-shipment schedule. We design a 4/3-approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.
In this paper, we studied the minimum latency conflict-free many-to-one data aggregation scheduling problem in multi-channel multi-hop wireless sensor networks: Given locations of all sensors and a base station, some ...
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ISBN:
(纸本)9781612842332
In this paper, we studied the minimum latency conflict-free many-to-one data aggregation scheduling problem in multi-channel multi-hop wireless sensor networks: Given locations of all sensors and a base station, some sensors which are called as sources, find a schedule such that data from all sources can be transmitted to the base station without any conflict and the latency is minimized. In this model, each sensor has three parameters which are transmission range r, interference range alpha r and carrier sensing range beta r where alpha, and beta are constant. There are lambda >= 1 available channels for communications. We designed an approximation algorithm with ratio (inverted right perpendicular a/lambda inverted left perpendicular + 11 inverted right perpendicular b/lambda inverted left perpendicular). This work improves our previous work [9] when lambda = 1. Extensive simulations evaluate the performance of the algorithm.
In the multicast k-tree routing problem, a data copy is sent from the source node to at most k destination nodes in every transmission. The goal is to minimize the total cost of sending data to all destination nodes, ...
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In the multicast k-tree routing problem, a data copy is sent from the source node to at most k destination nodes in every transmission. The goal is to minimize the total cost of sending data to all destination nodes, which is measured as the sum of the costs of all routing trees. This problem was formulated out of optical networking and has applications in general multicasting. Several approximation algorithms, with increasing performance, have been proposed in the last several years;the most recent ones rely heavily on a tree partitioning technique. In this paper, we present a further improved approximation algorithm along the line. The algorithm has a worst-case performance ratio of 5/4 rho + 3/2, where rho denotes the best approximation ratio for the Steiner minimum tree problem. The proofs of the technical routing lemmas also provide some insights into why such a performance ratio could be the best possible that one can get using this tree partitioning technique. (C) 2009 Elsevier B.V. All rights reserved.
We study the problem of maximising the lifetime of a sensor network for fault-tolerant target coverage in a setting with composite events. Here, a composite event is the simultaneous occurrence of a combination of ato...
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ISBN:
(纸本)9781450307437
We study the problem of maximising the lifetime of a sensor network for fault-tolerant target coverage in a setting with composite events. Here, a composite event is the simultaneous occurrence of a combination of atomic events, such as the detection of smoke and high temperature. We are given sensor nodes that have an initial battery level and can monitor certain event types, and a set of points at which composite events need to be detected. The points and sensor nodes are located in the Euclidean plane, and all nodes have the same sensing radius. The goal is to compute a longest activity schedule with the property that at any point in time, each event point is monitored by at least two active sensor nodes. We present a (6 + epsilon)-approximation algorithm for this problem by devising an approximation algorithm with the same ratio for the dual problem of minimising the weight of a fault-tolerant sensor cover and applying the Garg-Konemann algorithm. Our algorithm for the minimum-weight fault-tolerant sensor cover problem generalises previous approximation algorithms for geometric set cover with weighted unit disks and is obtained by enumerating properties of the optimal solution that guide a dynamic programming approach.
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