Results 11  20
of
249
Selecting Forwarding Neighbors in Wireless Ad Hoc Networks
, 2001
"... Broadcasting is a fundamental operation which is frequent in wireless ad hoc networks. A simple broadcasting mechanism, known as flooding, is to let every node retransmit the message to all its 1hop neighbors when receiving the first copy of the message. Despite its simplicity, flooding is very in ..."
Abstract

Cited by 74 (4 self)
 Add to MetaCart
Broadcasting is a fundamental operation which is frequent in wireless ad hoc networks. A simple broadcasting mechanism, known as flooding, is to let every node retransmit the message to all its 1hop neighbors when receiving the first copy of the message. Despite its simplicity, flooding is very inefficient and can result in high redundancy, contention, and collision. One approach to reducing the redundancy is to let each node forward the message only to a small subset of 1hop neighbors that cover all of the node's 2hop neighbors. In this paper, we propose two practical heuristics for selecting the minimum number of forwarding neighbors: an O(n log n) time algorithm that selects at most 6 times more forwarding neighbors than the optimum, and an O(n²) time algorithm with an improved approximation ratio of 3, where n is the number of 1 and 2hop neighbors. The best previously known algorithm, due to Bronnimann and Goodrich [2], guarantees O(1) approximation in O(n³ log n) time.
Improved Approximation Algorithms for Geometric Set Cover
, 2005
"... Given a collection S of subsets of some set U, and M ⊂ U, the set cover problem is to find the smallest subcollection C ⊂ S such that M is a subset of the union of the sets in C. While the general problem is NPhard to solve, even approximately, here we consider some geometric special cases, where u ..."
Abstract

Cited by 72 (6 self)
 Add to MetaCart
Given a collection S of subsets of some set U, and M ⊂ U, the set cover problem is to find the smallest subcollection C ⊂ S such that M is a subset of the union of the sets in C. While the general problem is NPhard to solve, even approximately, here we consider some geometric special cases, where usually U = ℜ d. Extending prior results[BG95], we show that approximation algorithms with provable performance exist, under a certain general condition: that for a random subset R ⊂ S and function f(), there is a decomposition of the complement U \ ∪Y∈RY into an expected f(R) regions, each region of a particular simple form. We show that under this condition, a cover of size O(f(C)) can be found. Our proof involves the generalization of shallow cuttings [Mat92] to more general geometric situations. We obtain constantfactor approximation algorithms for covering by unit cubes in ℜ³, for guarding a onedimensional terrain, and for covering by similarsized fat triangles in ℜ². We also obtain improved approximation guarantees for fat triangles, of arbitrary size, and for a class of fat objects.
Relay node placement in wireless sensor networks
 IEEE TRANSACTIONS ON COMPUTERS
, 2007
"... A wireless sensor network consists of many lowcost, lowpower sensor nodes, which can perform sensing, simple computation, and transmission of sensed information. Long distance transmission by sensor nodes is not energy efficient, since energy consumption is a superlinear function of the transmissi ..."
Abstract

Cited by 69 (6 self)
 Add to MetaCart
A wireless sensor network consists of many lowcost, lowpower sensor nodes, which can perform sensing, simple computation, and transmission of sensed information. Long distance transmission by sensor nodes is not energy efficient, since energy consumption is a superlinear function of the transmission distance. One approach to prolong network lifetime while preserving network connectivity is to deploy a small number of costly, but more powerful, relay nodes whose main task is communication with other sensor or relay nodes. In this paper, we assume that sensor nodes have communication range r> 0 while relay nodes have communication range R ≥ r, and study two versions of relay node placement problems. In the first version, we want to deploy the minimum number of relay nodes so that between each pair of sensor nodes, there is a connecting path consisting of relay and/or sensor nodes. In the second version, we want to deploy the minimum number of relay nodes so that between each pair of sensor nodes, there is a connecting path consisting solely of relay nodes. We present a polynomial time 7approximation algorithm for the first problem, and a polynomial time (5 + ɛ)approximation algorithm for the second problem, where ɛ> 0 can be any given constant.
Node Placement for Connected Coverage in Sensor Networks
, 2003
"... We address the problem of optimal node placement for ensuring connected coverage in sensor networks. We consider two different practical scenarios. In the first scenario, a certain region (or a set of regions) are to be provided connected coverage, while in the second case, a given set of n points a ..."
Abstract

Cited by 68 (1 self)
 Add to MetaCart
(Show Context)
We address the problem of optimal node placement for ensuring connected coverage in sensor networks. We consider two different practical scenarios. In the first scenario, a certain region (or a set of regions) are to be provided connected coverage, while in the second case, a given set of n points are to be covered and connected. For the first case, we provide solutions that are within a small factor of the optimum. For the second case, we present an algorithm that runs in polynomial time, and guarantees a constant factor approximation ratio.
Approximations for Steiner trees with minimum number of Steiner points
, 2001
"... ..."
(Show Context)
PolynomialTime Approximation Schemes for Packing and Piercing Fat Objects
 JOURNAL OF ALGORITHMS
, 2001
"... We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomialtime approxim ..."
Abstract

Cited by 50 (5 self)
 Add to MetaCart
(Show Context)
We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomialtime approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a dierent algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the rst PTAS for that problem. Abbreviated title. Packing and Piercing Fat Objects.
On Approximating Rectangle Tiling and Packing
 Proc Symp. on Discrete Algorithms (SODA
"... Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogrambased estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems tha ..."
Abstract

Cited by 47 (6 self)
 Add to MetaCart
(Show Context)
Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogrambased estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems that we tackle is the following: given an n \Theta n array A of positive numbers, find a tiling using at most p rectangles (that is, no two rectangles must overlap, and each array element must fall within some rectangle) that minimizes the maximum weight of any rectangle; here the weight of a rectangle is the sum of the array elements that fall within it. If the array A were onedimensional, this problem could be easily solved by dynamic programming. We prove that in the twodimensional case it is NPhard to approximate this problem to within a factor of 1:25. On the other hand, we provide a nearlinear time algorithm that returns a solution at most 2:5 times the optimal. Other rectangle tiling...
Lowcoordination topologies for redundancy in sensor networks
 In ACM MobiHoc
, 2005
"... Tiny, lowcost sensor devices are expected to be failureprone and hence in many realistic deployment scenarios for sensor networks these nodes are deployed in higher than necessary densities to meet operational goals. In this paper we address the question of how nodes should be managed in such dens ..."
Abstract

Cited by 43 (0 self)
 Add to MetaCart
Tiny, lowcost sensor devices are expected to be failureprone and hence in many realistic deployment scenarios for sensor networks these nodes are deployed in higher than necessary densities to meet operational goals. In this paper we address the question of how nodes should be managed in such dense sensor deployments so that the network topology formed by the active sensors is able to provide connectedcoverage to the entire area of interest and at the same time increase the lifetime of the network. In particular, we propose and study distributed, lowcoordination node wakeup schemes to efficiently construct multiple independent (nodedisjoint) sensor network topologies to achieve good fault tolerance. We propose and evaluate different distributed, random and patternbased wakeup policies for sensor nodes to construct connectedcovered topologies. Through analysis and simulations we demonstrate that in dense sensor deployment scenarios, these policies can construct nearoptimal topologies (within 2.7 % of the optimal) with zero coordination between nodes, as long as location information is available at the individual sensor nodes. Based on these observations, we develop and evaluate a few simple distributed, wakeup based topology construction algorithms that can realize similar performance bounds in realistic sensor deployments, with varying node densities. These algorithms differ in terms of the required level of coordination and the use of sensor location information, and generate connectedcovered topologies efficiently, with very low messageexchange overhead.
Constantfactor approximation for minimumweight (connected) dominating sets in unit disk graphs
 In: Proc. of the 9 th Int. Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX). (2006
, 2006
"... For a given graph with weighted vertices, the goal of the minimumweight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex correspond ..."
Abstract

Cited by 42 (5 self)
 Add to MetaCart
(Show Context)
For a given graph with weighted vertices, the goal of the minimumweight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex corresponds to a unit disk in the plane and two vertices are adjacent if and only if their disks have a nonempty intersection. We present the first constantfactor approximation algorithm for the minimumweight dominating set problem in unit disk graphs, a problem motivated by applications in wireless adhoc networks. The algorithm is obtained in two steps: First, the problem is reduced to the problem of covering a set of points located in a small square using a minimumweight set of unit disks. Then, a constantfactor approximation algorithm for the latter problem is obtained using enumeration and dynamic programming techniques exploiting the geometry of unit disks. Furthermore, we show how to obtain a constantfactor approximation algorithm for the minimumweight connected dominating set problem in unit disk graphs. Our techniques also yield a constantfactor approximation algorithm for the weighted disk cover problem (covering a set of points in the plane with unit disks of minimum total weight) and a 3approximation algorithm for the weighted forwarding set problem (covering a set of points in the plane with weighted unit disks whose centers are all contained in a given unit disk). 1