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13
Relay Placement for Higher Order Connectivity in Wireless Sensor Networks
"... Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number o ..."
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Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number of additional (relay) nodes so that the induced communication graph is 2connected 1. The problem is NPhard. In this paper we develop O(1)approximation algorithms that find close to optimal solutions in time O((kn) 2) for achieving kedge connectivity of n nodes. The worst case approximation guarantee is 10, but the algorithm produces solutions that are far better than this bound suggests. We also consider extensions to higher dimensions, and the scheme that we develop for points in the plane, yields a bound of 2dMST where dMST is the maximum degree of a minimumdegree Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles). We also prove that if the sensors are uniformly and identically distributed in a unit square, the expected number of relay nodes required goes to zero as the number of sensors goes to infinity.
Improved Approximation Algorithms for Relay Placement
"... Abstract. In the relay placement problem the input is a set of sensors and a number r ≥ 1, the communication range of a relay. In the onetier version of the problem the objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or rela ..."
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Cited by 15 (0 self)
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Abstract. In the relay placement problem the input is a set of sensors and a number r ≥ 1, the communication range of a relay. In the onetier version of the problem the objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance r if both vertices are relays and within distance 1 otherwise. The twotier version adds the restrictions that the path must go through relays, and not through sensors. We present a 3.11approximation algorithm for the onetier version and a PTAS for the twotier version. We also show that the onetier version admits no PTAS, assuming P � = NP. 1
Wireless network design via 3decompositions
 Inf. Process. Lett
"... We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset U ⊆ X of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set S ⊆ X − U o ..."
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Cited by 8 (3 self)
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We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset U ⊆ X of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set S ⊆ X − U of points so that the unitdisc graph of S + U is connected. Let ∆ be the smallest integer so that for any finite V ⊆ X for which the unitdisc graph is connected, this graph contains a spanning tree with maximum degree ≤ ∆. The best known approximation ratio for STMSP was ∆ − 1 [10]. We improve this ratio to ⌊( ∆ + 1)/2 ⌋ + 1 + ε. In the Minimum Power Spanning Tree (MPST) problem, V = X is finite, and the goal is to find a “range assignment ” {p(v) : v ∈ V} on the nodes so that the edge set {uv ∈ E: d(uv) ≤ min{p(u),p(v)}} contains a spanning tree, and ∑ v∈V p(v) is minimized. We consider a particular case {0,1}MPST of MPST when the distances are in {0,1}; here the goal is to find a minimum size set S ⊆ V of ”active ” nodes so that the graph (V,E0 + E1(S)) is connected, where E0 = {uv: d(uv) = 0}, and E1(S) is the set the edges in E1 = {uv: d(uv) = 1} with both endpoints in S. We will show that the (5/3+ε)approximation scheme for MPST of [1] achieves a ratio 3/2 for {0,1}distances. This answers an open question posed in [9].
An efficient relay sensors placing algorithm for connectivity in wireless sensor networks
 Lecture Notes in Computer Science
, 2006
"... Randomly deployed sensor networks often make initial communication gaps inside the deployed area, even in an extremely highdensity network. How to add relay sensors such that the underlying graph is connected and the number of relay sensors added is minimized is an important problem in wireless sen ..."
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Cited by 3 (0 self)
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Randomly deployed sensor networks often make initial communication gaps inside the deployed area, even in an extremely highdensity network. How to add relay sensors such that the underlying graph is connected and the number of relay sensors added is minimized is an important problem in wireless sensor networks. This paper presents an Efficient Relay Sensor Placing Algorithm (ERSPA) for solving such a problem. Compared with the minimum spanning tree algorithm and the greedy algorithm, ERSPA achieves better performance in terms of the number of relay sensors added. Simulation results show that the average number of relay sensors added by the minimal spanning tree algorithm is approximately two times that of the ERSPA algorithm.
An approximation algorithm for a bottleneck ksteiner tree problem in the euclidean plane
 Information Processing Letters
"... We study a bottleneck Steiner tree problem: given a set P ={p1,p2,...,pn} of n terminals in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points such that the length of the longest edges in the tree is minimized. The problem has applications in the design o ..."
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We study a bottleneck Steiner tree problem: given a set P ={p1,p2,...,pn} of n terminals in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points such that the length of the longest edges in the tree is minimized. The problem has applications in the design of wireless communication networks. We give a ratio1.866 approximation algorithm for the problem. © 2002 Elsevier Science B.V. All rights reserved.
Deterministic Deployment of Wireless Sensor Networks
, 2009
"... We propose a new heuristic for deterministic deployment of wireless sensor networks when 1connectivity and minimum cost are the two competing objectives. Given a set of data sources and a base station, our aim is to introduce the minimum number of relays to the network so that every sensor is conne ..."
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We propose a new heuristic for deterministic deployment of wireless sensor networks when 1connectivity and minimum cost are the two competing objectives. Given a set of data sources and a base station, our aim is to introduce the minimum number of relays to the network so that every sensor is connected to the base station via some multihop path. We assume that the data sources and base station lie in a plane, and that every sensor and relay has the same fixed communication radius. Our heuristic is based on the GEOSTEINER algorithms for the Steiner minimal tree problem, and proves to be much more accurate than the current best heuristics for the 1connected deployment problem, especially in the case of sparse data source distributions.
Improved Approximation Algorithms for SingleTiered Relay Placement ∗
, 2015
"... We consider the problem of SingleTiered Relay Placement with Basestations, which takes as input a set S of sensors and a set B of basestations described as points in a normed space (M,d), and real numbers 0 < r ≤ R. The objective is to place a minimum cardinality set Q of wireless relay nodes t ..."
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We consider the problem of SingleTiered Relay Placement with Basestations, which takes as input a set S of sensors and a set B of basestations described as points in a normed space (M,d), and real numbers 0 < r ≤ R. The objective is to place a minimum cardinality set Q of wireless relay nodes that connects S and B according to the following rules. The sensors in S can communicate within distance r, relay nodes in Q can communicate within distance R, and basestations are considered to have an infinite broadcast range. Together the sets S, B, and Q induce an undirected graph G = (V,E) defined as follows: V = S ∪ B ∪ Q and E = {uvu, v ∈ B} ∪ {uvu ∈ Q and v ∈ Q ∪ B and d(u, v) ≤ R} ∪ {uvu ∈ S and v ∈ S ∪ Q ∪ B and d(u, v) ≤ r}. Then Q connects S and B when this induced graph is connected. In the case of the
Approximation algorithms for VLSI routing
, 2000
"... This thesis gives improved approximation algorithms and heuristics for several NPhard problems arising in the global routing phase of physical VLSI design. In each of these problems interconnection topologies must be specified for nets consisting of a source and multiple sink terminals. Different o ..."
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This thesis gives improved approximation algorithms and heuristics for several NPhard problems arising in the global routing phase of physical VLSI design. In each of these problems interconnection topologies must be specified for nets consisting of a source and multiple sink terminals. Different optimization objectives are used, depending on the functionality of the nets. We address the singlenet routing problem under three of the most important objectives: minimizing length, skew, and number of buffers. We also address a multinet global buffered routing problem in which a large number of nets must be routed simultaneously using only buffers located in a given set of regions, each with prescribed capacity. The problem of finding a minimumlength interconnection of a net using only horizontal and vertical wires, the so called rectilinear Steiner tree (RST) problem, has long been one of the fundamental problems in the field of electronic design automation. In this thesis we give a new RST heuristic which has at its core a recent 3/2 approximation algorithm of Rajagopalan and Vazirani for the metric Steiner tree problem on quasibipartite graphs— these are graphs that do not contain edges connecting pairs of Steiner vertices. Our new RST