TY - JOUR

T1 - Improved approximation algorithms for single-tiered relay placement

AU - Calinescu, Gruia

AU - Grimmer, Benjamin

AU - Misra, Satyajayant

AU - Tongngam, Sutep

AU - Xue, Guoliang

AU - Zhang, Weiyi

N1 - Funding Information:
Gruia Calinescu research was supported in part by NSF Grant CCF-0515088. Benjamin Grimmer research was supported in part by a College of Science Undergraduate Summer Research Award. Satyajayant Misra research was done while at Arizona State University, and was supported in part by ARO Grant W911NF-04-1-0385, and NSF Grants CNS-1248109 and HRD-1345232. Sutep Tongngam research was done while at the Illinois Institute of Technology, and was supported in part by NSF Grant CCF-0515088. Guoliang Xue research was supported in part by NSF Grant CCF-1115129 and ARO Grant W911AF-09-1-0467. The information reported here does not reflect the position or the policy of the federal government. Weiyi Zhang research was done while at Arizona State University, and was supported in part by NSF Grant ANI-0312635.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We consider the problem of Single-Tiered Relay Placement with Basestations, which takes as input a set (Formula presented.) of sensors and a set (Formula presented.) of basestations described as points in a normed space (Formula presented.) , and real numbers (Formula presented.). The objective is to place a minimum cardinality set (Formula presented.) of wireless relay nodes that connects (Formula presented.) and (Formula presented.) according to the following rules. The sensors in (Formula presented.) can communicate within distance (Formula presented.) , relay nodes in (Formula presented.) can communicate within distance (Formula presented.) , and basestations are considered to have an infinite broadcast range. Together the sets (Formula presented.) , and (Formula presented.) induce an undirected graph (Formula presented.) defined as follows: (Formula presented.) and (Formula presented.) and (Formula presented.) and (Formula presented.) and (Formula presented.) and (Formula presented.). Then (Formula presented.) connects (Formula presented.) and (Formula presented.) when this induced graph is connected. In the case of the two-dimensional Euclidean plane, we get a (Formula presented.) -approximation algorithm, improving the previous best ratio of 3.11. Let (Formula presented.) be the maximum number of points on a unit ball with pairwise distance strictly bigger than 1. Under certain assumptions, we have a (Formula presented.) -approximation algorithm. When biconnectivity is required, we show that a variant of our previously proposed algorithm has approximation ratio of (Formula presented.). In the case of the two-dimensional Euclidean plane, our ratio of 7 improves our previous bound of 16.

AB - We consider the problem of Single-Tiered Relay Placement with Basestations, which takes as input a set (Formula presented.) of sensors and a set (Formula presented.) of basestations described as points in a normed space (Formula presented.) , and real numbers (Formula presented.). The objective is to place a minimum cardinality set (Formula presented.) of wireless relay nodes that connects (Formula presented.) and (Formula presented.) according to the following rules. The sensors in (Formula presented.) can communicate within distance (Formula presented.) , relay nodes in (Formula presented.) can communicate within distance (Formula presented.) , and basestations are considered to have an infinite broadcast range. Together the sets (Formula presented.) , and (Formula presented.) induce an undirected graph (Formula presented.) defined as follows: (Formula presented.) and (Formula presented.) and (Formula presented.) and (Formula presented.) and (Formula presented.) and (Formula presented.). Then (Formula presented.) connects (Formula presented.) and (Formula presented.) when this induced graph is connected. In the case of the two-dimensional Euclidean plane, we get a (Formula presented.) -approximation algorithm, improving the previous best ratio of 3.11. Let (Formula presented.) be the maximum number of points on a unit ball with pairwise distance strictly bigger than 1. Under certain assumptions, we have a (Formula presented.) -approximation algorithm. When biconnectivity is required, we show that a variant of our previously proposed algorithm has approximation ratio of (Formula presented.). In the case of the two-dimensional Euclidean plane, our ratio of 7 improves our previous bound of 16.

KW - Approximation algorithm

KW - Biconnectivity

KW - Steiner points

KW - Wireless network

UR - http://www.scopus.com/inward/record.url?scp=84961059767&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961059767&partnerID=8YFLogxK

U2 - 10.1007/s10878-014-9823-0

DO - 10.1007/s10878-014-9823-0

M3 - Article

AN - SCOPUS:84961059767

VL - 31

SP - 1280

EP - 1297

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 3

ER -