TY - JOUR

T1 - On minimizing the total power of k-strongly connected wireless networks

AU - Shpungin, Hanan

AU - Segal, Michael

N1 - Funding Information:
Acknowledgements The authors wish to thank Daniel Berend for long and fruitful discussions, valuable suggestions and a lot of help and support. The authors would also like to thank anonymous reviewers for their helpful comments that improved the paper. Hanan Shpungin has been supported in part by the Lynn and William Frankel Center for Computer Sciences. Work by Michael Segal has been supported by REMON (4G networking) consortium.

PY - 2010/5/1

Y1 - 2010/5/1

N2 - Given a wireless network, we want to assign each node a transmission power, which will enable transmission between any two nodes (via other nodes). Moreover, due to possible faults, we want to have at least k vertex-disjoint paths from any node to any other, where k is some fixed integer, depending on the reliability of the nodes. The goal is to achieve this directed k-strong connectivity with a minimal overall power assignment. The problem is NP-Hard for any k ≤ 1 already for planar networks. Here we first present an optimal power assignment for uniformly spaced nodes on a line for any k ≤ 1. We also prove a number of useful properties of power assignment which are also of independent interest. Based on it, we design an approximation algorithm for linear radio networks with factor min{2(Δ/δα}, where Δ and δ are the maximal and minimal distances between adjacent nodes respectively and parameter α ≤ 1 being the distance-power gradient. We then extend it to the weighted version. Finally, we develop an approximation algorithm with factor O(k 2), for planar case, which is, to the best of our knowledge, the first non-trivial result for this problem.

AB - Given a wireless network, we want to assign each node a transmission power, which will enable transmission between any two nodes (via other nodes). Moreover, due to possible faults, we want to have at least k vertex-disjoint paths from any node to any other, where k is some fixed integer, depending on the reliability of the nodes. The goal is to achieve this directed k-strong connectivity with a minimal overall power assignment. The problem is NP-Hard for any k ≤ 1 already for planar networks. Here we first present an optimal power assignment for uniformly spaced nodes on a line for any k ≤ 1. We also prove a number of useful properties of power assignment which are also of independent interest. Based on it, we design an approximation algorithm for linear radio networks with factor min{2(Δ/δα}, where Δ and δ are the maximal and minimal distances between adjacent nodes respectively and parameter α ≤ 1 being the distance-power gradient. We then extend it to the weighted version. Finally, we develop an approximation algorithm with factor O(k 2), for planar case, which is, to the best of our knowledge, the first non-trivial result for this problem.

KW - Approximation algorithms

KW - Connectivity

KW - Power assignment

KW - Wireless networks

UR - http://www.scopus.com/inward/record.url?scp=77954084313&partnerID=8YFLogxK

U2 - 10.1007/s11276-009-0189-7

DO - 10.1007/s11276-009-0189-7

M3 - Article

AN - SCOPUS:77954084313

VL - 16

SP - 1075

EP - 1089

JO - Wireless Networks

JF - Wireless Networks

SN - 1022-0038

IS - 4

ER -