Improved Approximation Algorithms for Relay Placement

In the relay placement problemthe input is a set of sensors and a number ri¾? 1, the communication range of a relay. 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 rif both vertices are relays and within distance 1 otherwise. We present a 3.11-approximation algorithm, and show that the problem admits no PTAS, assuming P${}\ne{}$NP.

[1]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[2]  Xiao-Dong Hu,et al.  Connected Set Cover Problem and Its Applications , 2006, AAIM.

[3]  Errol L. Lloyd,et al.  Relay Node Placement in Wireless Sensor Networks , 2011, IEEE Transactions on Computers.

[4]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[5]  Yang Yang,et al.  Minimum Spanning Tree with Neighborhoods , 2007, AAIM.

[6]  Hai Liu,et al.  Fault-Tolerant Relay Node Placement in Wireless Sensor Networks , 2005, COCOON.

[7]  Marek Karpinski,et al.  On Some Tighter Inapproximability Results (Extended Abstract) , 1999, ICALP.

[8]  Rong-chii Duh,et al.  Approximation of k-set cover by semi-local optimization , 1997, STOC '97.

[9]  Brenda S. Baker,et al.  Approximation algorithms for NP-complete problems on planar graphs , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[10]  Lusheng Wang,et al.  Approximations for Steiner Trees with Minimum Number of Steiner Points , 2000, Theor. Comput. Sci..

[11]  P. Berman,et al.  On Some Tighter Inapproximability Results , 1998, Electron. Colloquium Comput. Complex..

[12]  Eytan Modiano,et al.  Mobile backbone networks --: construction and maintenance , 2006, MobiHoc '06.

[13]  Joseph S. B. Mitchell,et al.  Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems , 1999, SIAM J. Comput..

[14]  Lusheng Wang,et al.  Relay sensor placement in wireless sensor networks , 2008, Wirel. Networks.

[15]  Ding-Zhu Du,et al.  An approach for proving lower bounds: solution of Gilbert-Pollak's conjecture on Steiner ratio , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[16]  Satyajayant Misra,et al.  Fault-Tolerant Relay Node Placement in Wireless Sensor Networks: Problems and Algorithms , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[17]  J. Orestes Cerdeira,et al.  Requiring Connectivity in the Set Covering Problem , 2005, J. Comb. Optim..

[18]  Erik D. Demaine,et al.  Deploying sensor networks with guaranteed capacity and fault tolerance , 2005, MobiHoc '05.