Complexity in geometric SINR

In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NP-completeness proofs in such a model. In particular, we prove two problems to be NP-complete: Scheduling and One-Shot Scheduling. The first problem consists in finding a minimum-length schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximum-weight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.

[1]  Madhav V. Marathe,et al.  Approximation Algorithms for Channel Assignment in Radio Networks , 1998 .

[2]  Rene L. Cruz,et al.  Optimal routing, link scheduling and power control in multihop wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[3]  Izhak Rubin,et al.  On the performance of graph-based scheduling algorithms for packet radio networks , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[4]  Anthony Ephremides,et al.  Scheduling broadcasts in multihop radio networks , 1990, IEEE Trans. Commun..

[5]  Anthony Ephremides,et al.  Wireless Link Scheduling With Power Control and SINR Constraints , 2006, IEEE Transactions on Information Theory.

[6]  Bruce E. Hajek,et al.  Link scheduling in polynomial time , 1988, IEEE Trans. Inf. Theory.

[7]  Aravind Srinivasan,et al.  End-to-end packet-scheduling in wireless ad-hoc networks , 2004, SODA '04.

[8]  J. Boudec,et al.  Optimal power control, scheduling, and routing in UWB networks , 2004, IEEE Journal on Selected Areas in Communications.

[9]  Anders Hansson,et al.  Comparison between graph-based and interference-based STDMA scheduling , 2001, MobiHoc '01.

[10]  S. Papavassiliou,et al.  Joint optimal channel base station and power assignment for wireless access , 1996, TNET.

[11]  Suresh Singh,et al.  PAMAS—power aware multi-access protocol with signalling for ad hoc networks , 1998, CCRV.

[12]  Harry B. Hunt,et al.  NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs , 1998, J. Algorithms.

[13]  Di Yuan,et al.  A column generation method for spatial TDMA scheduling in ad hoc networks , 2004, Ad Hoc Networks.

[14]  T. Moscibroda,et al.  The Worst-Case Capacity of Wireless Sensor Networks , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[15]  Roger Wattenhofer,et al.  Topology control meets SINR: the scheduling complexity of arbitrary topologies , 2006, MobiHoc '06.

[16]  Ness B. Shroff,et al.  On the Complexity of Scheduling in Wireless Networks , 2006, MobiCom '06.

[17]  Panganamala Ramana Kumar,et al.  Computing and communicating functions over sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[18]  Jimmi Grönkvist,et al.  Interference-based scheduling in spatial reuse TDMA , 2005 .

[19]  Kin K. Leung,et al.  Integrated link adaptation and power control for wireless IP networks , 2000, VTC2000-Spring. 2000 IEEE 51st Vehicular Technology Conference Proceedings (Cat. No.00CH37026).

[20]  Lili Qiu,et al.  Impact of Interference on Multi-Hop Wireless Network Performance , 2003, MobiCom '03.

[21]  Leandros Tassiulas,et al.  Cross-Layer Design for Power Efficiency and QoS Provisioning in Multi-Hop Wireless Networks , 2006, IEEE Transactions on Wireless Communications.

[22]  Roger Wattenhofer,et al.  The Complexity of Connectivity in Wireless Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[23]  Roger Wattenhofer,et al.  Coloring unstructured radio networks , 2005, SPAA '05.

[24]  Izhak Rubin,et al.  Impact of power control on the performance of ad hoc wireless networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[25]  Roger Wattenhofer,et al.  Protocol Design Beyond Graph-Based Models , 2006, HotNets.

[26]  Piyush Gupta,et al.  Critical Power for Asymptotic Connectivity in Wireless Networks , 1999 .

[27]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[28]  Paolo Santi,et al.  Computationally efficient scheduling with the physical interference model for throughput improvement in wireless mesh networks , 2006, MobiCom '06.

[29]  R. Wattenhofer,et al.  Interference arises at the receiver , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

[30]  Sajal K. Das,et al.  Rate Allocation and Admission Control for Differentiated Services in CDMA Data Networks , 2007, IEEE Transactions on Mobile Computing.

[31]  Subramanian Ramanathan,et al.  Scheduling algorithms for multihop radio networks , 1993, TNET.