On the Complexity of Scheduling in Wireless Networks
1 Department of EECE, Korea University of Technology and Education, 1800 Chungjeollo, Cheonan, Chungnam 330-708, Republic of Korea
2 D. E. Shaw & Co., L.P., 120 West Forty-Fifth Street, New York, NY 10036, USA
3 Departments of ECE & CSE, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210, USA
4 Department of ECE, University of Waterloo, 200 University Avenue, West Waterloo, ON, Canada, N2L 3G1
EURASIP Journal on Wireless Communications and Networking 2010, 2010:418934 doi:10.1155/2010/418934Published: 7 September 2010
We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of -hop interference models, under which no two links within a -hop distance can successfully transmit at the same time. For a given , we can obtain a throughput-optimal scheduling policy by solving the well-known maximum weighted matching problem. We show that for , the resulting problems are NP-Hard that cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, for geometric unit-disk graphs that can be used to describe a wide range of wireless networks, the problems admit polynomial time approximation schemes within a factor arbitrarily close to 1. In these network settings, we also show that a simple greedy algorithm can provide a 49-approximation, and the maximal matching scheduling policy, which can be easily implemented in a distributed fashion, achieves a guaranteed fraction of the capacity region for "all ." The geometric constraints are crucial to obtain these throughput guarantees. These results are encouraging as they suggest that one can develop low-complexity distributed algorithms to achieve near-optimal throughput for a wide range of wireless networks.