On the Complexity of Scheduling in Wireless Networks

• Published in: EURASIP journal on wireless communications and networking Vol. 2010; no. 1
• Main Authors: Joo, Changhee, Sharma, Gaurav, Shroff, Ness B., Mazumdar, Ravi R.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2010; Springer Nature B.V; SpringerOpen
• Subjects: Adaptive Cross-Layer Strategies for Fourth Generation Wireless Communications; Communications Engineering; Decomposition; Engineering; Fixed rates; Graphs; Information Systems Applications (incl.Internet); Networks; Optimization algorithms; Research Article; Signal,Image and Speech Processing; Studies; Wireless networks; Geometric Graph; Greedy Algorithm; Interference Model; Schedule Problem; Maximal Matchings
• ISSN: 1687-1499; 1687-1472; 1687-1499
• DOI: 10.1155/2010/418934

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.