Multi-dimensional Conflict Graph Based Computing for Optimal Capacity in MR-MC Wireless Networks

• Published in: 2010 IEEE 30th International Conference on Distributed Computing Systems pp. 774 - 783
• Main Authors: Hongkun Li, Yu Cheng, Chi Zhou, Pengjun Wan
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.01.2010
• Subjects: Capacity planning; Computer networks; Constraint optimization; Heuristic algorithms; Linear programming; Processor scheduling; Resource management; Routing; Throughput; Wireless networks
• ISBN: 142447261X; 9781424472611
• ISSN: 1063-6927
• DOI: 10.1109/ICDCS.2010.58

Optimal capacity analysis in multi-radio multi-channel wireless networks by nature incurs the formulation of a mixed integer programming, which is NP-hard in general. The current state of the art mainly resorts to heuristic algorithms to obtain an approximate solution. In this paper, we propose a novel concept of multi-dimensional conflict graph (MDCG). Based on MDCG, the capacity optimization issue can be accurately modeled as a linear programming (LP) multi-commodity flow (MCF) problem, augmented with maximal independent set (MIS) constraints. The MDCG-based solution will provide not only the maximum throughput or utility, but also the optimal configurations on routing, channel assignment, and scheduling. Moreover, the MDCG-based optimal capacity planning can exploit dynamic channel swapping, which is difficult to achieve for those existing heuristic algorithms. A particular challenge associated with the MDCG-based capacity analysis is to search exponentially many possible MISs. We theoretically show that in fact only a small set of critical MISs, termed as critical MIS set, will be scheduled in the optimal resource allocation. We then develop a polynomial computing method, based on a novel scheduling index ordering (SIO) concept, to search the critical MIS set. Extensive numerical results are presented to demonstrate the efficiency of the MDCG-based resource allocation compared to well-known heuristic algorithm presented in, and the efficiency of SIO-based MIS computing compared to the widely adopted random algorithm for searching MISs.