Low Delay Scheduling in Wireless Network

In a wireless network, a sophisticated algorithm is required to schedule simultaneous wireless transmissions while satisfying interference constraint that two neighboring nodes can not transmit simultaneously. The scheduling algorithm need to be excellent in performance while being simple and distributed so as to be implementable. The result of Tassiulas and Ephremides (1992) imply that the algorithm, scheduling transmissions of nodes in the 'maximum weight independent set' (MWIS) of network graph, is throughput optimal. However, algorithmically the problem of finding MWIS is known to be NP-hard and hard to approximate. This raises the following questions: is it even possible to obtain throughput optimal simple, distributed scheduling algorithm? if yes, is it possible to minimize delay of such an algorithm? Motivated by these questions, we first provide a distributed throughput optimal algorithm for any network topology. However, this algorithm may induce exponentially large delay. To overcome this, we present an order optimal delay algorithm for any non-expanding network topology. Networks deployed in geographic area, like wireless networks, are likely to be of this type. Our algorithm is based on a novel distributed graph partitioning scheme which may be of interest in its own right. Our algorithm for non-expanding graph takes O (n) total message exchanges or O(l) message exchanges per node to compute a schedule.