Node-based scheduling with provable evacuation time

This paper studies the link scheduling problem in multihop wireless networks without future packet arrivals, with an aim of minimizing the time interval needed for evacuating all the existing packets. We consider the scenario with single-hop traffic flows under the one-hop interference model. In this setting, the minimum evacuation time problem is equivalent to the classic multigraph edge coloring problem, which is generally NP-hard. Although many approximation algorithms have been studied, almost all of them require computing the schedules (or the colors) all at once, and thus have a complexity that is dependent on the number of packets in the network. This, however, renders these algorithms unsuitable for the considered application of link scheduling for packet evacuation, as they typically incur an impractically high complexity when there are a large number of initial packets waiting to be transmitted, even if the underlying network has a small size (i.e., the node count and the link count). Instead, it is desirable to compute the schedules (or the colors) in an online fashion, i.e., to quickly compute one schedule at a time. Unfortunately, none of the existing online algorithms can guarantee an approximation ratio better (or smaller) than 2. To that end, in this paper we suggest two scheduling algorithms using a node-based approach, and prove that their approximation ratios are both no worse (or greater) than 3 over 2. In addition, these scheduling algorithms can also serve as an alternative for achieving Shannon's bound, which is well known in the graph coloring literature.