Limitations of Current Wireless Scheduling Algorithms.

We consider the problem of scheduling wireless links in the physical model, where we seek a partition of a given a set of wireless links into the minimum number of subsets satisfying the signal-to-interference-and-noise-ratio SINR constraints. We consider the two families of approximation algorithms that are known to guarantee $$O\\log {n}$$ approximation for the scheduling problem, where n is the number of links. We present network constructions showing that the approximation ratios of those algorithms are no better than logarithmic, both in n and in $$\\varDelta $$, where $$\\varDelta $$ is a geometric parameter --- the ratio of the maximum and minimum link lengths.