What Is the Use Of Collision Detection (in Wireless Networks)?

Abstract

We show that the asymptotic gain in the time complexity when using collision detection depends heavily on the task by investigating three prominent problems for wireless networks, i.e. the maximal independent set (MIS), broadcasting and coloring problem. We present lower and upper bounds for all three problems for the Growth-Bounded Graph such as the Unit Disk Graph. We prove that the bene_t of collision detection ranges from an exponential improvement down to no asymptotic gain at all. In particular, for the broadcasting problem our deterministic algorithm is running in time O(Dlog n). It is an exponential im- provement over prior work, if the diameter D is polylogarithmic in the number of nodes n, i.e. D 2 O(logc n) for some constant c.