MAC Layer and Coloring

Abstract

The Medium Access Layer is part of the Data Link Layer (layer 2 of the OSI model) and sits directly on top of the Physical Layer (layer 1). Its purpose is to manage access to the shared wireless medium. If transmissions from two different nodes arrive simultaneously at a receiver, neither of them is received due to interference.

In this section we start by describing the problem in more detail and give a short and necessarily incomplete overview of some of the approaches that are widely used by the network community, such as CSMA, CSMA/CA, and TDMA (see [249] for a more detailed survey). Later on, we will introduce some other approaches for managing concurrent transmissions, namely scheduling, frequency assignment and coloring approaches. We will conclude the introductory section by introducing several variants of coloring problems and try to argument why coloring problems are an important and useful subject to study in order to understand and solve MAC layer issues. In Section 4.2 we present an overview of some distributed coloring algorithms. We start with simple heuristics and try to gradually develop more and more sophisticated methods. We then describe two completely different approaches to efficiently solve coloring problems in a nearly optimal fashion.While the second approach is based on a non-constructive combinatorial proof, the first one, called deterministic coin tossing, can lend itself to practical solutions to the coloring problem.