Simple Distributed Δ + 1 Coloring in the SINR Model

Abstract

In wireless ad hoc or sensor networks, distributed node coloring is a fundamental problem closely related to establishing efficient communication through TDMA schedules. For networks with maximum degree ∆, a ∆ + 1 coloring is the ultimate goal in the distributed setting as this is always possible. In this work we propose ∆ + 1 coloring algorithms for the synchronous and asynchronous setting. All algorithms have a runtime of O(∆ log n) time slots. This improves on the previous algorithms for the SINR model either in terms of the number of required colors or the runtime and matches the runtime of local broadcasting in the SINR model (which can be seen as a lower bound).

Experimental Evaluation of Distributed Node Coloring Algorithms for Wireless Networks

“…Rand4DColor is based on a very simple randomized algorithm well-known for message-passing models since decades [16,Chapter 10]. It has recently been proven to be efficient in the SINR model by Fuchs and Prutkin [2]. The phase-based algorithm computes a valid (∆ + 1)-coloring in O(∆ log n) time slots.…”

“…The algorithm ColorRed by Fuchs and Prutkin [2] computes a valid (∆+1)-coloring in O(∆ log n) time slots. ColorRed computes two levels of MISs, the first level MIS determines independent leaders, which then coordinate the activity of the remaining nodes.…”

“…All considered algorithms operate in the realistic signal-to-interference-and-noise-ratio (SINR) model of interference. We evaluate two recent coloring algorithms, Rand4DColor and ColorReduction (in the following ColorRed), proposed by Fuchs and Prutkin in [2], the MW-Coloring algorithm introduced by Moscibroda and Wattenhofer [3] and transferred to the SINR model by Derbel and Talbi [4], and a variant of the coloring algorithm of Yu et al [5]. We additionally consider several practical improvements to the algorithms and evaluate their performance in both static and dynamic scenarios.Our experiments show that Rand4DColor is very fast, computing a valid (4∆)-coloring in less than one third of the time slots required for local broadcasting, where ∆ is the maximum node degree in the network.…”

“…We denote the variant by YuColor and introduce it in Section 2.4. Finally, we consider two algorithms Fuchs and Prutkin proposed in [2,9]. Rand4DColor is a very simple randomized coloring algorithm that computes a (4∆)-coloring by simply selecting a new random color whenever a conflict is detected.…”

Brief Announcement

“…In this announcement, we briefly state recent results regarding more efficient distributed node coloring algorithms in the SINR model by Fuchs and Prutkin [6,7]. They adapted simple and well-known coloring algorithms from the messagepassing model to the SINR model.…”