A Note on Node Coloring in the SINR Model
نویسندگان
چکیده
A V-coloring of a graph G is a coloring of the nodes of G with V colors in such a way any two neighboring nodes have different colors. We prove that there exists a O(∆ log n) time distributed algorithm computing a O(∆)-coloring for unit disc graphs under the signal-tointerference-plus-noise ratio (SINR)-based physical model (∆ is the maximum degree of the graph). We also show that, for a well defined constant d, a d-hop O(∆)-coloring allows us to schedule an interference free MAC protocol under the physical SINR constraints. For instance this allows us to prove that any point-to-point message passing algorithm with running time τ can be simulated in the SINR model in O(∆(log n+ τ)) time using messages of well chosen size. All our algorithms are proved to be correct with high probability. Key-words: Node coloring, Distributed algorithms, SINR interference model, time complexity, Radio networks. ∗ Laboratoire d’Informatique Fondamentale de Lille (LIFL), Université de Lille 1 (USTL) – EPI DOLPHIN – INRIA LNE † corresponding author : [email protected] in ria -0 04 08 67 0, v er si on 4 22 O ct 2 00 9 A Note on Node Coloring in the SINR Model Résumé : A V-coloring of a graph G is a coloring of the nodes of G with V colors in such a way any two neighboring nodes have different colors. We prove that there exists a O(∆ log n) time distributed algorithm computing a O(∆)-coloring for unit disc graphs under the signal-tointerference-plus-noise ratio (SINR)-based physical model (∆ is the maximum degree of the graph). We also show that, for a well defined constant d, a d-hop O(∆)-coloring allows us to schedule an interference free MAC protocol under the physical SINR constraints. For instance this allows us to prove that any point-to-point message passing algorithm with running time τ can be simulated in the SINR model in O(∆(log n+ τ)) time using messages of well chosen size. All our algorithms are proved to be correct with high probability. Mots-clés : Node coloring, Distributed algorithms, SINR interference model, time complexity, Radio networks. in ria -0 04 08 67 0, v er si on 4 22 O ct 2 00 9 A Note on Node Coloring in the SINR Model 3
منابع مشابه
Simple Distributed Δ + 1 Coloring in the SINR Model
In wireless ad hoc 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 a very simple 4∆ coloring along with a color reduction technique to achieve ∆+ 1 colo...
متن کاملSimple Distributed Delta + 1 Coloring in the SINR Model
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. Al...
متن کاملExperimental Evaluation of Distributed Node Coloring Algorithms for Wireless Networks
In this paper we evaluate distributed node coloring algorithms for wireless networks using the network simulator Sinalgo [1]. 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-Co...
متن کاملA Note on Uniform Power Connectivity in the SINR Model
In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously....
متن کاملExperimental Evaluation of Distributed Node Coloring Algorithms in the SINR Model
Nodes in wireless ad hoc or sensor networks can only communicate efficiently when interference is kept low. One approach to minimizing interference is to limit the number of concurrently transmitting nodes in every neighborhood by using a periodic schedule. We periodically divide time into slots and assign one time slot to each sender. A sender is only allowed to transmit messages in its time s...
متن کامل