Radio Network Distributed Algorithms in the Unknown Neighborhood Model

The paper deals with radio network distributed algorithms where nodes are not aware of their one hop neighborhood. Given an n-node graph modeling a multihop network of radio devices, we give a O(log n) time distributed algorithm that computes w.h.p., a constant approximation value of the degree of each node. We also provide a O(∆ log n+ log n) time distributed algorithm that computes w.h.p., a constant approximation value of the local maximum degree of each node, where the global maximum degree ∆ of the graph is not known. Using our algorithms as a plug-and-play procedure, we show that many existing distributed algorithms requiring the knowledge of ∆ to execute efficiently can be run with essentially the same time complexity by using the local maximum degree instead of ∆. In other words, using the local maximum degree is sufficient to break the symmetry in a local and efficient manner. We illustrate this claim by investigating the complexity of some basic problems. First, we investigate the generic problem of simulating any classical message passing algorithm in the radio network model. Then, we study the fundamental edge/node coloring problem in the special case of unit disk graphs. The obtained results show that knowing the local maximum degree allows to coordinate the nodes locally and avoid intereferences in radio networks. Key-words: Distributed algorithms, time complexity, Radio networks. ∗ Laboratoire d’Informatique Fondamentale de Lille (LIFL), Université de Lille 1 (USTL). Supported by the DOLPHIN inria project team. † corresponding author : [email protected] ‡ Laboratoire d’Informatique Fondamentale de Lille (LIFL), Université de Lille 1 (USTL). Supported by the DOLPHIN inria project team. in ria -0 02 92 15 5, v er si on 3 15 J ul 2 00 8 Radio Network Distributed Algorithms in the Unknown Neighborhood Model Résumé : The paper deals with radio network distributed algorithms where nodes are not aware of their one hop neighborhood. Given an n-node graph modeling a multihop network of radio devices, we give a O(log n) time distributed algorithm that computes w.h.p., a constant approximation value of the degree of each node. We also provide a O(∆ log n+log n) time distributed algorithm that computes w.h.p., a constant approximation value of the local maximum degree of each node, where the global maximum degree ∆ of the graph is not known. Using our algorithms as a plugand-play procedure, we show that many existing distributed algorithms requiring the knowledge of ∆ to execute efficiently can be run with essentially the same time complexity by using the local maximum degree instead of ∆. In other words, using the local maximum degree is sufficient to break the symmetry in a local and efficient manner. We illustrate this claim by investigating the complexity of some basic problems. First, we investigate the generic problem of simulating any classical message passing algorithm in the radio network model. Then, we study the fundamental edge/node coloring problem in the special case of unit disk graphs. The obtained results show that knowing the local maximum degree allows to coordinate the nodes locally and avoid intereferences in radio networks. Mots-clés : Distributed algorithms, time complexity, Radio networks. in ria -0 02 92 15 5, v er si on 3 15 J ul 2 00 8 Radio Network Distributed Algorithms in the Unknown Neighborhood Model 3