A lower bound for radio broadcast
Journal of Computer and System Sciences
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Hardness and approximation of Gathering in static radio networks
PERCOMW '06 Proceedings of the 4th annual IEEE international conference on Pervasive Computing and Communications Workshops
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We study two algorithmical problems inspired from routing constraints in a multihop synchronous radio network. Our objective is to satisfy a given set of communication requests in the following model: nodes send omnidirectional radio transmissions in synchronous slots; during a given slot, a node can receive a message from an adjacent node if and only if no other neighbour is transmitting - otherwise, radio interferences may occur if two or more neighbors transmit in the same slot -. The objective is to minimize the number of slots used. The two problems differ in that the routing policy may be imposed (DAWN-path), or not (DAWN-request). In this second case, a path must be assigned for each request, to define the nodes to use to reach the destination from the source. We present some complexity results, in particular showing that both problems are NP-hard when the network is restricted to a tree. We also present a polynomial algorithm in O(n2K) when the number of requests is bounded (by above) by a constant K.