The MV-Decomposition: Definition and Application to the Distance-2 Broadcast Problem in Multi-Hops Radio Networks

Abstract : We present a new tool called the "mv- decomposition", and we describe some interesting algorithmic properties about it. We propose an algorithm with a complexity of $O(m)$ to build a mv-decomposition for each bipartite graph. We use this mv-decomposition to propose a solution to the distance-2 broadcast problem in a synchronous multi-hops radio networks where adjacent transmissions are subject to interferences. More precisely, we propose two algorithms of resolution: the first one guarantees a complete distance-2 broadcast scheme using $O((log n )2)$ slots for a time complexity of $O (m (log n)2)$, while the second builds a solution with a minimal number of transmissions for a time complexity of $O(m)$.