Link scheduling in sensor networks: distributed edge coloring revisited

We consider the problem of link scheduling in a sensor network employing a TDMA MAC protocol. Our link scheduling algorithm involves two phases. In the first phase, we assign a color to each edge in the network such that no two edges incident on the same node are assigned the same color. We propose a distributed edge coloring algorithm that needs at most (δ+1) colors, where δ is the maximum degree of the graph. To the best of our knowledge, this is the first distributed algorithm that can edge color a graph with at most (δ+1) colors. In the second phase, we map each color to a unique timeslot and attempt to identify a direction of transmission along each edge such that the hidden terminal and the exposed terminal problems are avoided. Next, considering topologies for which a feasible solution does not exist, we obtain a direction of transmission for each edge using additional timeslots, if necessary. Finally, we show that reversing the direction of transmission along every edge leads to another feasible direction of transmission. Using both the transmission assignments we obtain a TDMA MAC schedule, which enables two-way communication between every pair of neighbors. For acyclic topologies, we show that at most 2(δ+1) timeslots are required. Through simulations we show that for sparse graphs with cycles the number of timeslots assigned is close to 2(δ+1).