Gossiping on Interval Graphs

We present an algorithm that produces a schedule of transmissions to achieve gossiping in a system where nodes are equipped with radio transceivers; diierent nodes have transceivers with diierent ranges. We assume that all the nodes are placed on a line and that all communication occurs in one dimension. Finally, unlike traditional system models for gossiping, we assume that all nodes within range can hear a transmission and that simultaneous transmissions may cause information loss via collisions. The gossiping algorithm we develop decomposes a system connguration into a spine tree and uses this structure to recursively produce a transmission schedule. We illustrate this process via an extensive example.