Gossiping with Interference Constraints in Radio Chain Networks

Abstract

In this paper, we study the problem of gossiping with neighboring interference constraint in radio chain networks. Gossiping (also called total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and efficient algorithms that attain this makespan. We focus on the case where the transmission network is a chain (directed path or line) network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We assume that during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover we have neighboring interference constraints under which a node cannot receive a message if one of its neighbors is sending. A round consists of a set of non-interfering (or compatible) calls and uses one step. We completely solve the gossiping problem for P n , the chain network on n nodes, and give an algorithm that completes the gossiping in 3n − 5 rounds (for n > 3), which is exactly the makespan.

Gossiping with interference in radio ring networks

“…One can also try to determine the exact gossiping time for other simple topologies. In Bermond et al (2020), we completely solved the gossiping problem in radio chain networks with the same model proving that the makespan is 3n − 5 for n > 3. The case of grids might be solvable.…”

“…(2006) to O(n log n) with the help of probabilistic argument. In Bermond et al (2020), we completely solved the gossiping problem in radio chain networks with the same model and proved that the makespan is 3n − 5 for n > 3.…”

“…a node can receive or send, but cannot both receive and send during the same step. Furthermore, in order to model neighboring interferences, we use a primary node interference model like the one used in Bermond et al (2009Bermond et al ( , 2006Bermond et al ( , 2020; G asieniec and Potapov (2002); Klasing et al (2008). In this model, when one node is transmitting, its own power prevents any other signal to be properly received in its neighbors (near-far effect of antennas).…”

“…We first give a non trivial proof of the lower bounds. The tools developed in Bermond et al (2020) to design optimal protocols for chain networks cannot be used for rings. Though an optimal protocol can easily be found for n ≡ 0 (mod 12), for other congruences the problem is not easy as one of the difficulties is to ensure that a sender has a useful message to transmit.…”