Information gathering in ad-hoc radio networks with tree topology

Abstract

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-andforward protocol with running time O(n 1.5 ), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal.

Faster Information Gathering in Ad-Hoc Radio Tree Networks

“…In this model, we give a deterministic algorithm that completes information gathering in time O(n log log n). Our result significantly improves the previous upper bound of O(n log n) from [5]. To our knowledge, no lower bound for this problem is known, apart from the trivial bound of Ω(n) (since each rumor must be received by the root in a different time step).…”

“…Related work. The problem of information gathering for trees was introduced in [5], where the model without any collision detection was studied. In addition to the O(n log n)-time algorithm without aggregation -that we improve in this paper - [5] develops an O(n)-time algorithm for the model with aggregation, where a message can include any number of rumors.…”

“…The problem of information gathering for trees was introduced in [5], where the model without any collision detection was studied. In addition to the O(n log n)-time algorithm without aggregation -that we improve in this paper - [5] develops an O(n)-time algorithm for the model with aggregation, where a message can include any number of rumors. Another model studied in [5], called fire-and-forward, requires that a node cannot store any rumors; a rumor received by a node has to be either discarded or immediately forwarded.…”

“…In addition to the O(n log n)-time algorithm without aggregation -that we improve in this paper - [5] develops an O(n)-time algorithm for the model with aggregation, where a message can include any number of rumors. Another model studied in [5], called fire-and-forward, requires that a node cannot store any rumors; a rumor received by a node has to be either discarded or immediately forwarded. For fire-and-forward protocols, a tight bound of Θ(n 1.5 ) is given in [5].…”

“…Another model studied in [5], called fire-and-forward, requires that a node cannot store any rumors; a rumor received by a node has to be either discarded or immediately forwarded. For fire-and-forward protocols, a tight bound of Θ(n 1.5 ) is given in [5].…”