Deterministic broadcasting in ad hoc radio networks

Abstract

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario.For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time O(n 11/6 ). Next we show that broadcasting with acknowledgement is not possible in this model at all.For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs.

The Complexity of Making Unique Choices: Approximating 1-in-k SAT

“…Another application of the 1-in-kHS problem is to the computation of ad-hoc selective families. An (n, h)-selective family is a combinatorial object defined and studied in [2] to deal with a broadcast problem in a radio network of unknown topology. An (n, h)-selective family is a collection S of subsets of [n] such that for every set F ⊆ [n] such that |F | ≤ h there is a set S ∈ S such that |F ∩ S| = 1.…”

Reliable Broadcast in Wireless Mobile Ad Hoc Networks

“…Additionally, each round has R+3 slots out of which the first control slot has a duration of O(log n) and the others O (1). Hence, the overall duration of a round is in the order of O(D(log n + R + 2)) and finally O(D log n) for a constant R. The synchronous network model we use in this paper has been widely considered to analyze the complexity of the broadcasting problem [16], [17], [5], [18], [19].…”

“…Furthermore, when Δ = 7, the protocol is optimal for constant diameter networks [21]. Other deterministic broadcasting algorithms are given in [18], which consider networks with/without collision detection mechanisms. Although these solutions claim to operate correctly even if topology changes due to mobility, this is true in a limited sense.…”

“…For example, the solution described in [17] works correctly if mobility induced topology changes occur only at inter-frame boundaries, where a frame consists of a number of time-slots. Similarly, the solutions by Chlebus et al [18] do not explicitly take mobility into consideration.…”

Faster Information Gathering in Ad-Hoc Radio Tree Networks

“…The naïve RoundRobin algorithm (see the next section) completes broadcasting in time O(n 2 ). Following a sequence of papers [6,18,2,3,21,11] where this naïve bound was gradually improved, it is now known that broadcasting can be solved in time O(n log D log log(D∆/n)) [10], where D is the diameter of G and ∆ is its maximum in-degree. This nearly matches the lower bound of Ω(n log D) from [9].…”