Publication

The impact of mobility on the time complexity for deterministic broadcasting in radio networks

André Schiper, David Cavin, Yoav Sasson
2011
Journal Articles

Abstract

We study the time complexity for deterministic broadcasting algorithms in mobile radio networks. The broadcast operation consists of a source node successfully communicating its message to every other node. In multi-hop radio networks such as MANETs, the message may traverse multiple other nodes. Nodes have no prior knowledge besides the number n of nodes in the network and its diameter D. The problem we address has been extensively studied for static networks. Our work quantifies the impact of mobility. We consider three families of graphs: undirected graphs of constant contention degree, undirected graphs of non-constant contention degree and directed graphs of non-constant contention degree. We prove the lower bounds of Omega(n log n) time slots for the first family, Omega(n(2)/D-2 log D + D) time slots for the second and Omega(n(2)/D-2 log D + n log D) for the third. At the time of writing, the corresponding tightest lower bounds derived in the static case are, respectively, Omega(D log n), Omega(n log n log n/D) and Omega(n log D).

Official source

https://infoscience.epfl.ch/entities/publication/6d807140-7dca-4a90-b51d-3f3829a56881

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André Schiper, David Cavin, Yoav Sasson
2011
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6d807140-7dca-4a90-b51d-3f3829a56881

About this result

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (31)

Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. In formal terms, a directed graph is an ordered pair where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.

Graph (discrete mathematics)

In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.

Directed acyclic graph

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions.

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