We present a series of approximation algorithms for finding a small weakly-connected dominating set (WCDS) in a given graph to be used in clustering mobile ad hoc networks. The structure of a graph can be simplified using WCDS's and made more succinct for routing in ad hoc networks. The theoretical performance ratio of these algorithms is O(ln Δ) compared to the minimum size WCDS, where Δ is the maximum degree of the input graph. The first two algorithms are based on the centralized approximation algorithms of Guha and Khuller cite guha-khuller-1998 for finding small connected dominating sets (CDS's). The main contribution of this work is a completely distributed algorithm for finding small WCDS's and the performance of this algorithm is shown to be very close to that of the centralized approach. Comparisons between our work and some previous work (CDS-based) are also given in terms of the size of resultant dominating sets and graph connectivity degradation.

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Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks

This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. The widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors but does not know the entire network topology, is assumed. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before.It is shown that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires T(uVu) messages, where V is the set of processors in the network. It is proved that, if one counts messages of bounded length, then broadcast requires T(uEu) messages, where E is the set of edges in the network.Assuming an intermediate model in which each vertex knows the topology of the network in radius r ≥ 1 from itself, matching upper and lower bounds of T(min{uEu, uVu1+T(l)/r}) is proved on the number of messages of bounded length required for broadcast. Both the upper and lower bounds hold for both synchronous and asynchronous network models.The same results hold for the construction of spanning trees, and various other global tasks.

/pdf/a-trade-off-between-information-and-communication-in-21fuaza4gl.pdf

A trade-off between information and communication in broadcast protocols

In this paper, we address the Topology control with Cooperative Communication (TCC) problem in ad hoc wireless networks. Cooperative communication is a novel model introduced recently that allows combining partial messages to decode a complete message. The objective of the TCC problem is to obtain a strongly-connected topology with minimum total energy consumption. We show that the TCC problem is NIP-complete and design two distributed and localized algorithms to be used by the nodes to set up their communication ranges. Both algorithms can be applied on top of any symmetric, strongly-connected topology to reduce total power consumption. The first algorithm uses a distributed decision process at each node that makes use of only 2-hop neighborhood information. The second algorithm sets up the transmission ranges of nodes iteratively, over a maximum of six steps, using only 1-hop neighborhood information. We analyze the performance of our approaches through extensive simulation.

/pdf/topology-control-in-ad-hoc-wireless-networks-using-21rtxwpoh0.pdf

Topology control in ad hoc wireless networks using cooperative communication

Purpose – The purpose of this paper is to address the novel issues of executing graph optimization tasks on distributed simple growing biological systems.Design/methodology/approach – The author utilizes biological and physical processes to implement non‐classical, and in principle more powerful, computing devices. The author experimentally verifies his previously discovered techniques on approximating spanning trees during single cell ontogeny. Plasmodium, a vegetative stage of slime mold Physarum polycephalum, is used as experimental computing substrate to approximate spanning trees. Points of given data set are represented by positions of nutrient sources, then a plasmodium is placed on one of the data points. Plasmodium develops and span all sources of nutrients, connecting them by protoplasmic strands. The protoplasmic strands represent edges of the computed spanning tree.Findings – Offers experimental implementation of plasmodium devices for approximation of spanning tree.Practical implications – Th...

Growing spanning trees in plasmodium machines

We experimentally demonstrate that computation of spanning trees and implementation of general purpose storage-modification machines can be executed by a vegetative state of the slime mold Physarum polycephalum. We advance theory and practice of reaction-diffusion computing by studying a biological model of reaction-diffusion encapsulated in a membrane.

From reaction-diffusion to Physarum computing

A distributed algorithm based on echo algorithms is presented which constructs the minimum-weight spanning tree in a general undirected graph In the worst case, the algorithm needs at most (2m+2(n-1) log (n/2)) messages and (2d log n) time, where d is the diameter of the network In the best case, it needs only 2m messages and 2d time The algorithm works in phases, and each phase consists of a down wave and an up wave When the number of fragments is cut by at least one half in each phase, it needs at most O(log n) phases On average, the algorithm needs only (m) messages and O(d) time The algorithm itself is simple, so that other distributed algorithms based on it can be derived more easily >

A distributed algorithm for minimum weight spanning trees based on echo algorithms

The problem of scheduling n independent jobs on an m-dimensional hypercube system to minimize the finish time is discussed. After some preliminary definitions are given, it is shown that a simple nonpreemptive algorithm, called largest dimension first, can have an asymptotic optimal performance and an absolute bound no worse than 2-1/2/sup m/. An absolute lower bound for the schedules generated by any algorithm using decreasing dimension lists is proved. A preemptive scheduling algorithm is also given. >

/pdf/job-scheduling-on-a-hypercube-4t9jtdz4t3.pdf

Y. Zhu

Papers

A distributed algorithm for minimum weight spanning trees based on echo algorithms

Job scheduling on a hypercube