Energy conservation via domatic partitions

Abstract

Using a dominating set as a coordinator in wireless networks has been proposed in many papers as an energy conservation technique. Since the nodes in a dominating set have the extra burden of coordination, energy resources in such nodes will drain out more quickly than in other nodes. To maximize the lifetime of nodes in the network, it has been proposed that the role of coordinators be rotated among the nodes in the network. One abstraction that has been considered for the problem of picking a collection of coordinators and cycling through them, is the domatic partition problem. This is the problem of partitioning the set of the nodes of the network into dominating sets with the aim of maximizing the number of dominating sets. In this paper, we consider the k-domatic partition problem. A k-dominating set is a subset D of nodes such that every node in the network is at distance at most k from D. The k-domatic partition problem seeks to partition the network into maximum number of k-dominating sets. We point out that from the point of view of saving energy, it may be better to construct a k-domatic partition for k > 1.We present three deterministic, distributed algorithms for finding large k-domatic partitions for k > 1. Each of our algorithms constructs a k-domatic partition of size at least a constant fraction of the largest possible (k − 1)-domatic partition. Our first algorithm runs in constant time on unit ball graphs (UBGs) in Euclidean space assuming that all nodes know their positions in a global coordinate system. Our second algorithm drops knowledge of global coordinates and instead assumes that pairwise distances between neighboring nodes are known. This algorithm runs in O(log * n) time on UBGs in a metric space with constant doubling dimension. Our third algorithm drops all reliance on geometric information, using connectivity information only. This algorithm runs in O(log Δ · log * n) time on growth-bounded graphs. Euclidean UBGs, UBGs in metric spaces with constant doubling dimension, and growth-bounded graphs are successively more general models of wireless networks and Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. all three models include the well-known, but somewhat simplistic wireless network models such as unit disk graphs.

Optimal network locality in distributed virtualized data-centers

“…If the dominating distance of a dominator is extended to s hops, we call the set of dominators an s-dominating set. Given a graph G and a positive integer K, the problem of determining if there exists a domatic partition or s-domatic partition of size K is NP-complete [40,41].…”

“…A few recent papers have dealt with domatic partition in ad-hoc networks [43,41] and peer-to-peer networks [44]. These are works related to our algorithm development, although our objective is different.…”

Employing (1 − ∊) Dominating Set Partitions as Backbones in Wireless Sensor Networks

“…The problem of finding the maximum number of disjoint dominating sets in an arbitrary graph is known as the domatic partition problem [6]. The majority of the recent work [6] [10,11] [20,21] [22,23,24][27] focuses on designing centralized and distributed logarithmic or constant factor approximation solutions to the strict domatic partition problem which means the output of the algorithm should be the maximum number of disjoint fully dominating sets, where that maximum is never larger than the minimum degree δ plus one. Some of these works tie in the problem solution to maximizing the clustering or target coverage lifetime in sensor networks [22] [27].…”

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“…As noted in [11], it has become a key concept to measure the ability of networks to support efficient algorithms or to realize specific tasks efficiently. For wireless networks, this concept has found many uses in solving many distributed communication problems [12], distributed resourcemanagement [13], information exchange among producers and consumers [14], and for determining other performance qualities such as energy-conservation in wireless sensor networks [15].…”