Local Approximation Schemes for Ad Hoc and Sensor Networks

We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs

Scalable energy-efficient routing in mobile Ad hoc network

The quick deployment without any existing infrastructure makes mobile ad hoc networks (MANET) a striking choice for dynamic situations such as military and rescue operations, disaster recovery, and so on and so forth. However, routing remains one of the major issues in MANET due to the highly dynamic and distributed environment. Energy consumption is also a significant issue in ad hoc networks since the nodes are battery powered. This report discusses some major dominating set based approaches to perform energy efficient routing in mobile ad hoc networks. It also presents the performance results for each of these mentioned approaches in terms of throughput, average end to end delay and the life time in terms of the first node failure. Based on the simulation results, I identified the key issues in these protocols regarding network life time. In this report, I propose and discuss a new approach “Dynamic Dominating Set Generation Algorithm” (DDSG) to optimize the network life time. This algorithm dynamically selects dominating nodes during the process of routing and thus creates a smaller dominating set. DDSG algorithm thereby eliminates the energy consumption from the non-used dominating nodes. In order to further increase the network life time, the algorithm takes into consideration the threshold settings which helps to distribute the process of routing within the network. This helps to eliminate a single dominating node from getting drained out by continuous transmission and reception of packets. In this report, the detailed algorithmic design and performance results through simulation is discussed

Sampling of graph signals via randomized local aggregations

Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges arise and defining an efficient sampling strategy is not straightforward. Recently, several works have addressed this problem. The most common techniques select a subset of nodes to reconstruct the entire signal. However, such methods often require the knowledge of the signal support and the computation of the sparsity basis before sampling. Instead, in this paper we propose a new approach to this issue. We introduce a novel technique that combines localized sampling with compressed sensing. We first choose a subset of nodes and then, for each node of the subset, we compute random linear combinations of signal coefficients localized at the node itself and its neighborhood. The proposed method provides theoretical guarantees in terms of reconstruction and stability to noise for any graph and any orthonormal basis, even when the support is not known.Comment: IEEE Transactions on Signal and Information Processing over Networks, 201

Applications and Routing Management of Wireless Sensor Networks

In this paper, we first describe some current and future applications of sensor networks. We present the conceptual framework of distributed routing strategies for wireless sensor networks. We show that under reasonable assumptions, this routing scheme guarantees ‘shortest path property’ which is quite desirable for sensor networks. We then discuss how this framework can be used to support distributed applications for sensor nodes acting as mobile devices. These schemes work well in low mobility conditions. We also discuss the performance of these heuristics

Near-Optimal Distributed Approximation of Minimum-Weight Connected Dominating Set

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. MCDS is a classical NP-hard problem and the achieved approximation factor $O(\log n)$ is known to be optimal up to a constant factor, unless P=NP. Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be optimal modulo logarithmic factors (for any approximation), following [Das Sarma et al.---STOC'11].Comment: An extended abstract version of this result appears in the proceedings of 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014

Energy Constrained Dominating Set for Clustering in Wireless Sensor Networks

Using partitioning in wireless sensor networks to create clusters for routing, data management, and other protocols has been proven as a way to ensure scalability and to deal with sensor network shortcomings such as limited communication ranges and energy. Choosing a cluster head within each cluster is important because cluster heads use additional energy for their responsibilities and that burden needs to be carefully passed around. Many existing protocols either choose cluster heads randomly or use nodes with the highest remaining energy. We introduce the energy constrained minimum dominating set (ECDS) to model the problem of optimally choosing cluster heads with energy constraints. We propose a distributed algorithm for the constrained dominating set which runs in O(log n log Δ) rounds with high probability. We experimentally show that the distributed algorithm performs well in terms of energy usage, node lifetime, and clustering time and, thus, is very suitable for wireless sensor networks

On the Complexity of Local Distributed Graph Problems

This paper is centered on the complexity of graph problems in the well-studied LOCAL model of distributed computing, introduced by Linial [FOCS '87]. It is widely known that for many of the classic distributed graph problems (including maximal independent set (MIS) and $(\Delta+1)$-vertex coloring), the randomized complexity is at most polylogarithmic in the size $n$ of the network, while the best deterministic complexity is typically $2^{O(\sqrt{\log n})}$. Understanding and narrowing down this exponential gap is considered to be one of the central long-standing open questions in the area of distributed graph algorithms. We investigate the problem by introducing a complexity-theoretic framework that allows us to shed some light on the role of randomness in the LOCAL model. We define the SLOCAL model as a sequential version of the LOCAL model. Our framework allows us to prove completeness results with respect to the class of problems which can be solved efficiently in the SLOCAL model, implying that if any of the complete problems can be solved deterministically in $\log^{O(1)} n$ rounds in the LOCAL model, we can deterministically solve all efficient SLOCAL-problems (including MIS and $(\Delta+1)$-coloring) in $\log^{O(1)} n$ rounds in the LOCAL model. We show that a rather rudimentary looking graph coloring problem is complete in the above sense: Color the nodes of a graph with colors red and blue such that each node of sufficiently large polylogarithmic degree has at least one neighbor of each color. The problem admits a trivial zero-round randomized solution. The result can be viewed as showing that the only obstacle to getting efficient determinstic algorithms in the LOCAL model is an efficient algorithm to approximately round fractional values into integer values

Dominating sets and connected dominating sets in dynamic graphs

In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time O( 06\ub7polylog n) per update, where 06 is the maximum vertex degree in the graph. In both cases, we achieve an approximation ratio of O(log n), which is optimal up to a constant factor (under the assumption that P 6= NP). Although those two problems have been widely studied in the static and in the distributed settings, to the best of our knowledge we are the first to present efficient algorithms in the dynamic setting. As a further application of our approach, we also present an algorithm that maintains a Minimal Dominating Set in O(min( 06, m)) per update