DECK: A distributed, asynchronous and exact k-connectivity detection algorithm for Wireless Sensor Networks

Abstract

Wireless Sensor Networks (WSNs) are one of the widespread platforms for communications and remote sensing. A robust WSN should tolerate the failures of nodes without losing the connection to active nodes. A network is k-connected if all active nodes remain connected after failures in k-1 arbitrary nodes. Finding (detecting) the k value in a WSN is a significant operation to estimate the connectivity robustness, reliability and load balancing level of the network. Also, the detection of k values provides useful information for connectivity restoration, lower bound of node degree, critical nodes and possible cycles. In this paper, we propose an asynchronous distributed algorithm (DECK) for k-connectivity detection in WSNs. In the proposed algorithm, each node estimates a local k using its 2-hop neighborhood information and then a distributed linked list of minimum estimations is created between the nodes. Finally, the sink node validates the correctness of detected values by finding the number of node-disjoint paths to the node having the minimum estimation. We analyze our algorithm in detail, provide theoretical analysis, testbed experiments on the IRIS nodes and simulation results in the TOSSIM simulator by comparing with the other algorithms. The comprehensive testbed and simulation results show that the proposed algorithm always finds exact k values with reasonable energy consumption while the correct detection ratios of existing distributed algorithms on similar networks are usually less than 40%.

Introduction

Recent advances in communication and processing platforms have provided new perspectives, applications and challenges. Wireless sensor networks (WSNs) are one of the important platforms for communications that are composed of sensor nodes aiming to accomplish certain tasks. WSNs are increasingly being used in several applications such as disaster relief, military surveillance, underground mines, health care, intelligent systems and outer space exploration.

Generally, in WSNs the nodes connect to each other if they are in the radio range of each other. These autonomous nodes can collect sensed data from the environment and execute algorithms in a distributed manner to form self-organizing networks. Based on local processes, nodes can decide to transmit the sensed data to a special sink node which acts as a gateway between the WSN and its users. In a typical multi-hop sensor network application, the data may be aggregated and relayed to the sink or the commands may be sent from the sink and forwarded with some intermediate nodes to reach to a target node.

Due to challenging environmental conditions in these applications and also the limited energy source of nodes, each node may fail individually or collapse as groups of nodes. This situation increases the risk of partitioning in the network, which can make active nodes unreachable from the sink. Thus, the network connectivity should be maintained to achieve robust communication.

A k-connected WSN has at least k node-disjoint paths between the sink and other nodes, and the network remains connected after failures of any k-1 nodes. The k-connectivity related problems on WSNs have been subjected in various researches from different perspectives including power assignment, topology maintenance, node deployment and finally k-connectivity detection (i.e. finding the k value of a given network). From the power assignment viewpoint, the problem is how to set the minimum transmission ranges of nodes such that the resulting topologies become k-connected [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. The topology maintenance category includes approaches that repair WSN topologies to obtain k-connected networks [12], [13], [14], [15]. In the research thread related to the node deployment, one aim is to deploy nodes in a network area in a way that the network becomes k-connected [16], [17], [18], [19], [20], [21], [22]. Another aim in the node deployment research thread is to find the probability of the k-connectedness of a given network [23], [24], [25], [26], [27], [28], [29], [30]. Our concern is to find the k value of a network which is a significant operation that provides meaningful information about the fault tolerance status of the given network.

In this paper, we propose a distributed exact k-connectivity detection algorithm (DECK) which finds the k value of a given network. The proposed algorithm has 3 main phases. At the first phase, the sink starts the proposed algorithm and each node estimates a local k value from its 2-hop local subgraph. These estimated local values will be equal to or lower than the global k value. In the second phase, a distributed linked list is established between the nodes, which is built according to the minimum estimations. Finally, in the third phase, the sink validates the correctness of estimations and finds the exact global k value using the previously constructed linked list.

The rest of this paper is organized as follows. The related work is surveyed in Section 2. The problem formulation is given in Section 3. The description of DECK and its theoretical analysis are given in Section 4. The experimental analysis of the proposed algorithm with its counterparts is given in Section 5. Finally, conclusions are drawn in Section 6.