Fault-tolerant Virtual Backbone Research Articles

Computing Minimum k-Connected m-Fold Dominating Set in General Graphs

Connected dominating set (CDS) problem has been extensively studied in the literature due to its applications in many domains, including computer science and operations research. For example, CDS has been recommended to serve as a virtual backbone in wireless sensor networks (WSNs). Since sensor nodes in WSNs are prone to failures, it is important to build a fault-tolerant virtual backbone that maintains a certain degree of redundancy. A fault-tolerant virtual backbone can be modeled as a k-connected m-fold dominating set (k, m)-CDS. For a connected graph G = (V, E) and two fixed integers k and m, a node set C ⊆ V is a (k, m)-CDS of G if every node in V\C has at least m neighbors in C, and the subgraph of G induced by C is k-connected. Previous to this work, approximation algorithms with guaranteed performance ratio in a general graph were known only for k ≤ 3. This paper makes significant progress by presenting a (2k − 1)α0 approximation algorithm for general k and m with m ≥ k, where α0 is the performan...

Fault-Tolerant Virtual Backbone in Heterogeneous Wireless Sensor Network

To save energy and alleviate interferences in a wireless sensor network, the usage of virtual backbone was proposed. Because of accidental damages or energy depletion, it is desirable to construct a fault tolerant virtual backbone, which can be modeled as a $k$-connected $m$-fold dominating set (abbreviated as $(k,m)$-CDS) in a graph. A node set $C\subseteq V(G)$ is a $(k,m)$-CDS of graph $G$ if every node in $V(G)\backslash C$ is adjacent with at least $m$ nodes in $C$ and the subgraph of $G$ induced by $C$ is $k$-connected. In this paper, we present an approximation algorithm for the minimum $(3,m)$-CDS problem with $m\geq3$. The performance ratio is at most $\gamma$, where $\gamma=\alpha+8+2\ln(2\alpha-6)$ for $\alpha\geq4$ and $\gamma=3\alpha+2\ln2$ for $\alpha<4$, and $\alpha$ is the performance ratio for the minimum $(2,m)$-CDS problem. Using currently best known value of $\alpha$, the performance ratio is $\ln\delta+o(\ln\delta)$, where $\delta$ is the maximum degree of the graph, which is asymptotically best possible in view of the non-approximability of the problem. This is the first performance-guaranteed algorithm for the minimum $(3,m)$-CDS problem on a general graph. Furthermore, applying our algorithm on a unit disk graph which models a homogeneous wireless sensor network, the performance ratio is less than 27, improving previous ratio 62.3 by a large amount for the $(3,m)$-CDS problem on a unit disk graph.

Unique identity and localization based replica node detection in hierarchical wireless sensor networks

Clustering in Wireless sensor networks (WSN) is a prevalent Hierarchical network management technique. Though disjoint clusters are generally preferred, overlapping clusters find its prominence in some applications of inter-cluster routing, time-synchronization and node localization. Replica node detection is a major challenge in overlapping clusters. This paper aims at replica node detection in overlapping clusters based on two methods, Replica detection based on RFID (RDBRFID) and Replica detection based on Localization techniques (RDBLT). The first method uses RFID for unique node identification and the second method detects replica by identifying its locality based on received signal strength (RSSI) and Triangulation method. These methods are implemented and their performance is compared with Multicast and non clustered methods: Randomized multicast (RM), Line selected multicast (LSM), Fault tolerant virtual back bone tree (FTVBT) and K-coverage WSN. It is observed that RDBRFID exhibits better detection rate and lesser communication overhead due to its deterministic approach.

Approximation Algorithm for Minimum Weight Fault-Tolerant Virtual Backbone in Unit Disk Graphs

In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone can be modeled as a $k$-connected $m$-fold dominating set ($(k,m)$-CDS for short). In this paper, we present a constant approximation algorithm for the minimum weight $(k,m)$-CDS problem in unit disk graphs under the assumption that $k$ and $m$ are two fixed constants with $m\geq k$. Prior to this work, constant approximation algorithms are known for $k=1$ with weight and $2\leq k\leq 3$ without weight. Our result is the first constant approximation algorithm for the $(k,m)$-CDS problem with general $k,m$ and with weight. The performance ratio is $(\alpha+2.5k\rho)$ for $k\geq 3$ and $(\alpha+2.5\rho)$ for $k=2$, where $\alpha$ is the performance ratio for the minimum weight $m$-fold dominating set problem and $\rho$ is the performance ratio for the subset $k$-connected subgraph problem (both problems are known to have constant performance ratios.)

On Approximating Minimum 3-Connected $m$-Dominating Set Problem in Unit Disk Graph

Over years, virtual backbone has attracted lots of attention as a promising approach to deal with the broadcasting storm problem in wireless networks. Frequently, the problem of a quality virtual backbone is formulated as a variation of the minimum connected dominating set problem. However, a virtual backbone computed in this way is not resilient against topology change since the induced graph by the connected dominating set is one-vertex-connected. As a result, the minimum $k$ -connected $m$ -dominating set problem is introduced to construct a fault-tolerant virtual backbone. Currently, the best known approximation algorithm for the problem in unit disk graph by Wang assumes $k \leq 3$ and $m \geq 1$ , and its performance ratio is 280 when $k = m = 3$ . In this paper, we use a classical result from graph theory, Tutte decomposition, to design a new approximation algorithm for the problem in unit disk graph for $k \leq 3$ and $m \geq 1$ . In particular, the algorithm features with (a) a drastically simple structure and (b) a much smaller performance ratio, which is nearly 62 when $k = m = 3$ . We also conduct simulation to evaluate the performance of our algorithm.

Randomized fault-tolerant virtual backbone tree to improve the lifetime of wireless sensor networks

Backbone nodes are effective for routing in wireless networks because they reduce the energy consumption in sensor nodes. Packet delivery only occurs through the backbone nodes, which depletes the energy in the backbone drastically. Several backbone construction algorithms, including energy-aware virtual backbone tree, virtual backbone tree algorithm for minimal energy consumption and multihop cluster-based stable backbone tree, fail to form a complete backbone when converting important nodes, such as a cut vertex tree node to a non-backbone node. Thus we propose a fault-tolerant virtual backbone tree (FTVBT) algorithm that addresses all of these conflicts and we give theoretical derivations of the bounds for the probability that a sensor node can connect with the backbone. Furthermore, randomized FTVBT improves FTVBT by redistributing non-tree nodes randomly among all the eligible tree nodes based on their fitness values, thereby decreasing the rapid depletion of energy in a particular node and increasing the network lifetime. We performed simulations in NS2 and analyzed the experimental results.

On Construction of Quality Fault-Tolerant Virtual Backbone in Wireless Networks

In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the k-connected m-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded so far with arbitrary k ≥ 3 and m ≥ 1 pair. We propose a new strategy for computing a smaller-size 3-connected m-dominating set in a unit disk graph with any m ≥ 1. We show the approximation ratio of our algorithm is constant and its running time is polynomial. We also conduct a simulation to examine the average performance of our algorithm. Our result implies that while there exists a constant factor approximation algorithm for the k-connected m-dominating set problem with arbitrary k ≤ 3 and m ≥ 1 pair, the k-connected m-dominating set problem is still open with k > 3.

A distributed design for minimum 2-Connected m-Dominating Set in bidirectional wireless ad-hoc networks

Wireless ad-hoc network is widely used in many fields for its convenience and outstanding suitability. Because of the inherent lack of infrastructure and the nature of wireless channels, people select the k-Connected m-Dominating Set ((k, m)-CDS) in a network as a fault-tolerant virtual backbone to help the routing process, which will save the energy of non-dominators and improve the network performance significantly. Considering the economic cost and efficiency, we choose (2, m)-CDS as the object of this paper, which is helpful enough in practical applications and has a smaller size. We firstly study the existing algorithms for (k, m)-CDS and figure out the problems of these designs. Then we propose a new distributed algorithm named Dominating Set Based Algorithm (DSBA) with three sub-routines: Dominating Set Algorithm (DSA), Connection Algorithm (CA), and Connectivity Expansion Algorithm (CEA). Instead of commonly used Maximal Independent Set (MIS), we pick dominating set directly from the given graph, and then connect them by a two-step ring based connecting strategy to satisfy the 2-connectivity. We also provide the correctness and complexity analysis of DSBA. At last, we compare DSBA with the last construction Distributed Deterministic Algorithm (DDA) by several numerical experiments. The simulation results show that DSBA improves over 30 percent of the performance of DDA, proving that DSBA is more practical for real-world applications.

On the [formula omitted]-domination numbers of iterated line digraphs

An (h,k)-dominating set in a digraph G is a subset D of V(G) such that the subdigraph induced by D is h-connected and for every vertex v of G, v is in-dominated and out-dominated by at least k vertices in D. The (h,k)-domination number γh,k(G) of G is the minimum cardinality of an (h,k)-dominating set in G. An (h,k)-dominating set finds applications to fault-tolerant location problems of resources in communication networks and fault-tolerant virtual backbone in wireless networks.Let G be a connected d-regular digraph and 1≤k<d. Let Lm(G) denote the m-iterated line digraph of G. In this note, we show that γh,k(Lm(G))=kdm−1|V(G)| for all m≥2 and 0≤h≤min{k,⌊d2⌋}. From our results, the (h,k)-domination numbers of d-ary (generalized) de Bruijn and Kautz digraphs are determined for 0≤h≤min{k,⌊d2⌋}, which strengthen the previously known results on (generalized) de Bruijn and Kautz digraphs.

On minimum m-connected k-dominating set problem in unit disc graphs

Minimum m-connected k-dominating set problem is as follows: Given a graph G=(V,E) and two natural numbers m and k, find a subset S⊆V of minimal size such that every vertex in V∖S is adjacent to at least k vertices in S and the induced graph of S is m-connected. In this paper we study this problem with unit disc graphs and small m, which is motivated by the design of fault-tolerant virtual backbone for wireless sensor networks. We propose two approximation algorithms with constant performance ratios for m≤2. We also discuss how to design approximation algorithms for the problem with arbitrarily large m.