Distributed Connectivity Decomposition

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve information flow with size close to the connectivity by parallelizing it along the trees. More specifically, our distributed decomposition algorithms are as follows: (I) A decomposition of each undirected graph with vertex-connectivity $k$ into (fractionally) vertex-disjoint weighted dominating trees with total weight $\Omega(\frac{k}{\log n})$, in $\widetilde{O}(D+\sqrt{n})$ rounds. (II) A decomposition of each undirected graph with edge-connectivity $\lambda$ into (fractionally) edge-disjoint weighted spanning trees with total weight $\lceil\frac{\lambda-1}{2}\rceil(1-\varepsilon)$, in $\widetilde{O}(D+\sqrt{n\lambda})$ rounds. We also show round complexity lower bounds of $\tilde{\Omega}(D+\sqrt{\frac{n}{k}})$ and $\tilde{\Omega}(D+\sqrt{\frac{n}{\lambda}})$ for the above two decompositions, using techniques of [Das Sarma et al., STOC'11]. Moreover, our vertex-connectivity decomposition extends to centralized algorithms and improves the time complexity of [Censor-Hillel et al., SODA'14] from $O(n^3)$ to near-optimal $\tilde{O}(m)$. As corollaries, we also get distributed oblivious routing broadcast with $O(1)$-competitive edge-congestion and $O(\log n)$-competitive vertex-congestion. Furthermore, the vertex connectivity decomposition leads to near-time-optimal $O(\log n)$-approximation of vertex connectivity: centralized $\widetilde{O}(m)$ and distributed $\tilde{O}(D+\sqrt{n})$. The former moves toward the 1974 conjecture of Aho, Hopcroft, and Ullman postulating an $O(m)$ centralized exact algorithm while the latter is the first distributed vertex connectivity approximation

Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems

In many wireless networks, there is no fixed physical backbone nor centralized network management. The nodes of such a network have to self-organize in order to maintain a virtual backbone used to route messages. Moreover, any node of the network can be a priori at the origin of a malicious attack. Thus, in one hand the backbone must be fault-tolerant and in other hand it can be useful to monitor all network communications to identify an attack as soon as possible. We are interested in the minimum \emph{Connected Vertex Cover} problem, a generalization of the classical minimum Vertex Cover problem, which allows to obtain a connected backbone. Recently, Delbot et al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant approximation ratio of $2$ for this problem. In this paper, we propose a distributed and self-stabilizing version of their algorithm with the same approximation guarantee. To the best knowledge of the authors, it is the first distributed and fault-tolerant algorithm for this problem. The approach followed to solve the considered problem is based on the construction of a connected minimal clique partition. Therefore, we also design the first distributed self-stabilizing algorithm for this problem, which is of independent interest

Distributed Symmetry Breaking on Power Graphs via Sparsification

In this paper, we present efficient distributed algorithms for classical symmetry breaking problems, maximal independent sets (MIS) and ruling sets, in power graphs. We work in the standard CONGEST model of distributed message passing, where the communication network is abstracted as a graph $G$. Typically, the problem instance in CONGEST is identical to the communication network $G$, that is, we perform the symmetry breaking in $G$. In this work, we consider a setting where the problem instance corresponds to a power graph $G^k$, where each node of the communication network $G$ is connected to all of its $k$-hop neighbors. Our main contribution is a deterministic polylogarithmic time algorithm for computing $k$-ruling sets of $G^k$, which (for $k>1$) improves exponentially on the current state-of-the-art runtimes. The main technical ingredient for this result is a deterministic sparsification procedure which may be of independent interest. On top of being a natural family of problems, ruling sets (in power graphs) are well-motivated through their applications in the powerful shattering framework [BEPS JACM'16, Ghaffari SODA'19] (and others). We present randomized algorithms for computing maximal independent sets and ruling sets of $G^k$ in essentially the same time as they can be computed in $G$. We also revisit the shattering algorithm for MIS [BEPS JACM'16] and present different approaches for the post-shattering phase. Our solutions are algorithmically and analytically simpler (also in the LOCAL model) than existing solutions and obtain the same runtime as [Ghaffari SODA'16]

Broadcast in sparse conversion optical networks using fewest converters

Wavelengths and converters are shared by communication requests in optical networks. When a message goes through a node without a converter, the outgoing wavelength must be the same as the incoming one. This constraint can be removed if the node uses a converter. Hence, the usage of converters increases the utilization of wavelengths and allows more communication requests to succeed. Since converters are expensive, we consider sparse conversion networks, where only some specified nodes have converters. Moreover, since the usage of converters induces delays, we should minimize the use of available converters. The Converters Usage Problem (CUP) is to use a minimum number of converter so that each node can send messages to all the others (broadcasting). In this dissertation, we study the CUP in sparse conversion networks. We design a linear algorithm to find a wavelength assignment in tree networks such that, with the usage of a minimum number of available converters, every node can send messages to all the others. This is a generalization of [35], where each node has a converter. Our algorithm can assign wavelengths efficiently and effectively for one-to-one, multicast, and broadcast communication requests. A converter wavelength-dominates a node if there is a uniform wavelength path between them. The Minimal Wavelength Dominating Set Problem (MWDSP) is to locate a minimum number of converters so that all the other nodes in the network are wavelength-dominated. We use a linear complexity dynamic programming algorithm to solve the MWDSP for networks with bounded treewidth. One such solution provides a low bound for the optimal solution to the CUP

An improved MOEA/D algorithm for multi-objective multicast routing with network coding

Network coding enables higher network throughput, more balanced traffic, and securer data transmission. However, complicated mathematical operations incur when packets are combined at intermediate nodes, which, if not operated properly, lead to very high network resource consumption and unacceptable delay. Therefore, it is of vital importance to minimize various network resources and end-to-end delays while exploiting promising benefits of network coding. Multicast has been used in increasingly more applications, such as video conferencing and remote education. In this paper the multicast routing problem with network coding is formulated as a multi-objective optimization problem (MOP), where the total coding cost, the total link cost and the end-to-end delay are minimized simultaneously. We adapt the multi-objective evolutionary algorithm based on decomposition (MOEA/D) for this MOP by hybridizing it with a population-based incremental learning technique which makes use of the global and historical information collected to provide additional guidance to the evolutionary search. Three new schemes are devised to facilitate the performance improvement, including a probability-based initialization scheme, a problem-specific population updating rule, and a hybridized reproduction operator. Experimental results clearly demonstrate that the proposed algorithm outperforms a number of state-of-the-art MOEAs regarding the solution quality and computational time

Balancing the trade-off between cost and reliability for wireless sensor networks: a multi-objective optimized deployment method

The deployment of the sensor nodes (SNs) always plays a decisive role in the system performance of wireless sensor networks (WSNs). In this work, we propose an optimal deployment method for practical heterogeneous WSNs which gives a deep insight into the trade-off between the reliability and deployment cost. Specifically, this work aims to provide the optimal deployment of SNs to maximize the coverage degree and connection degree, and meanwhile minimize the overall deployment cost. In addition, this work fully considers the heterogeneity of SNs (i.e. differentiated sensing range and deployment cost) and three-dimensional (3-D) deployment scenarios. This is a multi-objective optimization problem, non-convex, multimodal and NP-hard. To solve it, we develop a novel swarm-based multi-objective optimization algorithm, known as the competitive multi-objective marine predators algorithm (CMOMPA) whose performance is verified by comprehensive comparative experiments with ten other stateof-the-art multi-objective optimization algorithms. The computational results demonstrate that CMOMPA is superior to others in terms of convergence and accuracy and shows excellent performance on multimodal multiobjective optimization problems. Sufficient simulations are also conducted to evaluate the effectiveness of the CMOMPA based optimal SNs deployment method. The results show that the optimized deployment can balance the trade-off among deployment cost, sensing reliability and network reliability. The source code is available on https://github.com/iNet-WZU/CMOMPA.Comment: 25 page

Cooperative localisation in underwater robotic swarms for ocean bottom seismic imaging.

Spatial information must be collected alongside the data modality of interest in wide variety of sub-sea applications, such as deep sea exploration, environmental monitoring, geological and ecological research, and samples collection. Ocean-bottom seismic surveys are vital for oil and gas exploration, and for productivity enhancement of an existing production facility. Ocean-bottom seismic sensors are deployed on the seabed to acquire those surveys. Node deployment methods used in industry today are costly, time-consuming and unusable in deep oceans. This study proposes the autonomous deployment of ocean-bottom seismic nodes, implemented by a swarm of Autonomous Underwater Vehicles (AUVs). In autonomous deployment of ocean-bottom seismic nodes, a swarm of sensor-equipped AUVs are deployed to achieve ocean-bottom seismic imaging through collaboration and communication. However, the severely limited bandwidth of underwater acoustic communications and the high cost of maritime assets limit the number of AUVs that can be deployed for experiments. A holistic fuzzy-based localisation framework for large underwater robotic swarms (i.e. with hundreds of AUVs) to dynamically fuse multiple position estimates of an autonomous underwater vehicle is proposed. Simplicity, exibility and scalability are the main three advantages inherent in the proposed localisation framework, when compared to other traditional and commonly adopted underwater localisation methods, such as the Extended Kalman Filter. The proposed fuzzy-based localisation algorithm improves the entire swarm mean localisation error and standard deviation (by 16.53% and 35.17% respectively) at a swarm size of 150 AUVs when compared to the Extended Kalman Filter based localisation with round-robin scheduling. The proposed fuzzy based localisation method requires fuzzy rules and fuzzy set parameters tuning, if the deployment scenario is changed. Therefore a cooperative localisation scheme that relies on a scalar localisation confidence value is proposed. A swarm subset is navigationally aided by ultra-short baseline and a swarm subset (i.e. navigation beacons) is configured to broadcast navigation aids (i.e. range-only), once their confidence values are higher than a predetermined confidence threshold. The confidence value and navigation beacons subset size are two key parameters for the proposed algorithm, so that they are optimised using the evolutionary multi-objective optimisation algorithm NSGA-II to enhance its localisation performance. Confidence value-based localisation is proposed to control the cooperation dynamics among the swarm agents, in terms of aiding acoustic exteroceptive sensors. Given the error characteristics of a commercially available ultra-short baseline system and the covariance matrix of a trilaterated underwater vehicle position, dead reckoning navigation - aided by Extended Kalman Filter-based acoustic exteroceptive sensors - is performed and controlled by the vehicle's confidence value. The proposed confidence-based localisation algorithm has significantly improved the entire swarm mean localisation error when compared to the fuzzy-based and round-robin Extended Kalman Filter-based localisation methods (by 67.10% and 59.28% respectively, at a swarm size of 150 AUVs). The proposed fuzzy-based and confidence-based localisation algorithms for cooperative underwater robotic swarms are validated on a co-simulation platform. A physics-based co-simulation platform that considers an environment's hydrodynamics, industrial grade inertial measurement unit and underwater acoustic communications characteristics is implemented for validation and optimisation purposes

Unified Role Assignment Framework For Wireless Sensor Networks

Wireless sensor networks are made possible by the continuing improvements in embedded sensor, VLSI, and wireless radio technologies. Currently, one of the important challenges in sensor networks is the design of a systematic network management framework that allows localized and collaborative resource control uniformly across all application services such as sensing, monitoring, tracking, data aggregation, and routing. The research in wireless sensor networks is currently oriented toward a cross-layer network abstraction that supports appropriate fine or course grained resource controls for energy efficiency. In that regard, we have designed a unified role-based service paradigm for wireless sensor networks. We pursue this by first developing a Role-based Hierarchical Self-Organization (RBSHO) protocol that organizes a connected dominating set (CDS) of nodes called dominators. This is done by hierarchically selecting nodes that possess cumulatively high energy, connectivity, and sensing capabilities in their local neighborhood. The RBHSO protocol then assigns specific tasks such as sensing, coordination, and routing to appropriate dominators that end up playing a certain role in the network. Roles, though abstract and implicit, expose role-specific resource controls by way of role assignment and scheduling. Based on this concept, we have designed a Unified Role-Assignment Framework (URAF) to model application services as roles played by local in-network sensor nodes with sensor capabilities used as rules for role identification. The URAF abstracts domain specific role attributes by three models: the role energy model, the role execution time model, and the role service utility model. The framework then generalizes resource management for services by providing abstractions for controlling the composition of a service in terms of roles, its assignment, reassignment, and scheduling. To the best of our knowledge, a generic role-based framework that provides a simple and unified network management solution for wireless sensor networks has not been proposed previously

Multi-vehicle refill scheduling with queueing

© 2017 We consider the problem of refill scheduling for a team of vehicles or robots that must contend for access to a single physical location for refilling. The objective is to minimise time spent in travelling to/from the refill station, and also time lost to queuing (waiting for access). In this paper, we present principled results for this problem in the context of agricultural operations. We first establish that the problem is NP-hard and prove that the maximum number of vehicles that can usefully work together is bounded. We then focus on the design of practical algorithms and present two solutions. The first is an exact algorithm based on dynamic programming that is suitable for small problem instances. The second is an approximate anytime algorithm based on the branch and bound approach that is suitable for large problem instances with many robots. We present simulated results of our algorithms for three classes of agricultural work that cover a range of operations: spot spraying, broadcast spraying and slurry application. We show that the algorithm is reasonably robust to inaccurate prediction of resource utilisation rate, which is difficult to estimate in cases such as spot application of herbicide for weed control, and validate its performance in simulation using realistic scenarios with up to 30 robots