Constrained Relay Node Placement Research Articles

An improved algorithm for delay constrained relay node deployment in wireless sensor networks

Given that Delay Constrained Relay Node Placement (DCRNP) problem is getting more and more attention in time-critical domains, this paper proposes an Improved Greedy-based Selection Algorithm (IGSA) to tackle such problem under delay and budget constraints. IGSA first employs communication cost matrix and Dijkstra’s algorithm to detect whether the problem is solvable, then selects the amount and locations of deployed relay nodes (RNs) layer by layer by continuously calling the greedy coverage algorithm until all sensors have a feasible path to the sink under a preset delay constraint, and finally removes redundant RNs to reach the approximate optimal solution. Extensive simulations show that our approach can save 15%–30% of deployed RNs than the Two-phase Set-Covering-based Algorithm (TSCA), which is the state-of-the-art algorithm for the DCRNP problem, only with a slight sacrifice of solving time. Meanwhile, Ad Hoc On-Demand Distance Vector (AODV) routing protocol is applied to further examine the performance of the deployment results solved by TSCA and IGSA, respectively. Results show that every RN deployed by IGSA is involved in data forwarding, while IGSA deploys leisure RNs which do not participate in the data forwarding. Besides, compared with TSCA, the network formed by IGSA has lower network delay in the data transmission process, and the energy consumption of the central node and throughput of the two topologies are almost at the same level.

Deploying Hierarchical Mesh Networks for Supporting Distributed Computing in Industrial Internet of Things

The centralized computing model in industrial Internet of Things (IIoT) leads to large delay and unbalanced traffic, which strictly restricts the adoption of IIoT in industrial applications demanding high network performance. To cope with the problem, researchers resort to the in-network computation model in which the computation capability is distributed among nodes in IIoT. Existing works on the in-network computation assume that the network connectivity built in advance meets the performance requirement of the in-network computation model. Nevertheless, no node placement methods have been proposed to build network connectivity supporting in-network computation. For this reason, we propose an in-network-computation-oriented node placement (INP) algorithm. The INP algorithm first decomposes the whole problem into several delay constrained relay node placement problems, and then, solves them sequentially. Moreover, we prove that the INP algorithm ensures explicit time complexity and approximation ratio. Finally, we verify the efficiency of this work through extensive simulations and preliminary experiments.

Relay Node Placement in Wireless Sensor Networks: From Theory to Practice

The increasingly wide utilization of Wireless Sensor Networks (WSNs) in industrial applications outstands the significance of the Delay Constrained Relay Node Placement (DCRNP) problem. Existing algorithms to the DCRNP problem are designed based on the ideal geometric disk wireless channel model, and no real-world deployments are performed to verify the effectiveness of these algorithms. However, the unreliable and unpredictable wireless links in WSNs may lead these algorithms to fail in practice. Therefore, we first conduct extensive real-world deployments under the guidance of existing algorithms to evaluate their performance and to gain some insights for designing practical deployment algorithms. The results exhibit that the WSNs built by existing algorithms have a favorable performance in end-to-end delay but a poor performance in reliability, which is mainly due to the lack of methods ensuring high-quality links. To this end, we first devise a Set-Covering-based Algorithm (SCA) which figures out the DCRNP problem while ensuring the quality of each link better than a given threshold. As our experiments also show that the fault-tolerant topology can significantly improve network reliability, we then design a $k$ k -Set-Covering-based Algorithm ( $k$ k SCA) to build fault-tolerant WSNs based on the methodology of SCA. Furthermore, the elaborate analysis proves that both SCA and $k$ k SCA are polynomial-time algorithms, and their approximation ratios are both O( $\ln n$ ln n ), where $n$ n is the number of sensor nodes. Finally, extensive experiments are performed under the guidance of SCA and $k$ k SCA to demonstrate the effectiveness of these two algorithms.

Relay Node Placement in Wireless Sensor Networks With Respect to Delay and Reliability Requirements

Wireless sensor networks are gradually employed in many applications that require reliable and real-time data transmission. As hop count is an important factor affecting end-to-end delay and reliability, we investigate the hop constrained relay node placement (HCRNP) problem in this paper. First, to achieve connectivity requirement, we study the connected HCRNP problem. Then, to design survivable network topologies against node failures, we study the 2-connected HCRNP problem. Correspondingly, two polynomial-time algorithms: cover-based 1-connected node placement (C1NP) and cover-based 2-connected node placement (C2NP) are proposed, respectively, to address the above two problems. Through rigorous analysis, we show that 1) C1NP has an approximation ratio better than existing algorithms for the connected HCRNP problem (i.e., O(1) for special settings and O(ln n) for arbitrary settings, where n is the number of SNs) and 2) C2NP is the first algorithm that can provide an explicit performance guarantee for the 2-connected HCRNP problem, i.e., whenever C2NP finds a feasible solution, the ratio of this solution to the optimal solution is guaranteed to be O(ln n). Finally, we verify the effectiveness of the proposed algorithms through extensive simulations.

Delay constrained relay node placement in two-tiered wireless sensor networks: A set-covering-based algorithm

As Wireless Sensor Networks (WSNs) are widely used in time-critical applications, e.g., factory automation and smart grid, the importance of Delay Constrained Relay Node Placement (DCRNP) problem is becoming increasingly noticeable. Considering the benefits in terms of energy efficiency and scalability brought by the two-tiered topology, this paper studies the DCRNP problem in two-tiered WSNs. To address the NP-hardness, a Two-phase Set-Covering-based Algorithm (TSCA) is proposed to approximately solve this problem. To be specific, in the first phase, a Connectivity-aware Covering Algorithm (CCA) places Relay Nodes (RNs) to fully cover distributed sensor nodes with respect to delay constraints, and meanwhile CCA tries to reduce the number of connected components in the topology constructed in this phase so as to save the RNs deployed to build network connectivity. In the second phase, the network connectivity is built in obedience to delay constraints by a Set-Covering-based Algorithm (SCA) through an iterative manner, which formulates the deployment of RNs at each iteration as the set covering problem and solves this problem using a classic set covering algorithm. In addition, the elaborated analysis of time complexity and approximation ratio of the proposed algorithms is given out. Finally, extensive simulations demonstrate that TSCA can significantly save deployed RNs in comparison to existing algorithms.

Delay Constrained Relay Node Placement in Wireless Sensor Networks: A Subtree-and-Mergence-based Approach

Wireless Sensor Networks (WSNs) are applied in many time-critical applications, e.g., industrial automation and smart grid. This highlights the importance of Delay Constrained Relay Node Placement (DCRNP) problem that builds a path fulfilling a specified delay constraint between each sensor and the sink by using a minimum number of relays. Due to the NP-hardness of the DCRNP problem, in this paper, a polynomial time Subtree-and-Mergence-based Algorithm (SMA) is proposed to approximately solve the DCRNP problem. First, a shortest path tree rooted at the sink and connecting all sensors is built to check the feasibility of the DCRNP problem. If the DCRNP problem is feasible, then the paths of this tree are progressively merged at some relays, which are not limited to those relays lying in the originally the originally built shortest path tree, to save deployed relays while maintaining the obedience of delay constraints. With the repetition of this mergence, the number of deployed relays is gradually reduced. Furthermore, the approximation ratio and the time complexity of the proposed SMA are elaborately analyzed. Finally, extensive simulations are conducted to demonstrate the effectiveness of this work. Simulation results show that SMA can significantly save deployed relays comparing with existing algorithms.

PSH: A Pruning and Substitution Based Heuristic Algorithm for Relay Node Placement in Two-Tiered Wireless Sensor Networks

Delay constrained relay node placement (DCRNP) problem minimizes the quantity of deployed relays that are employed to build at least one path between the sink and each sensor, while guaranteeing that the delay constraints for the built paths are fulfilled. Published literature only focus on the DCRNP problem in single-tiered wireless sensor networks (WSNs). Considering the benefits in terms of network scalability and energy consumption by the two-tiered network topology, this paper studies the DCRNP problem in two-tiered WSNs and proposes a pruning-and-substitution-based-heuristic (PSH) algorithm to solve the DCRNP problem. PSH consists of two phases, i.e., the covering phase and the connecting phase. In the covering phase, a shortest-path-based algorithm (SPA) is proposed to deploy relays at a subset of predetermined deployment locations such that each sensor is covered by at least one relay, meanwhile ensuring the obedience of delay constraints. Then, in the connecting phase, a tree-based connecting algorithm (TCA) is proposed to build the high-tier network connectivity. TCA first builds a shortest path tree to connect the relays deployed by SPA to the sink, and then, saves the deployed relays by gradually pruning or substituting them by the relays placed at the locations that several feasible paths pass through. The time complexity and the approximation ratio of this work are explicitly analyzed and extensive simulations are implemented to demonstrate its effectiveness.

One-Step Approach for Two-Tiered Constrained Relay Node Placement in Wireless Sensor Networks

We consider in this letter the problem of constrained relay node (RN) placement where sensor nodes must be connected to base stations by using a minimum number of RNs. The latter can only be deployed at a set of predefined locations, and the two-tiered topology is considered where only RNs are responsible for traffic forwarding. We propose a one-step constrained RN placement (OSRP) algorithm which yields a network tree. The performance of OSRP in terms of the number of added RNs is investigated in a simulation study by varying the network density, the number of sensor nodes, and the number of candidate RN positions. The results show that OSRP outperforms the only algorithm in the literature for two-tiered constrained RNs placement.

考虑时延约束的无线传感器网络中继节点部署算法

The delay constrained relay node placement (DCRNP) problem minimizes the quantity of deployed relay nodes that are employed to build at least one path between a sink and each sensor node and guarantees that the delay constraints for the built paths are ful lled. It has been proven that the DCRNP problem is NP-hard. This paper proposes a convergence-pruning-based relay node placement (CPRNP) algorithm to approximately solve the DCRNP problem. The CPRNP algorithm consists of two stages. In the rst stage, CPRNP identi es the convergences of all the paths meeting the delay constraint and forms a shortest-path tree that is rooted at the sink and connects all the sensors. In the second stage, the CPRNP gradually reduces the number of deployed relay nodes by deleting or substituting the nodes on the shortest-path tree. The simulation results con rm that CPRNP can signi cantly save deployed relay nodes compared to existing algorithms.

Approximation Algorithms for Constrained Relay Node Placement in Energy Harvesting Wireless Sensor Networks

The constrained relay node placement problem in a wireless sensor network seeks the deployment of a minimum number of relay nodes (RNs) in a set of candidate locations in the network to satisfy specific requirements, such as connectivity or survivability. In this paper, we study the constrained relay node placement problem in an energy-harvesting network in which the energy harvesting potential of the candidate locations are known a priori. Our aim is to place a minimum number of relay nodes, to achieve connectivity or survivability, while ensuring that the relay nodes harvest large amounts of ambient energy. We present the connectivity and survivability problems, discuss their NP-hardness, and propose polynomial time ${\mbi{\cal O}}$ (1)-approximation algorithms with low approximation ratios to solve them. We validate the effectiveness of our algorithms through numerical results to show that the RNs placed by our algorithms harvest 50% more energy on average than those placed by the algorithms unaware of energy harvesting. We also develop a unified-mixed integer linear program (MILP)-based formulation to compute a lower bound of the optimal solution for minimum relay node placement and demonstrate that the results of our proposed algorithms were on average within 1.5 times of the optimal.

Optimal relay node placement in delay constrained wireless sensor network design

The Delay Constrained Relay Node Placement Problem (DCRNPP) frequently arises in the Wireless Sensor Network (WSN) design. In WSN, Sensor Nodes are placed across a target geographical region to detect relevant signals. These signals are communicated to a central location, known as the Base Station, for further processing. The DCRNPP aims to place the minimum number of additional Relay Nodes at a subset of Candidate Relay Node locations in such a manner that signals from various Sensor Nodes can be communicated to the Base Station within a pre-specified delay bound. In this paper, we study the structure of the projection polyhedron of the problem and develop valid inequalities in form of the node-cut inequalities. We also derive conditions under which these inequalities are facet defining for the projection polyhedron. We formulate a branch-and-cut algorithm, based upon the projection formulation, to solve DCRNPP optimally. A Lagrangian relaxation based heuristic is used to generate a good initial solution for the problem that is used as an initial incumbent solution in the branch-and-cut approach. Computational results are reported on several randomly generated instances to demonstrate the efficacy of the proposed algorithm.

A Grid-Based Relay Node Placement Algorithm in Wireless Sensor Networks

The relay node placement in wireless sensor networks is usually constrained by physical factors, while most of present relay node placement approaches are unconstrained. To solve the problem, the paper presents a constrained relay node placement algorithm. Based on grid routing mechanism, the algorithm determines the grid intersections as candidates for the relay node locations, and places as fewer relay nodes as possible to assure the network connectivity. Consideration must be given to both the number of relay nodes and energy efficient, the paper uses the greedy norm and constrains to place relay nodes. By the analysis and study of the experiments, the performance of the proposed algorithm is more superior to the algorithm without constrains.

Two-Tiered Constrained Relay Node Placement in Wireless Sensor Networks: Computational Complexity and Efficient Approximations

In wireless sensor networks, relay node placement has been proposed to improve energy efficiency. In this paper, we study two-tiered constrained relay node placement problems, where the relay nodes can be placed only at some prespecified candidate locations. To meet the connectivity requirement, we study the connected single-cover problem where each sensor node is covered by a base station or a relay node (to which the sensor node can transmit data), and the relay nodes form a connected network with the base stations. To meet the survivability requirement, we study the 2-connected double-cover problem where each sensor node is covered by two base stations or relay nodes, and the relay nodes form a 2-connected network with the base stations. We study these problems under the assumption that R \ge 2r > 0, where R and r are the communication ranges of the relay nodes and the sensor nodes, respectively. We investigate the corresponding computational complexities, and propose novel polynomial time approximation algorithms for these problems. Specifically, for the connected single-cover problem, our algorithms have {\cal O}(1)-approximation ratios. For the 2-connected double-cover problem, our algorithms have {\cal O}(1)-approximation ratios for practical settings and {\cal O}(\ln n)-approximation ratios for arbitrary settings. Experimental results show that the number of relay nodes used by our algorithms is no more than twice of that used in an optimal solution.

Constrained Relay Node Placement in Wireless Sensor Networks: Formulation and Approximations

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> One approach to prolong the lifetime of a wireless sensor network (WSN) is to deploy some <emphasis emphasistype="boldital">relay nodes</emphasis> to communicate with the sensor nodes, other relay nodes, and the base stations. The relay node placement problem for wireless sensor networks is concerned with placing a minimum number of relay nodes into a wireless sensor network to meet certain connectivity or survivability requirements. Previous studies have concentrated on the <emphasis emphasistype="boldital">unconstrained</emphasis> version of the problem in the sense that relay nodes can be placed anywhere. In practice, there may be some physical constraints on the placement of relay nodes. To address this issue, we study <emphasis emphasistype="boldital">constrained</emphasis> versions of the relay node placement problem, where relay nodes can only be placed at a set of candidate locations. In the connected relay node placement problem, we want to place a minimum number of relay nodes to ensure that each sensor node is connected with a base station through a bidirectional path. In the survivable relay node placement problem, we want to place a minimum number of relay nodes to ensure that each sensor node is connected with two base stations (or the only base station in case there is only one base station) through two node-disjoint bidirectional paths. For each of the two problems, we discuss its computational complexity and present a framework of polynomial time <formula formulatype="inline"><tex Notation="TeX">$ {\cal O}(1)$</tex> </formula>-approximation algorithms with small approximation ratios. Extensive numerical results show that our approximation algorithms can produce solutions very close to optimal solutions. </para>