Approximating the Minimum Connected Dominating Set in Stochastic Graphs Based on Learning Automata

Connected dominating set (CDS) has a wide range of applications in multihop wireless networks. The Minimum CDS problem has been studied extensively in multihop wireless networks with uniform communication ranges. However, in practice, the nodes may have different communication ranges either because of the heterogeneity of the nodes, or due to interference mitigation, or due to a chosen range assignment for energy conservation. In this paper, we present a greedy approximation algorithm for computing a Minimum CDS in multihop wireless networks with disparate communications ranges and prove that its approximation ratio is better than the best one known in the literature. Our analysis utilizes a tighter relation between the independence number and the connected domination number.

Connected dominating set (CDS) has a wide range of applications in mutihop wireless networks. The Minimum CDS problem has been studied extensively in mutihop wireless networks with uniform communication ranges. However, in practice the nodes may have different communication ranges either because of the heterogeneity of the nodes, or due to interference mitigation, or due to a chosen range assignment for energy conservation. In this paper, we present a greedy approximation algorithm for computing a Minimum CDS in multihop wireless networks with disparate communications ranges and prove that its approximation ratio is better than the best one known in the literature. Our analysis utilizes a tighter relation between the independence number and the connected domination number.

The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Most previous works focused on solving MCDS problem in graphs with relatively small size, mainly due to the complexity of maintaining connectivity. This paper explores techniques for solving MCDS problem in massive real-world graphs with wide practical importance. Firstly, we propose a local greedy construction method with reasoning rule called 1hopReason. Secondly and most importantly, a hybrid dynamic connectivity maintenance method (HDC+) is designed to switch alternately between a novel fast connectivity maintenance method based on spanning tree and its previous counterpart. Thirdly, we adopt a two-level vertex selection heuristic with a newly proposed scoring function called chronosafety to make the algorithm more considerate when selecting vertices. We design a new local search algorithm called FastCDS based on the three ideas. Experiments show that FastCDS significantly outperforms five state-of-the-art MCDS algorithms on both massive graphs and classic benchmarks.

Wireless ad hoc and sensor networks play an important role in providing flexible deployment and mobile connectivity for next generation network. Since there is no fixed physical backbone infrastructure, some of the nodes are selected to form a virtual backbone. Efficient algorithms for identifying the Minimum Connected Dominating Set (MCDS) have many practical applications in wireless sensor networks deployment and management. We propose two algorithms in this paper for solving the MCDS problem. The first algorithm called Memetic Algorithm for the MCDS problem, or MA-MCDS shortly. This is a new hybrid algorithm based on genetic algorithm in addition to local search strategies for the MCDS problem. In order to achieve fast performance, MA-MCDS algorithm uses local search and intensification procedures in addition to genetic operations. In the second algorithm, simulated annealing is used to enhance a stochastic local search with the ability to of run away from local solutions. In addition, we present a new objective function that effectively measure the quality of the solutions of our proposed algorithms. Both algorithms are tested using different benchmark test graph sets available in the literature, and shows good results in terms of solution quality.

Connected dominating set (CDS) problem in unit disk graph has a significant impact on an efficient design of routing protocols in wireless sensor networks. In this paper, an algorithm is proposed for finding minimum connected dominating set (MCDS) using dominating set. Dominating sets are connected by using Steiner tree. The algorithm goes through three phases. In first phase dominating set is found, in second phase connectors are identified, connected through Steiner tree. In third phase the CDS obtained in second phase is pruned to obtain a MCDS. MCDS so constructed needs to adapt to the continual topology changes due to deactivation of a node due to exhaustion of battery power. These topological changes due to power constraints are taken care by a local repair algorithm that reconstructs the MCDS using only neighborhood information. Simulation results indicate both the heuristics are very efficient and result in near optimal MCDS.

Finding minimum weight connected dominating set in stochastic graph based on learning automata

Sampling algorithms for stochastic graphs: A learning automata approach

In the past 20 years, the connected dominating set (CDS) as a virtual backbone network has been widely used in the wireless networks. Many researchers have been devoted to designing approximate algorithms for CDS problem since constructing the minimum CDS (MCDS) is NP-hard problem. Different from the most existing algorithms with two phases, we employ greedy strategy to design a centralized algorithm GR_CDS in only one phase to get MCDS, with the time complexity of [Formula: see text]. Afterwards, another algorithm P_CDS is designed for pruning redundant nodes in the obtained MCDS with the time complexity of [Formula: see text].

Construction of minimum connected dominating set in wireless sensor networks using pseudo dominating set

A self-stabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external e.g., human intervention. A k-dominating set in a distributed system is a set of processors such that each processor outside the set has at least k neighbors in the set. In the past, a few self-stabilizing algorithms for minimal k-dominating set MKDS have been obtained. However, the presented self-stabilizing algorithms for MKDS work for either trees or a minimal 2-dominating set. Recently a self-stabilizing algorithm for MKDS in arbitrary graphs under a central daemon has been investigated. But so far, there is no algorithm for the MKDS problem in arbitrary graphs that works under a distributed daemon. In this paper, we propose a self-stabilizing algorithm for finding a MKDS under a distributed daemon model when operating in any general network graph. We further verify the correctness of the proposed algorithm Algorithm MKDS and prove that the worst case convergence time of the algorithm from any arbitrary initial state is On 2 steps where n is the number of nodes in the network.

In wireless networks, due to the lack of fixed infrastructure or centralized management, a connected dominating set (CDS) of the graph representing the network is an optimum candidate to serve as the virtual backbone of a wireless network. However, constructing a minimum CDS is NP-hard. Furthermore, almost all of the existing CDS construction algorithms neglect the diameter of a CDS, which is an important factor. In this paper, we investigate the problem of constructing a CDS with a bounded diameter in wireless networks and propose a heuristic algorithm, connected dominating sets with bounded diameters (CDS-BD), with constant performance ratios for both the size and diameter of the constructed CDS.

The Steiner tree problem in graphs (SPG) is one of the most studied problems in combinatorial optimization because of its theories and applications. It is one of the foundations to develop a Wireless Sensor Network (WSNs), such as multicast and topology design. SPG is an NP-Hard problem, and many heuristic and approximation algorithms have been proposed. Thus, this study proposes a Hybrid Genetic algorithm (HGA) to solve SPG. This study is the binary string representation for a set of chosen edges. To increase the diversity of the population and avoid falling into local optimization, we use a 2-longest Distance strategy, dynamic crossover rate, and chosen solutions must differ by at least 5%. The experiment results show that the HGA algorithm's running time equals 153.83% of the GA algorithm's, the deviation found by HGA, and the optimal distance only equals 65% that of GA.

This paper considers the problem of communication coverage for sustainable data forwarding in wireless sensor networks, where an energy-aware deployment model of relay nodes (RNs) is proposed. The model used in this paper considers constrained placement and is different from the existing one-tiered and two-tiered models. It supposes two different types of sensor nodes to be deployed, i) energy rich nodes (ERNs), and ii) energy limited nodes (ELNs). The aim is thus to use only the ERNs for relaying packets, while ELN's use will be limited to sensing and transmitting their own readings. A minimum number of RNs is added if necessary to help ELNs. This intuitively ensures sustainable coverage and prolongs the network lifetime. The problem is reduced to the traditional problem of minimum weighted connected dominating set (MWCDS) in a vertex weighted graph. It is then solved by taking advantage of the simple form of the weight function, both when deriving exact and approximate solutions. Optimal solution is derived using integer linear programming (ILP), and a heuristic is given for the approximate solution. Upper bounds for the approximation of the heuristic (versus the optimal solution) and for its runtime are formally derived. The proposed model and solutions are also evaluated by simulation. The proposed model is compared with the one-tiered and two-tiered models when using similar solution to determine RNs positions, i.e., minimum connected dominating set (MCDS) calculation. Results demonstrate the proposed model considerably improves the network life time compared to the one-tiered model, and this by adding a lower number of RNs compared to the two-tiered model. Further, both the heuristic and the ILP for the MWCDS are evaluated and compared with a state-of-the-art algorithm. The results show the proposed heuristic has runtime close to the ILP while clearly reducing the runtime compared to both ILP and existing heuristics. The results also demonstrate scalability of the proposed solution.

Steiner tree problem (STP) in graphs aims to find a tree of minimum weight in the graph that connects a given set of vertices. It is a classic NP-hard combinatorial optimization problem and has many applications in real world. Many approximate algorithms have been developed for STP, but they suffer from high computational complexity and weak worst-case solution guarantees, respectively. Heuristic algorithms are also developed. But each of them requires application domain knowledge to design and is only suitable for specific scenarios. In this paper, we design a novel framework Cherrypick based on novel graph embedding and deep reinforcement learning to tackle the STP. Given an STP instance, Cherrypick uses this embedding to encode its path-related information and sends the encoded graph to a deep reinforcement learning component based on deep Q network (DQN) to find solutions. We implement the Cherrypick and demonstrate its efficacy and efficiency with extensive experiments using real-world and synthetic datasets.

In this paper, a new structure for cooperative learning automata called extended learning automata (eDLA) is introduced. Based on the new structure, an iterative randomized heuristic algorithm using sampling is proposed for finding an optimal subgraph in a stochastic edge-weighted graph. Stochastic graphs are graphs in which the weights of edges have an unknown probability distribution. The proposed algorithm uses an eDLA to find a policy that leads to a subgraph that satisfy some restrictions such as minimum or maximum weight (length). At each stage of the proposed algorithm, the eDLA determines which edges should be sampled. The proposed eDLA-based sampling method may reduce unnecessary samples and hence decrease the time required for finding an optimal subgraph. It is shown that the proposed method converges to an optimal solution, the probability of which can be made arbitrarily close to 1 by using a sufficiently small learning parameter. A new variance-aware threshold value is also proposed that can significantly improve the convergence rate of the proposed eDLA-based algorithm. It is further shown that our algorithm is competitive in terms of the quality of the solution.