The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard problem with important applications. There has been much interest in developing heuristic algorithms for finding a "good" vertex cover in graphs. In practice, most heuristic algorithms for MinVC are based on the local search method. Previously, local search algorithms for MinVC have focused on solving academic benchmarks where the graphs are of relatively small size, and they are not suitable for solving massive graphs as they usually have highcomplexity heuristics. In this paper, we propose a simple and fast local search algorithm called FastVC for solving MinVC in massive graphs, which is based on two low-complexity heuristics. Experimental results on a broad range of real world massive graphs show that FastVC finds much better vertex covers (and thus also independent sets) than state of the art local search algorithms for MinVC.

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Balance between complexity and quality: local search for minimum vertex cover in massive graphs

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

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Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

Minimum vertex cover (MinVC) is a prominent NP-hard problem in artificial intelligence, with considerable importance in applications. Local search solvers define the state of the art in solving MinVC. However, there is no single MinVC solver that works best across all types of MinVC instances, and finding the most suitable solver for a given application poses considerable challenges. In this work, we present a new local search framework for MinVC called MetaVC, which is highly parametric and incorporates many effective local search techniques. Using an automatic algorithm configurator, the performance of MetaVC can be optimized for particular types of MinVC instances. Through extensive experiments, we demonstrate that MetaVC significantly outperforms previous solvers on medium-size hard instances, and shows competitive performance on large application instances. We further introduce a novel, neural network based method for enhancing the automatic configuration process, by identifying and terminating unpromising configuration runs. Our results present that MetaVC with the optimized configuration obtained using this method, called MetaVC2, can achieve improvements in the best known solutions for 16 large application instances.

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Local Search with Efficient Automatic Configuration for Minimum Vertex Cover

Industry 4.0 utilizes the Internet of Things (IoT) to rise the efficiency in manufacturing and automation where wireless sensor networks (WSNs) are crucial technologies for communication layer of IoT. WSNs include hundreds of small sized sensor nodes that have the abilities of wireless transmission and environmental sensing. Wireless transmission is prone to various attacks such as data manipulation since data communication is achieved through transfer of radio packets. A countermeasure of this issue is link monitoring by deploying secure points that can physically capture and inspect radio packets. Graph theory plays a critical role to solve various problems in WSNs. Finding minimum Vertex Cover (VC) is an important NP-Hard graph theoretic problem in which the minimum set of nodes (vertices) is aimed to select in such a way that each link should be incident to at least one node from this set. VC is a significant structure for WSNs where it perfectly fits for link monitoring when nodes in VC are set as secure points (monitors). Since sensor nodes are generally battery-powered and have limited transmission range, energy-efficient multi-hop communication to the sink node is of utmost importance. In weighted connected VC (WCVC) structure, subgraph induced by monitor nodes are connected where monitors are chosen according to their weights. When weights of nodes are assigned as reciprocal of their energies, an energy-efficient virtual backbone can be formed. We propose a novel metaheuristic WCVC algorithm for link monitoring and backbone formation in WSNs modeled as undirected graphs. Our proposed algorithm integrates a genetic search with a greedy heuristic to improve WCVC solution quality and decrease the search time. To evaluate the efficiencies of greedy heuristics, we adopt three different heuristics for WCVC problem. We implement our algorithm with its counterparts and reveal that the algorithm is favorable in terms of solution quality and resource consumption.

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Weighted Connected Vertex Cover Based Energy-Efficient Link Monitoring for Wireless Sensor Networks Towards Secure Internet of Things

Breadth-first search tree integrated vertex cover algorithms for link monitoring and routing in wireless sensor networks

Vertex covering has important applications for wireless sensor networks such as monitoring link failures, facility location, clustering, and data aggregation. In this study, we designed three algorithms for constructing vertex cover in wireless sensor networks. The first algorithm, which is an adaption of the Parnas & Ron’s algorithm, is a greedy approach that finds a vertex cover by using the degrees of the nodes. The second algorithm finds a vertex cover from graph matching where Hoepman’s weighted matching algorithm is used. The third algorithm firstly forms a breadth-first search tree and then constructs a vertex cover by selecting nodes with predefined levels from breadth-first tree. We show the operation of the designed algorithms, analyze them, and provide the simulation results in the TOSSIM environment. Finally we have implemented, compared and assessed all these approaches. The transmitted message count of the first algorithm is smallest among other algorithms where the third algorithm has turned out to be presenting the best results in vertex cover approximation ratio.

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Distributed vertex cover algorithms for wireless sensor networks

Vertex covering has important applications for wireless sensor networks such as monitoring link failures, facility location, clustering, and data aggregation. In this study, we designed three algorithms for constructing vertex cover in wireless sensor networks. The first algorithm, which is an adaption of the Parnas & Ron's algorithm, is a greedy approach that finds a vertex cover by using the degrees of the nodes. The second algorithm finds a vertex cover from graph matching where Hoepman's weighted matching algorithm is used. The third algorithm firstly forms a breadth-first search tree and then constructs a vertex cover by selecting nodes with predefined levels from breadth-first tree. We show the operation of the designed algorithms, analyze them, and provide the simulation results in the TOSSIM environment. Finally we have implemented, compared and assessed all these approaches. The transmitted message count of the first algorithm is smallest among other algorithms where the third algorithm has turned out to be presenting the best results in vertex cover approximation ratio.

Distributed Vertex Cover Algorithms For Wireless Sensor Networks

An undirected graph can be represented by G(V,E) where V is the set of vertices and E is the set of edges connecting vertices. The problem of finding a vertex cover (VC) is to identify a set of vertices VC such that at least one endpoint of every edge in E is incident to a vertex V in VC. Vertex cover is a very important graph theoretical structure for various types of communication networks such as wireless sensor networks, since VC can be used for link monitoring, clustering, backbone formation and data aggregation management. In this chapter, we will define vertex cover and related problems with their applications on communication networks and we will survey some important distributed algorithms on this research area.

Vedat Kavalci

Papers

Distributed vertex cover algorithms for wireless sensor networks

Distributed Vertex Cover Algorithms For Wireless Sensor Networks

On Vertex Cover Problems in Distributed Systems