We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

For the law enforcement agencies, lawful interception is still one of the main means to intercept a suspect or address most illegal actions. Due to its centralized management, however, it is easy to implement in traditional networks, but the cost is high. In view of this restriction, this paper aims to exploit software-defined network (SDN) technology to contribute to the next generation of intelligent lawful interception technology, i.e., to optimize the deployment of intercept access points (IAPs) in hybrid software-defined networks where both SDN nodes and non-SDN nodes exist simultaneously. In order to deploy IAPs, this paper puts forward an improved equal-cost multi-path shortest path algorithm and accordingly proposes three SDN interception models: T interception model, ECMP-T interception model and Fermat-point interception model. Considering the location relevance of all intercepted targets and the operation and maintenance cost of operators from the global perspective, by the way, we further propose a restrictive minimum vertex cover algorithm (RMVCA) in hybrid SDN. Implementing different SDN interception algorithms based RMVCA in real-world topologies, we can reasonably deploy the best intercept access point and intercept the whole hybrid SDN with the least SDN nodes, as well as significantly optimize the deployment efficiency of IAPs and improve the intercept link coverage in hybrid SDN, contributing to the implementation of lawful interception.

https://www.mdpi.com/1424-8220/21/2/428/pdf

On the Optimal Lawful Intercept Access Points Placement Problem in Hybrid Software-Defined Networks

The minimum vertex cover (MVC) problem is a well-studied NP-Complete problem and has various applications. In this paper, a new heuristic approach has been proposed to find the minimum vertex cover of a graph. The proposed algorithm has been tested on random graphs and BHOSLIB instances. The results have shown that the proposed algorithm can yield better solutions especially on dense graphs for solving the minimum vertex cover problem.

Dhananjay Tomar

Papers

An Improved Greedy Heuristic for Unweighted Minimum Vertex Cover