Test-cost-sensitive rough set based approach for minimum weight vertex cover problem

An efficient local search framework for the minimum weighted vertex cover problem

Minimum weighted vertex cover (MWVC) problem of weighted networks is one of the most important combinatorial optimization problems in network optimization. This paper models the MWVC problem as an asymmetric game on weighted networks. Then, an asynchronous game-based algorithm (AGB) is proposed to solve the MWVC problem, which can guarantee to obtain a vertex cover (VC). Numerical illustrations verify the performance of the proposed game solution on the representative weighted networks.

The minimum weight vertex cover problem (MWVCP) is one of the classic combinatorial optimisation problems. In this paper, we have proposed a modified jumping particle swarm optimisation approach, n...

The Weighted Constraint Satisfaction Problem (WCSP) is a very expressive framework for optimization problems. The Constraint Composite Graph (CCG) is a graphical representation of a given (Boolean) WCSP that facilitates its reduction to a Minimum Weighted Vertex Cover (MWVC) problem by introducing intelligently chosen auxiliary variables. It also enables kernelization: a maxflow procedure used to fix the optimal values of a subset of the variables before initiating search. In this paper, we present some CCG-based WCSP solvers and compare their performance against toulbar2, a state-of-the-art WCSP solver, on a variety of benchmark instances. We also study the effectiveness of kernelization.

The generalized vertex cover problem and some variations

Toward better approximation for the minimum-weighted vertex cover (MWVC) problem in multiagent systems, we present a distributed algorithm from the perspective of learning in games. For self-organized coordination and optimization, we see each vertex as a potential game player who makes decisions using local information of its own and the immediate neighbors. The resulting Nash equilibrium is classified into two categories, i.e., the inferior Nash equilibrium (INE) and the dominant Nash equilibrium (DNE). We show that the optimal solution must be a DNE. To achieve better approximation ratios, local rules of perturbation and weighted memory are designed, with the former destroying the stability of an INE and the latter facilitating the refinement of a DNE. By showing the existence of an improvement path from any INE to a DNE, we prove that when the memory length is larger than 1, our algorithm converges in finite time to DNEs, which could not be improved by exchanging the action of a selected node with all its unselected neighbors. Moreover, additional freedom for solution efficiency refinement is provided by increasing the memory length. Finally, intensive comparison experiments demonstrate the superiority of the presented methodology to the state of the art, both in solution efficiency and computation speed.

We introduce two generalizations of core percolation in graphs to hypergraphs, related to the minimum hyperedge cover problem and the minimum vertex cover problem on hypergraphs, respectively. We offer analytical solutions of these two core percolations for uncorrelated random hypergraphs whose vertex degree and hyperedge cardinality distributions are arbitrary but have nondiverging moments. We find that for several real-world hypergraphs their two cores tend to be much smaller than those of their null models, suggesting that covering problems in those real-world hypergraphs can actually be solved in polynomial time.

A rough set method for the minimum vertex cover problem of graphs

We present a deterministic distributed 2-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGEST model whose round complexity is \(O(\log n\log \varDelta / \log ^2\log \varDelta )\). This improves over the currently best known deterministic 2-approximation implied by [KVY94]. Our solution generalizes the \((2+\epsilon )\)-approximation algorithm of [BCS17], improving the dependency on \(\epsilon ^{-1}\) from linear to logarithmic. In addition, for every \(\epsilon =(\log \varDelta )^{-c}\), where \(c\ge 1\) is a constant, our algorithm computes a \(\left( 2+\epsilon \right) \)-approximation in \(O(\log {\varDelta }/\log \log {\varDelta })\) rounds (which is asymptotically optimal).

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.

 Abstract—Nowadays, the method of data mining, widely known as KDD (Knowledge-discovery in databases), is researched actively due to increasing amount of data. Decision tree, which is human-readable and understandable, is widely used in the field of rule extraction, data mining, and pattern recognition. Although decision tree is easy for quickly understanding the data, it has many faults in algorithm itself. In this paper, to compensate for these faults, we combined decision table (rough set theory) and ANN (Artificial Neural Network). With this combined algorithm, we could easily obtain more precise rules from iris data. Our experiment was in this order: 1) Find weights by using back propagation (bp) algorithm. (ANN). 2) Use dimensionality reduction method to delete huge amount of irrelevant data. (Rough set theory and decision table). 3) Make decision tree with pruned weights and rules. With ANN algorithm and decision table (dimensionality reduction method), we could easily notice the most influential (high entropy) character of iris data. With this algorithm, we could extract more precise and pruned rule from iris data sets.

Mutation operator is one of the mechanisms of evolutionary algorithms (EAs) and it can provide diversity in the search and help to explore the undiscovered search place. Quantum-behaved particle swarm optimization (QPSO), which is inspired by fundamental theory of PSO algorithm and quantum mechanics, is a novel stochastic searching technique and it may encounter local minima problem when solving multi-modal problems just as that in PSO. A novel mutation mechanism is proposed in this paper to enhance the global search ability of QPSO and a set of different mutation operators is introduced and implemented on the QPSO. Experiments are conducted on several well-known benchmark functions. Experimental results show that QPSO with some of the mutation operators is proven to be statistically significant better than the original QPSO.

The minimum vertex cover (MVC) problem is a classic NP-hard combinatorial optimization problem with extensive real-world applications. In this paper, we propose an efficient local search algorithm, InfVC, to solve the MVC in massive graphs, which comprises three ideas. First, we introduce an inference-driven optimization strategy that explores better feasible solutions through inference rules. Second, we develop a structural-determined perturbation strategy that is motivated by the structure features of high-quality solutions, prioritizing high-degree vertices into the candidate solution to guide the search process to some potential high-quality search area. Third, we design a self-adaptive local search framework that dynamically balances exploration and exploitation through a perturbation management mechanism. Extensive experiments demonstrate that InfVC outperforms all the state-of-the-art algorithms on almost massive instances.

Minimum Weighted Vertex Cover on Different Graphs and It's Algorithm

Rough sets and fuzzy sets are both theories for handling uncertain problems, and the viewpoints between them are different. They are complementary than competitive. Much seminal research has been carried out into combining them both; the results are rough fuzzy sets and fuzzy rough sets. In this paper, we introduce the idea of fuzzy rough sets in research of decision tables with quantitative data. Thus, we can handle the decision table directly without discretization. Combining the idea of variable precision rough sets, we make the form of the upper and lower approximation uniform.