In this paper, we present ASPEN+, which extends an existing ASP-based system, ASPEN,for collective entity resolution with two important functionalities: support for local merges and new optimality criteria for preferred solutions. Indeed, ASPEN only supports so-called global merges of entity-referring constants (e.g. author ids), in which all occurrences of matched constants are treated as equivalent and merged accordingly. However, it has been argued that when resolving data values, local merges are often more appropriate, as e.g. some instances of 'J. Lee' may refer to 'Joy Lee', while others should be matched with 'Jake Lee'. In addition to allowing such local merges, ASPEN+ offers new optimality criteria for selecting solutions, such as minimizing rule violations or maximising the number of rules supporting a merge. Our main contributions are thus (1) the formalisation and computational analysis of various notions of optimal solution, and (2) an extensive experimental evaluation on real-world datasets, demonstrating the effect of local merges and the new optimality criteria on both accuracy and runtime.

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 high-complexity heuristics. In this paper, we propose a simple and fast local search algorithms 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 cover (and thus also independent sets) than state of the art local search algorithms for MinVC.

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.

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 high-complexity heuristics. In this paper, we propose a simple and fast local search algorithms 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 cover (and thus also independent sets) than state of the art local search algorithms for MinVC.

Minimum Vertex Cover (MinVC) is a well known NP-hard combinatorial optimization problem, and local search has been shown to be one of the most effective approaches to this problem. State-of-the-art MinVC local search algorithms employ edge weighting techniques and prefer to select vertices with higher weighted score. These algorithms are not robust and especially have poor performance on instances with structures which defeat greedy heuristics. In this paper, we propose a vertex weighting scheme to address this shortcoming, and combine it within the current best MinVC local search algorithm NuMVC, leading to a new algorithm called TwMVC. Our experiments show that TwMVC outperforms NuMVC on the standard benchmarks namely DIMACS and BHOSLIB. To the best of our knowledge, TwMVC is the first MinVC algorithm that attains the best known solution for all instances in both benchmarks. Further, TwMVC shows superiority on a benchmark of real-world networks.