A popular model to measure the stability of a network is k-core - the maximal induced subgraph in which every vertex has at least k neighbors. Many studies maximize the number of vertices in k-core to improve the stability of a network. In this paper, we study the edge k-core problem: Given a graph G, an integer k and a budget b, add b edges to non-adjacent vertex pairs in G such that the k-core is maximized. We prove the problem is NP-hard and APX-hard. A heuristic algorithm is proposed on general graphs with effective optimization techniques. Comprehensive experiments on 9 real-life datasets demonstrate the effectiveness and the efficiency of our proposed methods.

Project management for virtual enterprise is a challenging task, current project system cannot support it very well because of the gap between enterprises. After analyzing the characteristics of virtual enterprise, the project domain was defined for supporting the virtual enterprise project management system. Then we discuss the information sharing mechanism between domains based on public, protected and primate library, and present a system architecture based on grid service. Experiments show that the proposed approach can be used in distributed project management environment, such as networked manufacture system.