Abstract Pattern matching in big graphs is important for different modern applications. Recently, this problem was defined in terms of multiple extensions of graph simulation, to reduce complexity and capture more meaningful results. These results were achieved through the relaxation of commonly used constraint in subgraph isomorphism pattern matching. Nevertheless, these graph simulation variant models are still too strict to provide results in many cases, especially when analyzed graphs contain anomalies and incomplete information. To deal with this issue, we introduce a new graph pattern matching (GPM) method, called partial simulation, capable of retrieving matches despite missing parts of the pattern graph, such as vertices and/or edges. Furthermore, considering the number and inequality of the outputs, we define a relevance function to compute a value expressing how each match vertex respects the pattern graph. Similarly, we define partial dual simulation GPM that returns vertices that satisfy a part of the dual simulation constraints and assigns a relevance value to them. Additionally, we provide distributed scalable algorithms to evaluate the proposed partial simulation methods based on the distributed vertex-centric programming paradigm. Finally, our experiments on real-world data graphs demonstrate the effectiveness of the proposed models and the efficiency of their associated algorithms.

Graph Edit Distance (GED) is a well-known measure used in the graph matching to measure the similarity/dissimilarity between two graphs by computing the minimum cost of edit operations needed to transform one graph into another. This process, Which appears to be simple, is known NP-hard and time consuming since the search space is increasing exponentially. One way to optimally solve this problem is by using Branch and Bound (B&B) algorithms, Which reduce the computation time required to explore the whole search space by performing an implicit enumeration of the search space instead of an exhaustive one based on a pruning technique. nevertheless, They remain inefficient when dealing with large problem instances due to the impractical running time needed to explore the whole search space. To overcome this issue, We propose in this paper three parallel B&B approaches based on shared memory to exploit the multi-core CPU processors: First, a work-stealing approach where several instances of the B&B algorithm explore a single search tree concurrently achieving speedups up to 24 × faster than the sequential version. Second, a tree-based approach where multiple parts of the search tree are explored simultaneously by independent B&B instances achieving speedups up to 28 × . Finally, Due to the irregular nature of the GED problem, two load-balancing strategies are proposed to ensure a fair workload between parallel processes achieving impressive speedups up to 300 × . all experiments have been carried out on well-known datasets

ABSTRACT The majority of key management schemes suffer from the physical compromising of nodes. This vulnerability allows an adversary to reproduce clones and inject them throughout the network to perform other types of attacks. Furthermore, adding new nodes to the network (for maintenance), which is an inevitable step to prolong its life or to repair voids, is the best opportunity to carry out the cloning attack. Our contribution in this paper is to perfectly secure network maintenance against the cloning attack, using a solution based on the digital signature of the base station. Our solution is based on the agreement that the base station should give to a new node to share a pairwise key with its neighbors. The conducted simulations under TinyOS SIMulator (TOSSIM) show that, in addition to perfect resilience, our approach is efficient in terms of time consumption and communication overhead. Copyright © 2014 John Wiley & Sons, Ltd.