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The big graph database provides strong modeling capabilities and efficient querying for complex applications. Subgraph isomorphism which finds exact matches of a query graph in the database efficiently, is a challenging problem. Current subgraph isomorphism approaches mostly are based on the pruning strategy proposed by Ullmann. These techniques have two significant drawbacks- first, they are unable to efficiently handle complex queries, and second, their implementations need the large indexes that require large memory resources. In this paper, we describe a new subgraph isomorphism approach, the HyGraph algorithm, that is efficient both in querying and with memory requirements for index creation. We compare the HyGraph algorithm with two popular existing approaches, GraphQL and Cypher using complexity measures and experimentally using three big graph data sets—(1) a country-level population database, (2) a simulated bank database, and (3) a publicly available World Cup big graph database. It is shown that the HyGraph solution performs significantly better (or equally) than competing algorithms for the query operations on these big databases, making it an excellent candidate for subgraph isomorphism queries in real scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible. [ABSTRACT FROM AUTHOR]

Graph data structure has been widely used across many application areas, such as web data, social network, and cheminformatics. The main benefit of storing data as graphs is there exists a rich set of graph algorithms and operations that can be used to solve various computing problems, including pattern matching, data mining, and image processing. Among these graph algorithms, the subgraph isomorphism problem is one of the most fundamental algorithms that can be utilized by many higher level applications. The subgraph isomorphism problem is defined as, given two graphs G and H , whether G contains a subgraph that is isomorphic to H. In this paper, we consider a special case of the subgraph isomorphism problem called the subgraph matching problem, which tests whether G is a subgraph of H. We propose a protocol that solve the subgraph matching problem in a privacy-preserving manner. The protocol allows two parties to jointly compute whether one graph is a subgraph of the other, while protecting the private information about the input graphs. The protocol is secure under the semi-honest setting, where each party performs the protocol faithfully. [ABSTRACT FROM AUTHOR]