"The supreme art of war is to subdue the enemy without fighting." This was Sun Tzu back in the 5th century BC. This quote is true to this day though, and our efforts to subdue the enemy are now based on fear. We have developed technologies and weapons to such an extent that they actually can destroy whole cities in the blink of an eye, often using hypersonic weapons. This also means that we've developed technologies and weapons to prevent such things from happening in the first place.

Algorithms for finding frequent and/or interesting subgraphs in a single large graph scenario are computationally intensive because of the graph isomorphism and the subgraph isomorphism problem. These problems are compounded by the size of most real-world datasets which have sizes in the order of 105 or 106. The SUBDUE algorithm developed by Cook and Holder finds the most compressing subgraph in a large graph. In order to perform the same task on real-world data sets efficiently, Cook et al. developed a parallel approach to SUBDUE called the SP-SUBDUE based on the MPI framework. This paper extends the work done by Cook et al. to improve the efficiency of MPI SUBDUE by modifying the evaluation phase. Our experiments show an improvement in speed-up while retaining the quality of the results of serial SUBDUE. The techniques that we have used in this study can also be used in similar algorithms which use static partitioning of the data and re-evaluation of locally interesting patterns over all the nodes of the cluster.

There are two primary types of graph-based data miners: frequent subgraph and compression-based miners. With frequent subgraph miners, the most interesting substructure is the largest one (or ones) that meet the minimum support. Whereas, compression-based graph miners discover those subgraphs that maximize the amount of compression that a particular substructure provides a graph. The algorithms associated with these two approaches are not only different, but they also may result in dramatic performance differences, as well as in the normative patterns being discovered. In order to compare these two types of graph-based approaches to knowledge discovery, in the following sections we will compare two publicly available applications: GASTON and SUBDUE.

Graph-based knowledge discovery has become a powerful tool in the machine learning and data mining areas. It provides a flexible and natural data representation to describe real world domains. In this research work we present a novel algorithm for graph-based approaches to deal with numerical attributes during the data processing phase implemented in the Subdue system. Our experimental results show that the use of numerical attributes increased classification accuracy in the Mutagenesis and PTC domains in 22% compared to the Subdue system when it does not use our numerical attributes handling approach. Our method also outperforms other author's results for the same domains, around 7% for the Mutagenesis domain and around 17% for the PTC domain.