Graph Mining Techniques

Graphs appear in several settings, like social networks, recommendation systems, computer communication networks, gene/protein biological networks, among others. A large amount of graph patterns, as well as graph generator models that mimic such patterns have been proposed over the last years. However, a deep and recurring question still remains: “What is a good pattern?” The answer is related to finding a pattern or a tool able to help distinguishing between actual real-world and fake graphs. Here we explore the ability of ShatterPlots, a simple and powerful algorithm to tease out patterns of real graphs, helping us to spot fake/masked graphs. The idea is to force a graph to reach a critical (“Shattering”) point, randomly deleting edges, and study its properties at that point.

Deadlock Prevention with Wormhole Routing

The problem of preventing deadlocks and livelocks in computer communication networks with wormhole routing is considered. The method to prevent deadlocks is to prohibit certain turns (i.e., the use of certain pairs of connected edges) in the routing process, in such a way that eliminates all cycles in the graph. A new algorithm that constructs a minimal (irreducible) set of turns that breaks all cycles and preserves connectivity of the graph is proposed and analyzed. The algorithm is tree-free and is considerably simpler than earlier cycle-breaking algorithms. The properties of the algorithm are proven, and lower and upper bounds for minimum cardinalities of cycle-breaking connectivity preserving sets for graphs of general topology, as well as for planar graphs, are presented. In particular, the algorithm guarantees that not more than 1/3 of all turns in the network become prohibited. Experimental results are presented on the fraction of prohibited turns, the distance dilation, as well as on the message delivery times and saturation loads for the proposed algorithm in comparison with known tree-based algorithms. The proposed algorithm outperforms the tree-based algorithms in all characteristics that were considered.