Constrained multilinear detection for faster functional motif discovery

Finding Path Motifs in Large Temporal Graphs Using Algebraic Fingerprints

We study a family of pattern-detection problems in vertex-colored temporal graphs. In particular, given a vertex-colored temporal graph and a multiset of colors as a query, we search for temporal paths in the graph that contain the colors specified in the query. These types of problems have several applications, for example, in recommending tours for tourists or detecting abnormal behavior in a network of financial transactions. For the family of pattern-detection problems we consider, we establish complexity results and design an algebraic-algorithmic framework based on constrained multilinear sieving. We demonstrate that our solution scales to massive graphs with up to a billion edges for a multiset query with 5 colors and up to 100 million edges for a multiset query with 10 colors, despite the problems being non-deterministic polynomial time-hard. Our implementation, which is publicly available, exhibits practical edge-linear scalability and is highly optimized. For instance, in a real-world graph dataset with >6 million edges and a multiset query with 10 colors, we can extract an optimal solution in <8 minutes on a Haswell desktop with four cores.

Detecting list-colored graph motifs in biological networks using branch-and-bound strategy

In this work, we study the list-colored graph motif problem, which was introduced to detect functional motifs in biological networks. Given a multi-set M of colors as the query motif and a list-colored graph G where each vertex in G is associated with a set of colors, the aim of this problem is to find a sub-graph of G whose vertex set is colored exactly as motif M. To solve this problem, we present a heuristic method to efficiently and accurately detect list-colored graph motifs in biological networks using branch-and-bound strategy. We transform the detection of list-colored graph motif to the search of connected induced sub-graphs in list-colored graph, where the vertices in the sub-graph are assigned to distinctive colors of query motif. This transformation enables our method to accurately discover the occurrences of query motif without enumerating and verifying all sub-graphs. Furthermore, a new initial vertex selection strategy based on the colors of vertices is proposed to accurately determine the search scope of motifs. Experiments conducted on metabolic networks and protein-interaction networks demonstrate that our method can achieve better performance in accuracy and efficiency in comparison to other existing methods.

RANGI: a fast list-colored graph motif finding algorithm

Given a multiset of colors as the query and a list-colored graph, i.e., an undirected graph with a set of colors assigned to each of its vertices, in the NP-hard list-colored graph motif problem the goal is to find the largest connected subgraph such that one can select a color from the set of colors assigned to each of its vertices to obtain a subset of the query. This problem was introduced to find functional motifs in biological networks. We present a branch-and-bound algorithm named RANGI for finding and enumerating list-colored graph motifs. As our experimental results show, RANGI's pruning methods and heuristics make it quite fast in practice compared to the algorithms presented in the literature. We also present a parallel version of RANGI that achieves acceptable scalability.