Hunting Temporal Bumps in Graphs with Dynamic Vertex Properties

Abstract

Given a time interval and a graph where vertices exhibit a property of interest (PoI) dynamically, an interesting question is: where (i.e., which part of the graph) and when (i.e., which time sub-interval) does the PoI occur frequently? To our knowledge, no work has been done to answer this question to date. We address this issue in this paper. Specifically, given (i) a time interval composed of multiple time slots and (ii) a graph where each vertex either exhibits or does not exhibit the PoI in each time slot, our objective is to find a pair of a connected sub-graph and a time sub-interval (which we refer to as a temporal bump), such that the discrepancy between the numbers of times that vertices in this sub-graph exhibit and do not exhibit the PoI during this time sub-interval is maximized. Due to the NP-hardness of this problem, initially, we propose two approximation algorithms. The first one achieves a tight approximation guarantee, at the cost of a weak scalability to the number of time slots. The second one achieves a strong scalability to the number of time slots, at the price of a loose approximation guarantee. Then, we propose two heuristic algorithms that have no non-trivial approximation guarantee, but produce similar solutions with, and are considerably faster than, the two approximation algorithms. Experiments on real datasets show that, in comparison with baselines built using related existing techniques, our algorithms hunt bumps with significantly higher discrepancies, while scaling well to large graphs, and thus are more suitable for answering the aforementioned question.