Space-Query Tradeoffs in Range Subgraph Counting and Listing

Abstract

This paper initializes the study of range subgraph counting and range subgraph listing, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as opposed to all, vertices. In the first problem, there is an undirected graph G where each vertex carries a real-valued attribute. Given an interval q and a pattern Q, a query counts the number of occurrences of Q in the subgraph of G induced by the vertices whose attributes fall in q. The second problem has the same setup except that a query needs to enumerate (rather than count) those occurrences with a small delay. In both problems, our goal is to understand the tradeoff between space usage and query cost, or more specifically: (i) given a target on query efficiency, how much pre-computed information about G must we store? (ii) Or conversely, given a budget on space usage, what is the best query time we can hope for? We establish a suite of upper-and lower-bound results on such tradeoffs for various query patterns.

On Reporting Durable Patterns in Temporal Proximity Graphs

“…While [32,52] have provable guarantees, the algorithms are expensive, requiring time super-linear in the number of edges to report all durable triangles. Recently, Deng et al [18] proposed algorithms to report or count triangles (and other simple patterns) in time super-linear in the graph size. In contrast, we work with an implicit representation of the proximity graph and design algorithms that run in time near-linear in the number of nodes and output size.…”