Space-Query Tradeoffs in Range Subgraph Counting and Listing

TL;DR

This paper explores the balance between pre-computation space and query efficiency in range subgraph counting and listing, providing bounds and tradeoffs for practical graph analytics on vertex-selected subgraphs.

Contribution

It introduces the problems of range subgraph counting and listing, and establishes theoretical bounds on space-query tradeoffs for these problems.

Findings

Derived upper bounds for query time given space constraints.

Established lower bounds indicating the limitations of space-query tradeoffs.

Provided insights into efficient graph analytics for subgraphs induced by attribute ranges.

Abstract

This paper initializes the study of {\em range subgraph counting} and {\em 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 {\em space usage} and {\em 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.