A Sublinear Algorithm for Approximate Shortest Paths in Large Networks

Abstract

Computing distances and finding shortest paths in massive real-world networks is a fundamental algorithmic task in network analysis. There are two main approaches to solving this task. On one end are traversal-based algorithms like bidirectional breadth-first search (BiBFS), which have no preprocessing step but are slow on individual distance inquiries. On the other end are indexing-based approaches, which create and maintain a large index. This allows for answering individual inquiries very fast; however, index creation is prohibitively expensive. We seek to bridge these two extremes: quickly answer distance inquiries without the need for costly preprocessing. We propose a new algorithm and data structure, WormHole, for approximate shortest path computations. WormHole leverages structural properties of social networks to build a sublinearly sized index, drawing upon the core-periphery decomposition of Ben-Eliezer et al. [10]. Empirically, WormHole's preprocessing time improves upon index-based solutions by orders of magnitude: indexing billion edges graphs takes only a few minutes. Real time performance is consistently much faster than in BiBFS. The acceleration comes at the cost of a minor accuracy trade-off. We complement these empirical results with provable theoretical guarantees.