Deterministic Performance Guarantees for Bidirectional BFS on Real-World Networks

Abstract

A common technique for speeding up shortest path queries in graphs is to use a bidirectional search, i.e., performing a forward search from the start and a backward search from the destination until a common vertex on a shortest path is found. In practice, this has a massive impact on performance in some real-world networks, while it seems to save only a constant factor in other types of networks. Although finding shortest paths is a ubiquitous problem, only few studies have attempted to explain the apparent asymptotic speedups on some networks using average case analysis on certain models of real-world network.

In this paper we provide a new perspective on this, by analyzing deterministic properties that allow theoretical analysis and that can be easily checked on any particular instance. We prove that these parameters imply sublinear running time for the bidirectional breadth-first search in several regimes, some of which are tight. Furthermore, we perform experiments on a large set of real-world networks and show that our parameters capture the concept of practical running time well.