  A common technique to speed 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 tremendous impact on the performance on some
real-world networks, while it only seems to save a constant factor on other
types of networks. Even though finding shortest paths is a ubiquitous problem,
there are only few studies attempting to understand the apparently asymptotic
speedups on some networks, using average case analysis on certain models for
real-world networks.
  In this paper we give a new perspective on this, by analyzing deterministic
properties that permit theoretical analysis and that can easily be 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. Moreover, we perform experiments on a large set of real-world
networks showing that our parameters capture the concept of practical running
time well.
