  A drawback of the classic approach for complexity analysis of distributed
graph problems is that it mostly informs about the complexity of notorious
classes of ``worst case'' graphs. Algorithms that are used to prove a tight
(existential) bound are essentially optimized to perform well on such worst
case graphs. However, such graphs are often either unlikely or actively avoided
in practice, where benign graph instances usually admit much faster solutions.
  To circumnavigate these drawbacks, the concept of universal complexity
analysis in the distributed setting was suggested by [Kutten and Peleg,
PODC'95] and actively pursued by [Haeupler et al., STOC'21]. Here, the aim is
to gauge the complexity of a distributed graph problem depending on the given
graph instance. The challenge is to identify and understand the graph property
that allows to accurately quantify the complexity of a distributed problem on a
given graph.
  In the present work, we consider distributed shortest paths problems in the
HYBRID model of distributed computing, where nodes have simultaneous access to
two different modes of communication: one is restricted by locality and the
other is restricted by congestion. We identify the graph parameter of
neighborhood quality and show that it accurately describes a universal bound
for the complexity of certain class of shortest paths problems in the HYBRID
model.

Distributed, Parallel, and Cluster Computing;Computational Complexity