  By considering the task of finding the shortest walk through a network we
find an algorithm for which the run time is not as O(2^n), with n being the
number of nodes, but instead scales with the number of nodes in a coarsened
network. This coarsened network has a number of nodes related to the number of
dense regions in the original graph. Since we exploit a form of local community
detection as a preprocessing, this work gives support to the project of
developing heuristic algorithms for detecting dense regions in networks:
preprocessing of this kind can accelerate optimization tasks on networks. Our
work also suggests a class of empirical conjectures for how structural features
of efficient networked systems might scale with system size.
