- Published 2010 in J. Graph Algorithms Appl.

We study a point pattern detection problem on networks, motivated by applications in geographical analysis, such as crime hotspot detection. Given a network N (a connected graph with non-negative edge lengths) together with a set of sites, which lie on the edges or vertices of N , we look for a connected subnetwork F of N of small total length that contains many sites. The edges of F can form parts of the edges of N . We consider different variants of this problem where N is either a general graph or restricted to a tree, and the subnetwork F that we are looking for is either a simple path, a path with self-intersections at vertices, or a tree. We give polynomial-time algorithms, NPhardness and NP-completeness proofs, approximation algorithms, and also fixed-parameter tractable algorithms.

@article{Buchin2010FindingTM,
title={Finding the Most Relevant Fragments in Networks},
author={Kevin Buchin and Sergio Cabello and Joachim Gudmundsson and Maarten L{\"{o}ffler and Jun Luo and G{\"{u}nter Rote and Rodrigo I. Silveira and Bettina Speckmann and Thomas Wolle},
journal={J. Graph Algorithms Appl.},
year={2010},
volume={14},
pages={307-336}
}