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Finding the Most Relevant Fragments in Networks

By Kevin Buchin, Sergio Cabello, Joachim Gudmundsson, Maarten Löffler, Jun Luo, Günter Rote, Rodrigo I. Silveira, Bettina Speckmann and Thomas Wolle


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 aconnected subnetworkF 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 or a tree. We give polynomial-time algorithms, NP-hardness and NP-completeness proofs, approximation algorithms, and also fixed-parameter tractable algorithms

Year: 2010
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