Geodesic
Finding the Most Relevant Fragments in Networks
Journal of Graph Algorithms and Applications, Tome 14 (2010) no. 2, pp. 307-336.

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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 or a tree. We give polynomial-time algorithms, NP-hardness and NP-completeness proofs, approximation algorithms, and also fixed-parameter tractable algorithms. 
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     author = {Kevin Buchin and Sergio Cabello and Joachim Gudmundsson and Maarten L\"offler and Jun Luo and G\"unter Rote and Rodrigo Silveira and Bettina Speckmann and Thomas Wolle},
     title = {Finding the {Most} {Relevant} {Fragments} in {Networks}},
     journal = {Journal of Graph Algorithms and Applications},
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Kevin Buchin; Sergio Cabello; Joachim Gudmundsson; Maarten Löffler; Jun Luo; Günter Rote; Rodrigo Silveira; Bettina Speckmann; Thomas Wolle. Finding the Most Relevant Fragments in Networks. Journal of Graph Algorithms and Applications, Tome 14 (2010) no. 2, pp. 307-336. doi : 10.7155/jgaa.00209. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00209/

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