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Algorithms 2015, 8(4), 810-831; doi:10.3390/a8040810

Finding Supported Paths in Heterogeneous Networks

1
LINA, UMR CNRS 6241, Université de Nantes, Nantes 44322, France
2
Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Berlin D-10587, Germany
This paper is an extended version of our paper published in the Proceedings of the 11th International Symposium on Experimental Algorithms (SEA 2012), Bordeaux, France, 7–9 June 2012, originally entitled “Algorithms for Subnetwork Mining in Heterogeneous Networks”.
*
Author to whom correspondence should be addressed.
Academic Editor: Giuseppe Lancia
Received: 17 June 2015 / Revised: 25 September 2015 / Accepted: 29 September 2015 / Published: 9 October 2015
(This article belongs to the Special Issue Algorithmic Themes in Bioinformatics)
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Abstract

Subnetwork mining is an essential issue in the analysis of biological, social and communication networks. Recent applications require the simultaneous mining of several networks on the same or a similar vertex set. That is, one searches for subnetworks fulfilling different properties in each input network. We study the case that the input consists of a directed graph D and an undirected graph G on the same vertex set, and the sought pattern is a path P in D whose vertex set induces a connected subgraph of G. In this context, three concrete problems arise, depending on whether the existence of P is questioned or whether the length of P is to be optimized: in that case, one can search for a longest path or (maybe less intuitively) a shortest one. These problems have immediate applications in biological networks and predictable applications in social, information and communication networks. We study the classic and parameterized complexity of the problem, thus identifying polynomial and NP-complete cases, as well as fixed-parameter tractable and W[1]-hard cases. We also propose two enumeration algorithms that we evaluate on synthetic and biological data. View Full-Text
Keywords: NP-hard problems; directed acyclic graphs; longest path problem; shortest path problem; protein interaction networks; metabolic networks NP-hard problems; directed acyclic graphs; longest path problem; shortest path problem; protein interaction networks; metabolic networks
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Fertin, G.; Komusiewicz, C.; Mohamed-Babou, H.; Rusu, I. Finding Supported Paths in Heterogeneous Networks. Algorithms 2015, 8, 810-831.

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