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.
Highlights
The use of social and telecommunication networks has dramatically increased recently, resulting in new prominent applications of network analysis
SP, L ONGEST S UPPORTED PATH (LSP)and S HORTEST S UPPORTED PATH (SSP); arrows indicate that a result is implied by another result in the table
S UPPORTED PATH belongs to a new type of subnetwork mining problems, arising from recent applications of biological, social or information networks: several graphs, of various types, represent different relations between objects, and a subset of objects is sought, with particular properties in each network
Summary
The use of social and telecommunication networks has dramatically increased recently, resulting in new prominent applications of network analysis. The study of multi-dimensional mining started several years ago, but it mainly concerns homogeneous representations of data: directed graph alignment [4], undirected graph alignment [5], relational data mining [6] and social networks mining [2] are several examples. Such approaches found applications in computational biology [7,8,9], and showed their limits, due to the multiple types of biological networks that are used to describe different views of the same biological process. This multi-dimensional mining approach has led to the discovery of novel biological insights [3,15,16,17]
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