541 research outputs found
Incremental complexity of a bi-objective hypergraph transversal problem
The hypergraph transversal problem has been intensively studied, from both a
theoretical and a practical point of view. In particular , its incremental
complexity is known to be quasi-polynomial in general and polynomial for
bounded hypergraphs. Recent applications in computational biology however
require to solve a generalization of this problem, that we call bi-objective
transversal problem. The instance is in this case composed of a pair of
hypergraphs (A, B), and the aim is to find minimal sets which hit all the
hyperedges of A while intersecting a minimal set of hyperedges of B. In this
paper, we formalize this problem, link it to a problem on monotone boolean
-- formulae of depth 3 and study its incremental complexity
Predicting Multi-actor collaborations using Hypergraphs
Social networks are now ubiquitous and most of them contain interactions
involving multiple actors (groups) like author collaborations, teams or emails
in an organizations, etc. Hypergraphs are natural structures to effectively
capture multi-actor interactions which conventional dyadic graphs fail to
capture. In this work the problem of predicting collaborations is addressed
while modeling the collaboration network as a hypergraph network. The problem
of predicting future multi-actor collaboration is mapped to hyperedge
prediction problem. Given that the higher order edge prediction is an
inherently hard problem, in this work we restrict to the task of predicting
edges (collaborations) that have already been observed in past. In this work,
we propose a novel use of hyperincidence temporal tensors to capture time
varying hypergraphs and provides a tensor decomposition based prediction
algorithm. We quantitatively compare the performance of the hypergraphs based
approach with the conventional dyadic graph based approach. Our hypothesis that
hypergraphs preserve the information that simple graphs destroy is corroborated
by experiments using author collaboration network from the DBLP dataset. Our
results demonstrate the strength of hypergraph based approach to predict higher
order collaborations (size>4) which is very difficult using dyadic graph based
approach. Moreover, while predicting collaborations of size>2 hypergraphs in
most cases provide better results with an average increase of approx. 45% in
F-Score for different sizes = {3,4,5,6,7}
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