1,736 research outputs found
Span-core Decomposition for Temporal Networks: Algorithms and Applications
When analyzing temporal networks, a fundamental task is the identification of
dense structures (i.e., groups of vertices that exhibit a large number of
links), together with their temporal span (i.e., the period of time for which
the high density holds). In this paper we tackle this task by introducing a
notion of temporal core decomposition where each core is associated with two
quantities, its coreness, which quantifies how densely it is connected, and its
span, which is a temporal interval: we call such cores \emph{span-cores}.
For a temporal network defined on a discrete temporal domain , the total
number of time intervals included in is quadratic in , so that the
total number of span-cores is potentially quadratic in as well. Our first
main contribution is an algorithm that, by exploiting containment properties
among span-cores, computes all the span-cores efficiently. Then, we focus on
the problem of finding only the \emph{maximal span-cores}, i.e., span-cores
that are not dominated by any other span-core by both their coreness property
and their span. We devise a very efficient algorithm that exploits theoretical
findings on the maximality condition to directly extract the maximal ones
without computing all span-cores.
Finally, as a third contribution, we introduce the problem of \emph{temporal
community search}, where a set of query vertices is given as input, and the
goal is to find a set of densely-connected subgraphs containing the query
vertices and covering the whole underlying temporal domain . We derive a
connection between this problem and the problem of finding (maximal)
span-cores. Based on this connection, we show how temporal community search can
be solved in polynomial-time via dynamic programming, and how the maximal
span-cores can be profitably exploited to significantly speed-up the basic
algorithm.Comment: ACM Transactions on Knowledge Discovery from Data (TKDD), 2020. arXiv
admin note: substantial text overlap with arXiv:1808.0937
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
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