Disentangling the Computational Complexity of Network Untangling
Abstract
We study the network untangling problem introduced by Rozenshtein, Tatti, and Gionis [DMKD 2021], which is a variant of Vertex Cover on temporal graphs  graphs whose edge set changes over discrete time steps. They introduce two problem variants. The goal is to select at most $k$ time intervals for each vertex such that all timeedges are covered and (depending on the problem variant) either the maximum interval length or the total sum of interval lengths is minimized. This problem has data mining applications in finding activity timelines that explain the interactions of entities in complex networks. Both variants of the problem are NPhard. In this paper, we initiate a multivariate complexity analysis involving the following parameters: number of vertices, lifetime of the temporal graph, number of intervals per vertex, and the interval length bound. For both problem versions, we (almost) completely settle the parameterized complexity for all combinations of those four parameters, thereby delineating the border of fixedparameter tractability.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.02668
 arXiv:
 arXiv:2204.02668
 Bibcode:
 2022arXiv220402668F
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Artificial Intelligence;
 Computer Science  Discrete Mathematics