Optimizing Reachability Sets in Temporal Graphs by Delaying

24^th October 2019, 14:00 EEE 6.05
Argyrios Deligkas
University of Liverpool

Abstract

A temporal graph is a dynamic graph, where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays on the availability of the edges, affect the reachability sets from given sources.The questions about reachability sets are motivated by numerous applications of temporal graphs in network epidemiology, or scheduling problems in supply
networks in manufacturing. We study the computational complexity of several optimization problems with different reachability objectives and in particular the
control mechanism based on natural operations of delaying time events. The first one, termed merging, is global and batches together consecutive time labels
in the whole network simultaneously, which corresponds to postponing all events until a particular time. The second one, imposes independent delays on the
time labels of every edge of the graph. We provide a thorough investigation of the computational complexity of different objectives related to reachability sets
when these operations are used. For the merging operation, we prove NP-hardness results for several minimization and maximization reachability objectives,
even for very simple graph structures. For the second operation, we prove that the minimization problems are NP-hard when the number of allowed delays is
bounded. We complement this with a polynomial-time algorithm for the case of unbounded delays.