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We study how we can accelerate the spreading of information in temporalgraphs via delaying operations; a problem that captures real-world applicationsvarying from information flows to distribution schedules. In a temporal graphthere is a set of fixed vertices and the available connections between themchange over time in a predefined manner. We observe that, in some cases, thedelay of some connections can in fact decrease the time required to reach fromsome vertex (source) to another vertex (target). We study how we can minimizethe maximum time a set of source vertices needs to reach every other vertex ofthe graph when we are allowed to delay some of the connections of the graph.For one source, we prove that the problem is W[2]-hard and NP-hard, whenparameterized by the number of allowed delays. On the other hand, we derive apolynomial-time algorithm for one source and unbounded number of delays. Thisis the best we can hope for; we show that the problem becomes NP-hard whenthere are two sources and the number of delays is not bounded. We complementour negative result by providing an FPT algorithm parameterized by thetreewidth of the graph plus the lifetime of the optimal solution. Finally, weprovide polynomial-time algorithms for several classes of graphs.

Minimizing Reachability Times on Temporal Graphs via Shifting Labels