Temporal graphs (in which edges are active at specified times) are of
particular relevance for spreading processes on graphs, e.g.~the spread of
disease or dissemination of information. Motivated by real-world applications,
modification of static graphs to control this spread has proven a rich topic
for previous research. Here, we introduce a new type of modification for
temporal graphs: the number of active times for each edge is fixed, but we can
change the relative order in which (sets of) edges are active. We investigate
the problem of determining an ordering of edges that minimises the maximum
number of vertices reachable from any single starting vertex;
epidemiologically, this corresponds to the worst-case number of vertices
infected in a single disease outbreak. We study two versions of this problem,
both of which we show to be \NP-hard, and identify cases in which the problem
can be solved or approximated efficiently.Comment: Author final version, to appear in Journal of Computer and System
Sciences. Material from the previous version has been reorganised
substantially, and some results have been strengthene
