Search and sweep numbers of finite directed acyclic graphs

AbstractThe search number of a graph is the least number of searchers needed to find any (possibly infinitely fast) intruder hiding in the vertices or edges of the graph. The sweep number is the least number of searchers required if the searchers and intruder are constrained to the vertices (e.g. the edges may represent doors between rooms). In a directed acyclic graph the searchers are allowed to traverse the edges only in the given direction. The search number for directed acyclic graphs is determined. Bounds are given for the sweep number and it is determined exactly for two classes of directed acyclic graphs