We present an algorithm for constructing a depth-first search tree in planar digraphs; the algorithm can be implemented in the complexity class AC1(UL∩co-UL), which is contained in AC2. Prior to this (for more than a quarter-century), the fastest uniform deterministic parallel algorithm for this problem had a runtime of O(log 10n) (corresponding to the complexity class AC10⊆NC11). We also consider the problem of computing depth-first search trees in other classes of graphs and obtain additional new upper bounds.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Networks and Communications