Average-case analysis of incremental topological ordering

Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worst-case insertion sequences or only evaluated experimentally on random DAGs. We present the first average-case analysis of incremental topological ordering algorithms. We prove an expected runtime of O(n(2) polylog(n)) under insertion of the edges of a complete DAG in a random order for the algorithms of Alpern et al. (1990) [4], Katriel and Bodlaender (2006) 118], and Pearce and Kelly (2006) [23]. (C) 2009 Elsevier B.V. All rights reserved.