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 averagecase analysis of incremental topological ordering algorithms. We prove an expected runtime of ( 2 polylog( )) under insertion of the edges of a complete DAG in a random order for the algorithms of Alpern et al. (SODA, 1990), Katriel and Bodlaender (TALG, 2006), and Pearce and Kelly (JEA, 2006).

• Type: Journal
• Year: 2010
• Where: DAM
• Authors: Deepak Ajwani, Tobias Friedrich
• Keywords: DAM 2010, Directed Acyclic Graph, Incremental Topological Ordering, Worst-case Insertion Sequences