Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Introduction to algorithms
Incremental algorithms for minimal length paths
Journal of Algorithms
On competitive on-line algorithms for the dynamic priority-ordering problem
Information Processing Letters
On the computational complexity of dynamic graph problems
Theoretical Computer Science
Maintaining a topological order under edge insertions
Information Processing Letters
A uniform approach to semi-dynamic problems on digraphs
Theoretical Computer Science - Special issue: graph theoretic concepts in computer science
Incremental evaluation of computational circuits
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A phase transition phenomenon in a random directed acyclic graph
Random Structures & Algorithms
On-line Graph Algorithms for Incremental Compilation
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
A fully dynamic reachability algorithm for directed graphs with an almost linear update time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Online Cycle Detection and Difference Propagation: Applications to Pointer Analysis
Software Quality Control
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Algorithms (TALG)
A dynamic topological sort algorithm for directed acyclic graphs
Journal of Experimental Algorithmics (JEA)
An O(n2.75) algorithm for online topological ordering
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
An O(n2.75) algorithm for incremental topological ordering
ACM Transactions on Algorithms (TALG)
A new approach to incremental topological ordering
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Average-case analysis of incremental topological ordering
Discrete Applied Mathematics
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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 online topological ordering algorithms. We prove an expected runtime of O(n2 polylog(n)) 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). This is much less than the best known worst-case bound O(n2.75) for this problem.