An O(n2.75) algorithm for incremental topological ordering

Authors:
Deepak Ajwani;Tobias Friedrich;Ulrich Meyer
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;J.W. Goethe University, Frankfurt/Main, Germany
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2008

Citing 12
Cited 2

Two algorithms for maintaining order in a list

STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On competitive on-line algorithms for the dynamic priority-ordering problem

Information Processing Letters
Maintaining a topological order under edge insertions

Information Processing Letters
Incremental evaluation of computational circuits

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On-line Graph Algorithms for Incremental Compilation

WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Uniform hashing in constant time and linear space

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Online topological ordering

ACM Transactions on Algorithms (TALG)
A dynamic topological sort algorithm for directed acyclic graphs

Journal of Experimental Algorithmics (JEA)
A tight analysis of the Katriel–Bodlaender algorithm for online topological ordering

Theoretical Computer Science
A dichromatic framework for balanced trees

SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Depth-first search and linear grajh algorithms

SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Average-case analysis of online topological ordering

ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation

Average-case analysis of incremental topological ordering

Discrete Applied Mathematics
Topological ordering algorithm for LDAG

Information Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a simple algorithm which maintains the topological order of a directed acyclic graph (DAG) with n nodes, under an online edge insertion sequence, in O(n2.75) time, independent of the number m of edges inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m3/2 log n, m3/2 + n2 log n}) by Katriel and Bodlaender [2006]. We also provide an empirical comparison of our algorithm with other algorithms for incremental topological sorting.