On competitive on-line algorithms for the dynamic priority-ordering problem
Information Processing Letters
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
Incremental evaluation of computational circuits
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Incremental Graph Evaluation
A dynamic topological sort algorithm for directed acyclic graphs
Journal of Experimental Algorithmics (JEA)
A batch algorithm for maintaining a topological order
ACSC '10 Proceedings of the Thirty-Third Australasian Conferenc on Computer Science - Volume 102
Topological ordering algorithm for LDAG
Information Processing Letters
| Hi-index | 0.89 |
We study the problem of incrementally maintaining a topological sorting in a large DAG. The Discovery Algorithm (DA) of Alpern et al. [Proc. 1st Annual ACM-SIAM Symp. on Discrete Algorithms, 1990, pp. 32-42] computes a cover K of nodes such that a solution to the modified problem can be found by changing node priorities within K only. It achieves a runtime complexity that is polynomially bounded in terms of the minimal cover size k.The temporary space complexity of DA grows quickly with increasing number of added edges and cover size. We introduce the Depth-First Discovery Algorithm (DFDA), which uses depth-first search to reduce the temporary space of DA from O(|A| × ||-K||) to O(|A| + ||K||), where |A| is the number of edges to add and ||K|| is the extended size of the cover. DFDA is simpler than DA and performs better in our empirical tests.