Affiliation:
1. Università di Roma “La Sapienza”, Rome, Italy
2. Università di Roma “Tor Vergata”, Rome, Italy
Abstract
We present an algorithm for directed acyclic graphs that breaks through the
O
(
n
2
) barrier on the single-operation complexity of fully dynamic transitive closure, where
n
is the number of edges in the graph. We can answer queries in
O
(
n
ε
) worst-case time and perform updates in
O
(
n
ω(1,ε,1)−ε
+
n
1+ε
) worst-case time, for any ε∈[0,1], where ω(1,ε,1) is the exponent of the multiplication of an
n
×
n
ε
matrix by an
n
ε
×
n
matrix. The current best bounds on ω(1,ε,1) imply an
O
(
n
0.575
) query time and an
O
(
n
1.575
) update time in the worst case. Our subquadratic algorithm is randomized, and has one-sided error. As an application of this result, we show how to solve single-source reachability in
O
(
n
1.575
) time per update and constant time per query.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference17 articles.
1. Aho A. Hopcroft J. and Ullman J. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley Reading Mass. Aho A. Hopcroft J. and Ullman J. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley Reading Mass.
2. Matrix multiplication via arithmetic progressions
3. Demetrescu C. and Italiano G. F. 2001. Maintaining dynamic matrices for fully dynamic transitive closure. Tech. Rep. arXiv:cs.DS/0104002. Demetrescu C. and Italiano G. F. 2001. Maintaining dynamic matrices for fully dynamic transitive closure. Tech. Rep. arXiv:cs.DS/0104002.
4. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity
Cited by
33 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Sensitivity and Dynamic Distance Oracles via Generic Matrices and Frobenius Form;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06
2. Deterministic Fully Dynamic SSSP and More;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06
3. Subquadratic dynamic path reporting in directed graphs against an adaptive adversary;Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing;2022-06-09
4. Online cycle detection for models with mode-dependent input and output dependencies;Journal of Systems Architecture;2021-05
5. Dynamic Matrix Inverse: Improved Algorithms and Matching Conditional Lower Bounds;2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS);2019-11