Year: 2011
Type: preprint
Abstract: We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two algorithms, one suited to sparse graphs, and the other to dense graphs. The former takes the minimum of O(m^{3/2}) and O(mn^{2/3}) time to insert m arcs into an n-vertex graph; the latter takes O(n^2 log(n)) time. Our sparse algorithm is considerably simpler than a previous O(m^{3/2})-time algorithm; it is also faster on graphs of sufficient density. The time bound of our dense algorithm beats the previously best time bound of O(n^{5/2}) for dense graphs. Our algorithms rely for their efficiency on topologically ordered vertex numberings; bounds on the size of the numbers give bound on running times.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: CT: Authenticating Reality, Efficient Graph Algorithms and Data Structures - Theory and Practice, HEC: Collaborative Research: Techniques for Streaming File Systems and Databases, Collaborative Research: Understanding, Coping with, and Benefiting from Intractibility., Collaborative Research: Adversarial Contention Resolution, CSR-AES: Feedback-Driven Adaptive Multithreading, HEC: Collaborative Research: Techniques for Streaming File Systems and Databases, Collaborative Research: High-Performance Data Access through Memory Abstraction, HECURA: Microdata Storage Systems for High-End Computing, CPA: Practical Cache-Oblivious B-Trees, Collaborative Research: Adversarial Contention Resolution
OpenAlex ID: W2950014258