# Faster Algorithms for Online Topological Ordering

@article{Kavitha2007FasterAF, title={Faster Algorithms for Online Topological Ordering}, author={Telikepalli Kavitha and Rogers Mathew}, journal={ArXiv}, year={2007}, volume={abs/0711.0251} }

We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications, including online cycle detection, which is to discover the first edge that introduces a cycle under an arbitrary sequence of edge insertions in a directed graph. In this paper we present efficient algorithms for the online topological ordering problem.
We…

## 10 Citations

Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

- Computer ScienceACM Trans. Algorithms
- 2012

We present two online algorithms for maintaining a topological order of a directed n-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles m…

Faster Algorithms for Incremental Topological Ordering

- Computer ScienceICALP
- 2008

This work presents two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created, using a deterministic and a randomized method.

A New Approach to Incremental Cycle Detection and Related Problems

- Computer Science, MathematicsACM Trans. Algorithms
- 2016

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.…

Incremental Topological Ordering and Strong Component Maintenance

- Computer ScienceArXiv
- 2008

An on-line algorithm for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created, which takes O(m^{1/2}) amortized time per arc.

A new approach to incremental topological ordering

- Computer Science, MathematicsSODA
- 2009

A new algorithm is presented that has a total cost of O(n2logn) for maintaining the topological ordering throughout all the edge additions of the graph G, and which is more efficient than existing algorithms.

Incremental Topological Sort and Cycle Detection in Õ ( m √ n ) Expected Total Time

- Computer Science
- 2017

A novel technique is introduced that allows us to improve upon the state of the art for a wide range of graph sparsity and has a total expected update time of Õ(m √ n) for both the incremental cycle detection and the topological sort problems.

A Labeling Approach to Incremental Cycle Detection

- Computer ScienceArXiv
- 2013

A new technique for incremental cycle detection is introduced that allows for both bounds (up to a logarithmic factor) to be obtained and seems more amiable for distributed implementation.

AUTOMATICALLY PARALLELIZING LEGACY BINARY CODE FOR MULTICORE ARCHITECTURES

- Computer Science
- 2009

It is found that n-gram (i.e., repeated instruction sequences) parallelism does exist, but it is not easily leveraged and it is believed that efforts that consider input data can help liberate high-order parallelism from almost all "sequential" codes.

Recent Advances in Fully Dynamic Graph Algorithms

- Computer ScienceArXiv
- 2021

A quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.

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