# Improved dynamic reachability algorithms for directed graphs

@article{Roditty2002ImprovedDR, title={Improved dynamic reachability algorithms for directed graphs}, author={Liam Roditty and Uri Zwick}, journal={The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.}, year={2002}, pages={679-688} }

We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) a decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in O(mn) total expected time, essentially the time needed for computing the transitive closure of the initial…

## 17 Citations

Decrementai Transitive Closure and Shortest Paths for Planar Digraphs and Beyond

- Mathematics, Computer ScienceSODA
- 2018

The tools used to obtain the best state-of-the-art decremental algorithms for reachability and approximate shortest paths in directed graphs can be successfully combined with the existence of small separators in certain graph classes.

Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs

- Computer ScienceSTOC
- 2014

A randomized algorithm is obtained which achieves an Õ (mn0.984) expected total update time for SSR and (1 + ε)-approximate SSSP, where Õ(·) hides poly log n and this algorithm serves as a building block for several other dynamic algorithms.

Faster Fully Dynamic Transitive Closure in Practice

- Computer ScienceSEA
- 2020

This paper engineer new algorithms to maintain all-pairs reachability information which are simple and space-efficient and outperform all state-of-the-art algorithms on all types of input considerably in practice.

Decremental single-source reachability in planar digraphs

- Mathematics, Computer ScienceSTOC
- 2017

These results constitute the first almost optimal (up to polylogarithmic factors) algorithms for both directed planar graphs for non-trivial reachability-type problems, for which only polynomial bounds are known in general graphs.

Improved Fully Dynamic Reachability Algorithm for Directed Graph

- Computer ScienceArXiv
- 2007

The proposed algorithm combines existing fully dynamic reachability algorithm with well known witness counting technique to improve efficiency of maintaining reachability information when edges are deleted.

Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components

- Computer ScienceTALG
- 2013

A new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph that processes any sequence of edge deletions in <i>O</i>(<i>mn</i>) time and answers queries in constant time is presented.

Near-Optimal Algorithms for Reachability, Strongly-Connected Components and Shortest Paths in Partially Dynamic Digraphs

- Mathematics, Computer ScienceArXiv
- 2020

This thesis presents new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions, and obtains the first randomized data structure to maintain SSR and SCCs in near-optimal total update time in a graph undergoing edge deletions.

Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components

- Computer ScienceSODA 2013
- 2013

A new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph that processes any sequence of edge deletions in O(mn) time and answers queries in constant time is presented.

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.

ARROW: Approximating Reachability Using Random Walks Over Web-Scale Graphs

- Computer Science2019 IEEE 35th International Conference on Data Engineering (ICDE)
- 2019

This paper proposes a first practical attempt to address reachability query processing issues by abandoning the traditional indexing approach altogether and operating directly on the graph as it evolves, and shows that ARROW, despite its simplicity, is near-accurate and scales to graphs with tens of Millions of vertices and hundreds of millions of edges.