A fully dynamic reachability algorithm for directed graphs with an almost linear update time

DMCA

A fully dynamic reachability algorithm for directed graphs with an almost linear update time (2004)

Cached

Download Links

Other Repositories/Bibliography

DBLP

by Liam Roditty , Uri Zwick

Venue:	In Proc. of ACM Symposium on Theory of Computing
Citations:	39 - 2 self

BibTeX

@INPROCEEDINGS{Roditty04afully,
    author = {Liam Roditty and Uri Zwick},
    title = {A fully dynamic reachability algorithm for directed graphs with an almost linear update time},
    booktitle = {In Proc. of ACM Symposium on Theory of Computing},
    year = {2004},
    pages = {184--191}
}

OpenURL

Abstract

We obtain a new fully dynamic algorithm for the reachability problem in directed graphs. Our algorithm has an amortized update time of O(m+n log n) and a worst-case query time of O(n), where m is the current number of edges in the graph, and n is the number of vertices in the graph. Each update operation either inserts a set of edges that touch the same vertex, or deletes an arbitrary set of edges. The algorithm is deterministic and uses fairly simple data structures. This is the first algorithm that breaks the O(n 2) update barrier for all graphs with o(n 2)edges. One of the ingredients used by this new algorithm may be interesting in its own right. It is a new dynamic algorithm for strong connectivity in directed graphs with an interesting persistency property. Each insert operation creates a new version of the graph. A delete operation deletes edges from all versions. Strong connectivity queries can be made on each version of the graph. The algorithm handles each update in O(mα(m, n)) amortized time, and each query in O(1) time, where α(m, n) is a functional inverse of Ackermann’s function appearing in the analysis of the union-find data structure. Note that the update time of O(mα(m, n)), in case of a delete operation, is the time needed for updating all versions of the graph. Categories and Subject Descriptors G.2.2 [Discrete Mathematics]: Graph Theory—Graph algorithms, Path and circuit problems

Keyphrases

dynamic reachability algorithm linear update time directed graph update time delete operation deletes edge new version arbitrary set dynamic algorithm circuit problem update barrier current number new dynamic algorithm new algorithm first algorithm delete operation functional inverse simple data structure union-find data structure interesting persistency property worst-case query time algorithm handle strong connectivity query graph theory graph algorithm update operation subject descriptor reachability problem insert operation strong connectivity discrete mathematics

DMCA