Testing acyclicity of directed graphs in sublinear time

Michael A. Bender, Dana Ron

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper initiates the study of testing properties of directed graphs. In particular, the paper considers the most basic property of directed graphs-acyclicity. Because the choice of representation affects the choice of algorithm, the two main representations of graphs are studied. For the adjacency matrix representation, most appropriate for dense graphs, a testing algorithm is developed that requires query and time complexity of Õ (1/∈2), where ∈ is a distance parameter independent of the size of the graph. The algorithm, which can probe the adjacency matrix of the graph, accepts every graph that is acyclic, and rejects, with probability at least 2/3, every graph whose adjacency matrix should be modified in at least ∈ fraction of its entries so that it become acyclic. For the incidence list representation, most appropriate for sparse graphs, an Ω(|V|1/3) lower bound is proved on the number of queries and the time required for testing, where V is the set of vertices in the graph. These results stand in contrast to what is known about testing acyclicity in undirected graphs.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 27th International Colloquium, ICALP 2000, Proceedings
EditorsUgo Montanari, Jose D. P. Rolim, Emo Welzl
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540450221
StatePublished - 2000
Event27th International Colloquium on Automata, Languages and Programming, ICALP 2000 - Geneva, Switzerland
Duration: 9 Jul 200015 Jul 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Colloquium on Automata, Languages and Programming, ICALP 2000


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