TY - GEN

T1 - Testing acyclicity of directed graphs in sublinear time

AU - Bender, Michael A.

AU - Ron, Dana

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84974603941&partnerID=8YFLogxK

U2 - 10.1007/3-540-45022-x_68

DO - 10.1007/3-540-45022-x_68

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AN - SCOPUS:84974603941

SN - 9783540450221

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 809

EP - 820

BT - Automata, Languages and Programming - 27th International Colloquium, ICALP 2000, Proceedings

A2 - Montanari, Ugo

A2 - Rolim, Jose D. P.

A2 - Welzl, Emo

PB - Springer Verlag

T2 - 27th International Colloquium on Automata, Languages and Programming, ICALP 2000

Y2 - 9 July 2000 through 15 July 2000

ER -