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
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
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 -