Affiliation:
1. Columbia University, New York, NY, USA
Abstract
We consider the problem of finding a cycle in a sparse directed graph
G
that is promised to be far from acyclic, meaning that the smallest
feedback arc set
, i.e., a subset of edges whose deletion results in an acyclic graph, in
G
is large. We prove an information-theoretic lower bound, showing that for
N
-vertex graphs with constant outdegree, any algorithm for this problem must make Ω̄(N
5/9
) queries to an adjacency list representation of
G
. In the language of property testing, our result is an Ω̄(N
5/9)
lower bound on the query complexity of one-sided algorithms for testing whether sparse digraphs with constant outdegree are far from acyclic. This is the first improvement on the Ω (√
N
) lower bound, implicit in the work of Bender and Ron, which follows from a simple birthday paradox argument.
Funder
NSF
Simons Collaboration on Algorithms and Geometry
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
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