TY - GEN
T1 - Almost optimal distribution-free sample-based testing of k-modality
AU - Ron, Dana
AU - Rosin, Asaf
N1 - Publisher Copyright: © 2020 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - For an integer k ≥ 0, a sequence σ = σ1,..., σn over a fully ordered set is k-modal, if there exist indices 1 = a0 < a1 < · · · < ak+1 = n such that for each i, the subsequence σai,..., σai+1 is either monotonically non-decreasing or monotonically non-increasing. The property of k-modality is a natural extension of monotonicity, which has been studied extensively in the area of property testing. We study one-sided error property testing of k-modality in the distribution-free sample-based model. We prove an upper bound of1 O (√kn log k/ε) on the sample complexity, and an almost matching lower bound of Ω (√kn/ε). When the underlying distribution is uniform, we obtain a completely tight bound of Θ (√kn/ε), which generalizes what is known for sample-based testing of monotonicity under the uniform distribution.
AB - For an integer k ≥ 0, a sequence σ = σ1,..., σn over a fully ordered set is k-modal, if there exist indices 1 = a0 < a1 < · · · < ak+1 = n such that for each i, the subsequence σai,..., σai+1 is either monotonically non-decreasing or monotonically non-increasing. The property of k-modality is a natural extension of monotonicity, which has been studied extensively in the area of property testing. We study one-sided error property testing of k-modality in the distribution-free sample-based model. We prove an upper bound of1 O (√kn log k/ε) on the sample complexity, and an almost matching lower bound of Ω (√kn/ε). When the underlying distribution is uniform, we obtain a completely tight bound of Θ (√kn/ε), which generalizes what is known for sample-based testing of monotonicity under the uniform distribution.
KW - Distribution-free property testing
KW - K-modality
KW - Sample-based property testing
UR - http://www.scopus.com/inward/record.url?scp=85091270930&partnerID=8YFLogxK
U2 - https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.27
DO - https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.27
M3 - منشور من مؤتمر
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2020
A2 - Byrka, Jaroslaw
A2 - Meka, Raghu
T2 - 23rd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 24th International Conference on Randomization and Computation, APPROX/RANDOM 2020
Y2 - 17 August 2020 through 19 August 2020
ER -