TY - CHAP

T1 - Estimating the distance to a monotone function

AU - Ailon, Nir

AU - Chazelle, Bernard

AU - Comandur, Seshadhri

AU - Liu, Ding

PY - 2004

Y1 - 2004

N2 - In standard property testing, the task is to distinguish between objects that have a property ℘ and those that are ε-far from ℘, for some ε > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy ℘. This implies that property testing in and of itself cannot be expected to yield any information whatsoever about the distance from the object to the property. We address this problem in this paper, restricting our attention to monotonicity testing. A function f : {1, . . . ,n} → R is at distance εf from being monotone if it can (and must) be modified at εfn places to become monotone. For any fixed δ > 0, we compute, with probability at least 2/3, an interval [(1/2-δ)ε, ε] that encloses εf. The running time of our algorithm is O(εf-1 log log εf-1 log n), which is optimal within a factor of log log εf-1 and represents a substantial improvement over previous work. We give a second algorithm with an expected running time of O(εf-1 log n log log log n).

AB - In standard property testing, the task is to distinguish between objects that have a property ℘ and those that are ε-far from ℘, for some ε > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy ℘. This implies that property testing in and of itself cannot be expected to yield any information whatsoever about the distance from the object to the property. We address this problem in this paper, restricting our attention to monotonicity testing. A function f : {1, . . . ,n} → R is at distance εf from being monotone if it can (and must) be modified at εfn places to become monotone. For any fixed δ > 0, we compute, with probability at least 2/3, an interval [(1/2-δ)ε, ε] that encloses εf. The running time of our algorithm is O(εf-1 log log εf-1 log n), which is optimal within a factor of log log εf-1 and represents a substantial improvement over previous work. We give a second algorithm with an expected running time of O(εf-1 log n log log log n).

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U2 - 10.1007/978-3-540-27821-4_21

DO - 10.1007/978-3-540-27821-4_21

M3 - Chapter

AN - SCOPUS:35048845592

SN - 3540228942

SN - 9783540228943

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

SP - 229

EP - 236

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

A2 - Jansen, Klaus

A2 - Khanna, Sanjeev

A2 - Rolim, Jose D. P.

A2 - Ron, Dana

PB - Springer Verlag

ER -