Abstract | ||
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We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains.
1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the upper bound [MATH HERE] in the usual uniform model, and prove an [MATH HERE] upper bound in the distribution-free setting.
2. We show a tight lower bound of [MATH HERE] queries for testing convexity of functions f : [n]ϵ → R on the line. This lower bound applies to both adaptive and non-adaptive algorithms, and matches the upper bound from item 1, showing that adaptivity does not help in this setting.
3. Moving to higher dimensions, we consider the case of a stripe [3] × [n]. We construct an adaptive tester for convexity of functions f : [3] × [n] → R with query complexity O(log2n). We also show that any non-adaptive tester must use [MATH HERE] queries in this setting. Thus, adaptivity yields an exponential improvement for this problem.
4. For functions f : [n]d → R over domains of dimension d ≥ 2, we show a non-adaptive query lower bound [MATH HERE].
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Year | DOI | Venue |
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2020 | 10.5555/3381089.3381214 | SODA '20: ACM-SIAM Symposium on Discrete Algorithms
Salt Lake City
Utah
January, 2020 |
Field | DocType | Citations |
Discrete mathematics,Convexity,Computer science | Conference | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Aleksandrs Belovs | 1 | 131 | 14.50 |
Eric Blais | 2 | 286 | 22.49 |
Abhinav Bommireddi | 3 | 0 | 0.34 |