Abstract
We study the relation between the query complexity of adaptive and non-adaptive testers in the dense graph model. It has been known for a couple of decades that the query complexity of non-adaptive testers is at most quadratic in the query complexity of adaptive testers. We show that this general result is essentially tight; that is, there exist graph properties for which any non-adaptive tester must have query complexity that is almost quadratic in the query complexity of the best general (i.e., adaptive) tester. More generally, for every q: Nrightarrow N such that q(n)≤q √n and constant c\in[1,2], we show a graph property that is testable in Θ(q(n) queries, but its non-adaptive query complexity is Θ(q(n) c}), omitting poly(log n) factors and ignoring the effect of the proximity parameter ϵ. Furthermore, the upper bounds hold for one-sided error testers, and are at most quadratic in 1/ϵ. These results are obtained through the use of general reductions that transport properties of ordered structured (like bit strings) to those of unordered structures (like unlabeled graphs). The main features of these reductions are query-efficiency and preservation of distance to the properties. This method was initiated in our prior work (ECCC, TR20-149), and we significantly extend it here.
Original language | English |
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Title of host publication | Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021 |
Publisher | IEEE Computer Society |
Pages | 269-275 |
Number of pages | 7 |
ISBN (Electronic) | 9781665420556 |
State | Published - 2022 |
Externally published | Yes |
Event | 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 - Virtual, Online, United States Duration: 7 Feb 2022 → 10 Feb 2022 |
Publication series
Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 2022-February |
ISSN (Print) | 0272-5428 |
Conference
Conference | 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 |
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Country/Territory | United States |
City | Virtual, Online |
Period | 7/02/22 → 10/02/22 |
Bibliographical note
Publisher Copyright:© 2022 IEEE.
Keywords
- Non adaptive vs Adaptive queries
- Property Testing