Abstract
This paper develops a new technique for proving amortized, randomized cell-probe lower bounds on dynamic data structure problems. We introduce a new randomized nondeterministic four-party communication model that enables 'accelerated', error-preserving simulations of dynamic data structures. We use this technique to prove an Ω(n(log n/log log n)2) cell-probe lower bound for the dynamic 2D weighted orthogonal range counting problem (2D-ORC) with n/poly log n updates and n queries, that holds even for data structures with exp(-Ω(n)) success probability. This result not only proves the highest amortized lower bound to date, but is also tight in the strongest possible sense, as a matching upper bound can be obtained by a deterministic data structure with worst-case operational time. This is the first demonstration of a 'sharp threshold' phenomenon for dynamic data structures. Our broader motivation is that cell-probe lower bounds for exponentially small success facilitate reductions from dynamic to static data structures. As a proof-of-concept, we show that a slightly strengthened version of our lower bound would imply an Ω((log n/log log n)2) lower bound for the static 3D-ORC problem with O(n logO(1) n) space. Such result would give a near quadratic improvement over the highest known static cell-probe lower bound, and break the long standing Ω(log n) barrier for static data structures.
Original language | English |
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Title of host publication | Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 |
Publisher | IEEE Computer Society |
Pages | 305-314 |
Number of pages | 10 |
ISBN (Electronic) | 9781509039333 |
DOIs | |
State | Published - 14 Dec 2016 |
Externally published | Yes |
Event | 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick, United States Duration: 9 Oct 2016 → 11 Oct 2016 |
Publication series
Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 2016-December |
ISSN (Print) | 0272-5428 |
Conference
Conference | 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 |
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Country/Territory | United States |
City | New Brunswick |
Period | 9/10/16 → 11/10/16 |
Bibliographical note
Publisher Copyright:© 2016 IEEE.