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||American English|
|Title of host publication||Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016|
|Publisher||IEEE Computer Society|
|Number of pages||10|
|State||Published - 14 Dec 2016|
|Event||57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick, United States|
Duration: 9 Oct 2016 → 11 Oct 2016
|Name||Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS|
|Conference||57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016|
|Period||9/10/16 → 11/10/16|
Bibliographical notePublisher Copyright:
© 2016 IEEE.