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DIMACS Theory of Computing Seminar

An Adaptive Step Toward the Multiphase Conjecture

Omri Weinstein

Location:  Core 301
Date & time: Wednesday, 26 February 2020 at 11:00AM - 12:00PM

Abstract: In 2010, Patrascu proposed the Multiphase problem, as a candidate for proving polynomial
lower bounds on the operational time of dynamic data structures. Patrascu conjectured that any data
structure for the Multiphase problem must make n^eps cell-probes in either the update or query phase,
and showed that this would imply similar unconditional lower bounds on many important dynamic data
structure problems. There has been almost no progress on this conjecture in the past decade. We show
an \(~\Omega(\sqrt{n})\) cell-probe lower bound on the Multiphase problem for data structures with general
(adaptive) updates, and queries with unbounded but "layered" adaptivity. This result captures all known
set-intersection data structures and significantly strengthens previous Multiphase lower bounds which
only captured non-adaptive data structures.

Our main technical result is a communication lower bound on a 4-party variant of Patrascu's NOF Multiphase
game, using information complexity techniques. We show that this communication lower bound implies the
first polynomial \((n^{1+ 1/k})\) lower bound on the number of wires required to compute a *linear* operator using
*nonlinear* (degree-k) gates, a longstanding open question in circuit complexity.

Joint work with Young Kun Ko.

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