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MADALGO Theory Seminar

MADALGO Seminar: Huacheng Yu (Stanford University): "Cell-probe Lower Bounds for Dynamic Problems via a New Communication Model"

2016.02.15 | Katrine Østerlund Rasmussen

Date Tue 29 Mar
Time 14:15 15:00
Location Nygaard-395

Title
Cell-probe Lower Bounds for Dynamic Problems via a New Communication Model

Abstract
In this paper, we develop a new communication model to prove a data structure lower bound for the dynamic interval union problem. The problem is to maintain a multiset of intervals I over [0, n] with integer coordinates, supporting the following operations: 

- insert(a, b): add an interval [a, b] to I, provided that a and b are integers in [0, n]; 

- delete(a, b): delete a (previously inserted) interval [a, b] from I; 

- query(): return the total length of the union of all intervals in I. 

It is related to the two-dimensional case of Klee's measure problem. We prove that there is a distribution over sequences of operations with O(n) insertions and deletions, and O(n^0.01) queries, for which any data structure with any constant error probability requires Omega(n log n) time in expectation. Interestingly, we use the sparse set disjointness protocol of Hastad and Wigderson [ToC'07] to speed up a reduction from a new kind of nondeterministic communication games, for which we prove lower bounds. 

For applications, we prove lower bounds for several dynamic graph problems by reducing them from dynamic interval union.

Lecture / talk