TY - GEN

T1 - Cell-probe lower bounds for dynamic problems via a new communication model

AU - Yu, Huacheng

N1 - Publisher Copyright:
© 2016 ACM.

PY - 2016/6/19

Y1 - 2016/6/19

N2 - 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: 1) insert(a, b), add an interval [a, b] to I, provided that a and b are integers in [0,n]; 2) delete(a, b), delete an (existing) interval [a, b] from I; 3) 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(n0.01) queries, for which any data structure with any constant error probability requires Ω(nlogn) time in expectation. Interestingly, we use the sparse set disjointness protocol of Håstad and Wigderson 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.

AB - 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: 1) insert(a, b), add an interval [a, b] to I, provided that a and b are integers in [0,n]; 2) delete(a, b), delete an (existing) interval [a, b] from I; 3) 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(n0.01) queries, for which any data structure with any constant error probability requires Ω(nlogn) time in expectation. Interestingly, we use the sparse set disjointness protocol of Håstad and Wigderson 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.

KW - Cell-probe model

KW - Klee's measure problem

KW - Lower bound

UR - http://www.scopus.com/inward/record.url?scp=84979238814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979238814&partnerID=8YFLogxK

U2 - 10.1145/2897518.2897556

DO - 10.1145/2897518.2897556

M3 - Conference contribution

AN - SCOPUS:84979238814

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 362

EP - 374

BT - STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Mansour, Yishay

A2 - Wichs, Daniel

PB - Association for Computing Machinery

T2 - 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016

Y2 - 19 June 2016 through 21 June 2016

ER -