Data Structures Lower Bounds and Popular Conjectures

TL;DR

This paper explores the relationships between key conjectures in data structures and circuit complexity, establishing connections that imply super-linear lower bounds for certain explicit computational problems.

Contribution

It links the Network Coding Conjecture to data structure problems and circuit lower bounds, providing new insights into their interdependencies.

Findings

Connection between NCC and data structure problems established

Implication of super-linear circuit lower bounds for explicit functions

Insights into the relative strength of conjectures in complexity theory

Abstract

In this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. We establish a connection between the Network Coding Conjecture (NCC) of Li and Li and several data structure like problems such as non-adaptive function inversion of Hellman and the well-studied problem of polynomial evaluation and interpolation. In turn these data structure problems imply super-linear circuit lower bounds for explicit functions such as integer sorting and multi-point polynomial evaluation.