DeepAI AI Chat
Log In Sign Up

An Optimal Algorithm for Certifying Monotone Functions

04/04/2022
by   Meghal Gupta, et al.
MIT
Toyota Technological Institute at Chicago
0

Given query access to a monotone function f{0,1}^n→{0,1} with certificate complexity C(f) and an input x^⋆, we design an algorithm that outputs a size-C(f) subset of x^⋆ certifying the value of f(x^⋆). Our algorithm makes O(C(f) ·log n) queries to f, which matches the information-theoretic lower bound for this problem and resolves the concrete open question posed in the STOC '22 paper of Blanc, Koch, Lange, and Tan [BKLT22]. We extend this result to an algorithm that finds a size-2C(f) certificate for a real-valued monotone function with O(C(f) ·log n) queries. We also complement our algorithms with a hardness result, in which we show that finding the shortest possible certificate in x^⋆ may require Ω(nC(f)) queries in the worst case.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/19/2022

The Query Complexity of Certification

We study the problem of certification: given queries to a function f : {...
03/21/2020

Black-box Methods for Restoring Monotonicity

In many practical applications, heuristic or approximation algorithms ar...
11/09/2022

Shortest Cycles With Monotone Submodular Costs

We introduce the following submodular generalization of the Shortest Cyc...
10/03/2019

Finding monotone patterns in sublinear time

We study the problem of finding monotone subsequences in an array from t...
10/25/2021

Parameterized Convexity Testing

In this work, we develop new insights into the fundamental problem of co...
07/14/2022

A Query-Optimal Algorithm for Finding Counterfactuals

We design an algorithm for finding counterfactuals with strong theoretic...
10/01/2020

Understanding the hardness of approximate query processing with joins

We study the hardness of Approximate Query Processing (AQP) of various t...