Improved Lower Bounds for Submodular Function Minimization

07/09/2022
∙
by   Deeparnab Chakrabarty, et al.
∙
0
∙

We provide a generic technique for constructing families of submodular functions to obtain lower bounds for submodular function minimization (SFM). Applying this technique, we prove that any deterministic SFM algorithm on a ground set of n elements requires at least Ί(n log n) queries to an evaluation oracle. This is the first super-linear query complexity lower bound for SFM and improves upon the previous best lower bound of 2n given by [Graur et al., ITCS 2020]. Using our construction, we also prove that any (possibly randomized) parallel SFM algorithm, which can make up to 𝗉𝗈𝗅𝗒(n) queries per round, requires at least Ί(n / log n) rounds to minimize a submodular function. This improves upon the previous best lower bound of ΊĖƒ(n^1/3) rounds due to [Chakrabarty et al., FOCS 2021], and settles the parallel complexity of query-efficient SFM up to logarithmic factors due to a recent advance in [Jiang, SODA 2021].

READ FULL TEXT

page 1

page 2

page 3

page 4

research
∙ 11/15/2019

New Query Lower Bounds for Submodular Function MInimization

We consider submodular function minimization in the oracle model: given ...
research
∙ 11/14/2021

A Polynomial Lower Bound on the Number of Rounds for Parallel Submodular Function Minimization and Matroid Intersection

Submodular function minimization (SFM) and matroid intersection are fund...
research
∙ 09/08/2023

Parallel Submodular Function Minimization

We consider the parallel complexity of submodular function minimization ...
research
∙ 11/12/2020

FPT-Algorithms for the l-Matchoid Problem with Linear and Submodular Objectives

We design a fixed-parameter deterministic algorithm for computing a maxi...
research
∙ 01/05/2020

New lower bounds for Massively Parallel Computation from query complexity

Roughgarden, Vassilvitskii, and Wang (JACM 18) recently introduced a nov...
research
∙ 12/02/2021

Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness

We study the complexity of optimizing highly smooth convex functions. Fo...
research
∙ 11/09/2022

Shortest Cycles With Monotone Submodular Costs

We introduce the following submodular generalization of the Shortest Cyc...

Please sign up or login with your details

Forgot password? Click here to reset