Quantum and classical query complexities of local search are polynomially related

Miklos Santha, Mario Szegedy

Research output: Contribution to journalConference article

13 Citations (Scopus)

Abstract

Let f be an integer valued function on a finite set V. We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phrased as: for a fixed neighborhood structure G(V, E) find a vertex x ∈ V such that f(x) is not bigger than any value that f takes on some neighbor of x. The complexity of the algorithm is measured by the number of questions of the form "what is the value of f on z?" We show that the deterministic, randomized and quantum query complexities of the problem are polynomially related. This generalizes earlier results of Aldous and Aaronson and solves the main open problem in [1].

Original languageEnglish (US)
Pages (from-to)494-501
Number of pages8
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - Jan 1 2004
EventProceedings of the 36th Annual ACM Symposium on Theory of Computing - Chicago, IL, United States
Duration: Jun 13 2004Jun 15 2004

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Decision trees
  • Local optimization
  • Neighborhood structure
  • PLO
  • Quantum computationquery model

Cite this

@article{038a308e341d41f481e9742f9d6978de,
title = "Quantum and classical query complexities of local search are polynomially related",
abstract = "Let f be an integer valued function on a finite set V. We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phrased as: for a fixed neighborhood structure G(V, E) find a vertex x ∈ V such that f(x) is not bigger than any value that f takes on some neighbor of x. The complexity of the algorithm is measured by the number of questions of the form {"}what is the value of f on z?{"} We show that the deterministic, randomized and quantum query complexities of the problem are polynomially related. This generalizes earlier results of Aldous and Aaronson and solves the main open problem in [1].",
keywords = "Decision trees, Local optimization, Neighborhood structure, PLO, Quantum computationquery model",
author = "Miklos Santha and Mario Szegedy",
year = "2004",
month = "1",
day = "1",
language = "English (US)",
pages = "494--501",
journal = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",
issn = "0734-9025",
publisher = "Association for Computing Machinery (ACM)",

}

TY - JOUR

T1 - Quantum and classical query complexities of local search are polynomially related

AU - Santha, Miklos

AU - Szegedy, Mario

PY - 2004/1/1

Y1 - 2004/1/1

N2 - Let f be an integer valued function on a finite set V. We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phrased as: for a fixed neighborhood structure G(V, E) find a vertex x ∈ V such that f(x) is not bigger than any value that f takes on some neighbor of x. The complexity of the algorithm is measured by the number of questions of the form "what is the value of f on z?" We show that the deterministic, randomized and quantum query complexities of the problem are polynomially related. This generalizes earlier results of Aldous and Aaronson and solves the main open problem in [1].

AB - Let f be an integer valued function on a finite set V. We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phrased as: for a fixed neighborhood structure G(V, E) find a vertex x ∈ V such that f(x) is not bigger than any value that f takes on some neighbor of x. The complexity of the algorithm is measured by the number of questions of the form "what is the value of f on z?" We show that the deterministic, randomized and quantum query complexities of the problem are polynomially related. This generalizes earlier results of Aldous and Aaronson and solves the main open problem in [1].

KW - Decision trees

KW - Local optimization

KW - Neighborhood structure

KW - PLO

KW - Quantum computationquery model

UR - http://www.scopus.com/inward/record.url?scp=4544268402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544268402&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:4544268402

SP - 494

EP - 501

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

SN - 0734-9025

ER -