The query complexity of finding local minima in the lattice

Amos Beimel, Felix Geller, Eyal Kushilevitz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper we study the query complexity of finding local minimum points of a boolean function. This task occurs frequently in exact learning algorithms for many natural classes, such as monotone DNF, O(log n)-term DNF, unate DNF, and decision trees. On the negative side, we prove that any (possibly randomized) algorithm that produces a local minimum of a function f chosen from a sufficiently "rich" concept class, using a membership oracle for f, must ask Ω(n2) membership queries in the worst case. In particular, this lower bound applies to the class of decision trees. A simple algorithm is known that achieves this lower bound. On the positive side, we show that for the class O(log n)-term DNF finding local minimum points requires only Θ(n log n) membership queries (and more generally Θ(tn) membership queries for t-term DNF with t ≤ n). This efficient procedure improves the time and query complexity of known learning algorithms for the class O(log n)-term DNF.

Original languageEnglish
Pages (from-to)69-83
Number of pages15
JournalInformation and Computation
Issue number1
StatePublished - 25 Nov 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


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