ON MINIMA OF FUNCTIONS, INTERSECTION PATTERNS OF CURVES, AND DAVENPORT-SCHINZEL SEQUENCES.

Micha Sharir, Ron Livne

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Several results are presented related to the problem of estimating the complexity M(f//1,. . . , f//N) of the pointwise minimum of n continuous univariate or bivariate functions f//1,. . . , f//N under the assumption that no pair (or triple) of these functions intersect in more than some fixed number s of points. The main result is that in the one-dimensional case M(f//I,. . . , f//N) is the functional inverse of Ackermann's function). In the two-dimensional case, the problem is substantially harder, and the authors have only some initial estimates on M. The treatment of the two-dimensional problem is based on certain properties of the intersection patterns of a collection of planar Jordan curves.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherIEEE
Pages312-320
Number of pages9
ISBN (Print)0818606444
StatePublished - 1985
Externally publishedYes

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428

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