TY - GEN

T1 - ON MINIMA OF FUNCTIONS, INTERSECTION PATTERNS OF CURVES, AND DAVENPORT-SCHINZEL SEQUENCES.

AU - Sharir, Micha

AU - Livne, Ron

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022181922&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022181922

SN - 0818606444

T3 - Annual Symposium on Foundations of Computer Science (Proceedings)

SP - 312

EP - 320

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - IEEE

ER -