Lower Bounds for Algebraic Computation Trees of Functions with Finite Domains

1991 ◽  
Vol 20 (4) ◽  
pp. 655-668 ◽  
Author(s):  
Andrew Chi-Chih Yao
Keyword(s):  
Lower Bounds ◽  
Algebraic Computation ◽  
Computation Trees ◽  
Finite Domains

SOME LOWER BOUNDS ON GEOMETRIC SEPARABILITY PROBLEMS

2006 ◽  
Vol 16 (01) ◽  
pp. 1-26 ◽  
Author(s):  
ESTHER M. ARKIN ◽  
FERRAN HURTADO ◽  
JOSEPH S. B. MITCHELL ◽  
CARLOS SEARA ◽  
STEVEN S. SKIENA
Keyword(s):  
Lower Bounds ◽  
Point Sets ◽  
Tree Model ◽  
Algebraic Computation ◽  
Computation Tree

We obtain lower bounds in the algebraic computation tree model for deciding the separability of two disjoint point sets. In particular, we show Ω(n log n) time lower bounds for separability by means of strips, wedges, wedges with apices on a given line, fixed-slopes double wedges, and triangles, which match the complexity of the existing algorithms, and therefore prove their optimality.

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