scholarly journals On Topological Lower Bounds for Algebraic Computation Trees

2015 ◽  
Vol 17 (1) ◽  
pp. 61-72 ◽  
Author(s):  
Andrei Gabrielov ◽  
Nicolai Vorobjov
Keyword(s):  
Lower Bounds ◽  
Algebraic Computation ◽  
Computation Trees

scholarly journals Complexity Lower Bounds for Approximation Algebraic Computation Trees

1999 ◽  
Vol 15 (4) ◽  
pp. 499-512 ◽  
Author(s):  
Felipe Cucker ◽  
Dima Grigoriev
Keyword(s):  
Lower Bounds ◽  
Algebraic Computation ◽  
Complexity Lower Bounds ◽  
Computation Trees

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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