Unformatted text preview: n cells. You can ﬁnd the leftmost cell in O ( n ). Then by visiting a cell next to the current one and reporting xcoordinate of the site of the cell, you can obtain the solution of S , [ x i 1 , x i 2 , ··· , x i n ] in O ( n ). Therefore S ∝ O ( n ) V and the lower bound L V of V is the following: L V = Ω( n log n )O ( n ) = Ω( n log n ) [ x 1 , x 2 , · · · x n ] ( x i 1 , 0) ( x i 2 , 0) ( x i n , 0) [( x 1 , 0) , ( x 2 , 0) , · · · ( x n , 0)] O ( n ) O ( n ) [ x i 1 , x i 2 , · · · x i n ] Input of sorting problem Output of sorting problem Compute the Voronoi diagram Walk around to the next cells and report xcoordinates. Figure 1: Lower bound of computing the Voronoi diagram 1...
View
Full Document
 Spring '08
 Unkown
 Algorithms, Voronoi diagram, Johann Peter Gustav Lejeune Dirichlet, Mathematical diagram

Click to edit the document details