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 x-coordinate 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 x-coordinates. Figure 1: Lower bound of computing the Voronoi diagram 1...
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- Spring '08
- Algorithms, Voronoi diagram, Johann Peter Gustav Lejeune Dirichlet, Mathematical diagram