mathe进来啊。

Zig 2002-03-11 09:22:00

回复人： mathe() ( ) 信誉：100 2002-3-5 13:04:26 得分:0

在ACM上有一篇文章，给出了O(n log^2(n))的算法，不过实在太复杂了，
下面是其中的一段话
Consider the folIowing variation of the largest empty rectangle problem (which we call the
largest empty comer rectangle (LECR) problem): Given a rectangle containing a ser, S, of n points,
find the largest-area empty subrecLangle such that the following conditions hold:
(a) Either its top edge is flush with the top edge of the given rectangle or its top-rightmost
comer is one of the given points.
(b) Its left-bottommost corner is one of the given points.
(c) Its sides are paraRe1 to those of the original rectangIe and is contained in this rectangle.
ChazeIIe et al. [4] have shown that if T((n) denotes the time to solve the largest-area empty comer
rectangle problem for any set., S, of n points then the largest-area empty rectangle problem for any
set, s’. can be solved in O(T(n) + n log n) time. In this paper, we provide two algorithms to solve the
largest empty comer rectangle problem. Section II provides a simple algorithm that takes
O(n log3n) time and Section V provides a more complicated one which only takes O(n log2n) time.
The memory required by both thesk algorithms is O(n). Analogous to the largest-area empty corner
rectangle problem, we can also define the largest-perimeter empty corner rectangle problem and if
the latter problem can be solved in ?$t) time for any set, S, of n points then arguments similar to
those given in 141 can be used to solve the largest-perimeter empty rectangle problem in
0($,(n) + n log n) time for any set, s’. In se&on VI, we point out that the algorithms given in
sections II and V can be modified to compute the largest-perimeter empty comer rectangle in
O(n Iog2n) and 001 log n) time, respectively. Since Sl(n log n) is a lower bound on the time required
to compute the largest-area and the Iargest -perimeter rectangles [S], our second algorithm for corn-
puting the largest-perimeter empty comer rectangle is optimal within amultiplicative constant and the
correspond.ing algorithm for computing the largest-area empty rectangle Is optimal within a log n
factor.

这个你是从什么地方找到的啊，我想看的说。能不能upload一下？

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