Re: A computational geometry problem

Ben Sunshine-Hill <[email protected]>
Newsgroups gmane.games.devel.algorithms
Message-ID <[email protected]>
On Sat, Aug 22, 2009 at 8:17 AM, J.-R. Jiang <[email protected]>wrote:

> Problem: Given n lines, determine a point minimizing the summation of the
> distances from the point to the n lines.
>

This is a Least Absolute Deviations problem, which are normally solved by
simplex methods; see the Wikipedia page for more details. If an O(n^3)
running time is acceptable to you, however, a minimal solution will always
be found at the intersection of two of the lines, so you can just check all
the intersection points if you like.

Ben

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