Shortest Paths in Two Intersecting Pencils of Lines
نویسنده
چکیده
Suppose one has a line arrangement and one wants to find a shortest path from one point lying on a line of the arrangement to another such point. We look at a special case: the arrangement consists of two intersecting pencils (sets of lines where all intersect in a point), and the path endpoints are at opposite corners of the largest quadrilateral formed. The open problem was to find a shortest path in o(n) time. We prove here that there are only two possible shortest paths, and the shortest path can thus be computed in O(n) time.
منابع مشابه
On shortest paths in line arrangements
In this paper, we show that the shortest path between two points in a grid-like arrangement of two pencils of lines has a particularly simple structure, as was previously conjectured. This gives a linear-time algorithm for computing shortest paths in such arrangements.
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