Efficient computation of rectilinear geodesic voronoi neighbor in presence of obstacles
In this paper, we present an algorithm to compute the rectilinear geodesic voronoi neighbor of an arbitrary query point q among a set S of m points in the presence of a set O of n vertical line segment obstacles inside a rectangular floor. The distance between a pair of points α and Β is the shortest rectilinear distance avoiding the obstacles in O and is denoted by δ(α,Β). The rectilinear geodesic voronoi neighbor of an arbitrary query point q, (RGVN(q)) is the point p i ∃ S such that δ(q,p i ) is minimum. The algorithm suggests a preprocessing of the elements of the set S and O in O((m+n)log(m+n)) time such that for any arbitrary query point q, the RGVN query can be answered in O(max(logm, logn)) time. The space required for storing the preprocessed information is O(n+mlogm). If the points in S are placed on the boundary of the rectangular floor, a different technique is adopted to decrease the space complexity to O(m+n). The latter algorithm works even when the obstacles are rectangles instead of line segments.
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