Space-efficient Algorithms for Visibility Problems in Simple Polygon

Given a simple polygon P consisting of n vertices, we study the problem of designing space-efficient algorithms for computing (i) the visibility polygon of a point inside P , (ii) the weak visibility polygon of a line segment inside P and (iii) the minimum link path between a pair of points inside P . For problem (i) two algorithms are proposed. The first one is an in-place algorithm where the input array may be lost. It uses only O(1) extra space apart from the input array. The second one assumes that the input is given in a read-only array, and it needs O( √ n) extra space. The time complexity of both the algorithms are O(n). For problem (ii), we have assumed that the input polygon is given in a readonly array. Our proposed algorithm runs in O(n) time using O(1) extra space. For problem (iii) the time and space complexities of our proposed algorithm are O(kn) and O(1) respectively; k is the length (number of links) in a minimum link path between the given pair of points.