Characterizing and recognizing weak visibility polygons

An algorithm for recognizing palm polygons

“…Thus, it remains open whether a palm polygon can be recognized in O(n) time. The technique in our recognition algorithm of scanning only the visibility polygon from each edge has also been used by Ghosh et al 1993 to recognize a weak visibility polygon. It will be interesting if the same technique can be used to give algorithms for other problems.…”

“…They have shown that, under this characterization, the class of palm polygons contains several known classes of polygons such as star-shaped polygons, weak visibility polygons, spiral polygons. Moreover, the shortest path has been used for computing weak visibility polygons (Guibas et al 1987), for characterizing and recognizing weak visibility polygons (Ghosh et al 1993), for computing a minimum link path (Ghosh 1991) and for solving several other problems. The above results clearly establish that studying geodesic properties in connection with special classes of polygons is an interesting and important issue in computational geometry.…”

Computing the maximum clique in the visibility graph of a simple polygon

“…3c). Once v m is located, the maximum hidden vertex set in C(v j , v k ) (denoted as MH(v j , v k )) can be computed using the following lemma of Ghosh et al [12] (after a minor modification). Let SMH(v j , v k ) denote the size of MH(v j , v k ).…”

“…Here, we present an O(ne) time algorithm for computing the maximum hidden vertex set in G if G is the visibility of a convex fan P and the Hamiltonian cycle C in G that corresponds to the boundary of P is given along with G. Our algorithm is based on the relationship between Euclidean shortest paths in P and hidden vertex set in G as observed by Ghosh et al [12]. We present the algorithm in Section 3.…”

“…Shermer [20] showed that the maximum independent set problem is also NP-hard. An independent set in the visibility graph is also called hidden set which has been studied by Eidenbenz [6,7], Ghosh et al [12] and Lin and Skiena [16]. Further, Lin and Skiena [16] showed that the problems of finding a minimum vertex cover and a maximum dominating set in the visibility graph of a simple polygon are NP-hard.…”