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For a set of n disjoint line segments S in R 2 , the visibility testing problem (VTP) is to test whether the query point p sees a query segment s ∈ S. For this configuration, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from any query point p can be computed quickly. In this paper, we solve VTP in… (More)

Given a set S of n disjoint line segments in R 2 , the visibility counting problem (VCP) is to preprocess S such that the number of segments in S visible from any query point p can be computed quickly. This problem can trivially be solved in logarithmic query time using O(n 4) preprocessing time and space. Gudmundsson and Morin proposed a 2-approximation… (More)

For a simple polygon P of size n, we define weak visibility counting problem (WVCP) as finding the number of visible segments of P from a query line segment pq. We present different algorithms to compute WVCP in sub-linear time. In our first algorithm, we spend O(n 7) time to preprocess the polygon and build a data structure of size O(n 6), so that we can… (More)

Given a terrain and a query point p on or above it, we want to count the number of triangles of terrain that are visible from p. We present an approximation algorithm to solve this problem. We implement the algorithm and then we run it on the real data sets. The experimental results show that our approximation solution is very close to the real solution and… (More)

We consider approximation of diameter of a set S of n points in dimension m. E˜gecio˜glu and Kalantari [8] have shown that given any p ∈ S, by computing its farthest in S, say q, and in turn the farthest point of q, say q , we have diam(S) ≤ √ 3 d(q, q). Furthermore, iteratively replacing p with an appropriately selected point on the line segment pq, in at… (More)

For a set of n disjoint line segments S in R 2 , the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from a query point p can be computed quickly. This problem can be solved in logarithmic query time using O(n 4) preprocessing time and space. In this paper, we propose a randomized approximation algorithm… (More)

The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph K(r, s, t) into 5-cycles was first considered by Mahmoodian and Mirzakhani (1995). They stated some necessary conditions and conjectured that these conditions are also sufficient. Since then, many cases of the problem have been solved by various authors;… (More)

We use the matrix product formalism to find exact ground states of two new spin-1 quantum chains with nearest neighbor interactions. One of the models, model I, describes a one-parameter family of quantum chains for which the ground state can be found exactly. In certain limit of the parameter, the Hamiltonian turns into the interesting case H = i (S i · S… (More)

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