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#### Approximation algorithms for visibility computation and testing over a terrain

, Article Applied Geomatics ; Volume 9, Issue 1 , 2017 , Pages 53-59 ; 18669298 (ISSN) ; Ghodsi, M ; Güdükbay, U ; Golkari, M ; Sharif University of Technology
Springer Verlag
2017

Abstract

Given a 2.5D terrain and a query point p on or above it, we want to find the triangles of terrain that are visible from p. We present an approximation algorithm to solve this problem. We implement the algorithm and test it on real data sets. The experimental results show that our approximate solution is very close to the exact solution and compared to the other similar works, the computational cost of our algorithm is lower. We analyze the computational complexity of the algorithm. We consider the visibility testing problem where the goal is to test whether a given triangle of the terrain is visible or not with respect to p. We present an algorithm for this problem and show that the average...

#### Descriptive Complexity for Counting Problems

, M.Sc. Thesis Sharif University of Technology ; Ebrahimi Boroojeni, Javad (Supervisor)
Abstract

Descriptive complexity refers to the difficulty of expressing a problem in a formal language, allowing for a complete and precise description of the problem, including output specifications for function problems. Despite the success of the descriptive approach in computational complexity, this approach has been predominantly used for decision problems. In contrast to decision problems, a counting problem can be considered as a function with the range of natural numbers. This thesis focuses on the examination of counting problems from a descriptive perspective, exploring the connection between their descriptive and computational versions. Toward this goal, weighted logic is utilized to...

#### Visibility testing and counting

, Article Information Processing Letters ; Volume 115, Issue 9 , September , 2015 , Pages 649-654 ; 00200190 (ISSN) ; Ghodsi, M ; Zarei, A ; Pourreza, M ; Sharif University of Technology
Elsevier
2015

Abstract

For a set of n disjoint line segments S in R2, 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 expected logarithmic query time using quadratic preprocessing time and space. Moreover, we propose a (1+δ)-approximation algorithm for VCP using at most quadratic preprocessing time and space. The query time of this method is Oε (1/δ 2√n) where Oε (f(n))=O(f(n)nε) and ε>0 is an arbitrary constant number

#### Visibility testing and counting

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 28 May 2011 through 31 May 2011, Jinhua ; Volume 6681 LNCS , 2011 , Pages 343-351 ; 03029743 (ISSN) ; 9783642212031 (ISBN) ; Zarei, A ; Sharif University of Technology
2011

Abstract

For a set of n disjoint line segments S in R2, 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. For this configuration, the visibility testing problem (VTP) is to test whether p sees a fixed segment s. These problems can be solved in logarithmic query time by using O(n4) preprocessing time and space. In this paper, we approximately solve this problem using quadratic preprocessing time and space. Our methods are superior to current approximation algorithms in terms of both approximation factor and preprocessing cost. In this paper, we propose a 2-approximation algorithm for the VCP using at...

#### Weak visibility counting in simple polygons

, Article Journal of Computational and Applied Mathematics ; Volume 288 , November , 2015 , Pages 215-222 ; 03770427 (ISSN) ; Daneshpajouh, S ; Alipour, S ; Ghodsi, M ; Sharif University of Technology
Elsevier
2015

Abstract

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(n7) time to preprocess the polygon and build a data structure of size O(n6), so that we can optimally answer WVCP in O(logn) time. Then, we reduce the preprocessing costs to O(n4+ε) time and space at the expense of more query time of O(log5n). We also obtain a trade-off between preprocessing and query time costs. Finally, we propose an approximation method to reduce the preprocessing costs to O(n2) time and space and O(n1/2+ε) query...

#### A new double-counting cancellation technique for ray tracing using separation angle distribution

, Article 2008 IEEE International RF and Microwave Conference, RFM 2008, Kuala Lumpur, 2 December 2008 through 4 December 2008 ; April , 2008 , Pages 306-310 ; 9781424428663 (ISBN) ; Shishegar, A. A ; Sharif University of Technology
2008

Abstract

This paper presents a new efficient and accurate method to overcome the double-counting problem of ray tracing in indoor environments. The conventional method of modeling the transmitter using an icosahedron inscribed in the unit sphere is used. The separation angle distribution of the source rays over the faces of the icosahedron is calculated prior to the start of the tracing procedure. These angles are used to cancel the double-counting problem in the post processing stage. To validate our proposed method, an electromagnetic problem that has analytical solution is presented and the ray tracing results are compared to this solution. The simulation results agree with analytical solution...

#### An improved constant-factor approximation algorithm for planar visibility counting problem

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2 August 2016 through 4 August 2016 ; Volume 9797 , 2016 , Pages 209-221 ; 03029743 (ISSN) ; 9783319426334 (ISBN) ; Ghodsi, M ; Jafari, A ; Sharif University of Technology
Springer Verlag
2016

Abstract

Given a set S of n disjoint line segments in ℝ2, 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(n4) preprocessing time and space. Gudmundsson and Morin proposed a 2-approximation algorithm for this problem with a tradeoff between the space and the query time. They answer any query in Oε(n1−α) with Oε(n2+2α) of preprocessing time and space, where α is a constant 0 ≤ α ≤ 1, ε > 0 is another constant that can be made arbitrarily small, and Oε(f(n)) = O(f(n)nε). In this paper, we propose a randomized approximation algorithm...

#### Randomized approximation algorithms for planar visibility counting problem

, Article Theoretical Computer Science ; Volume 707 , 2018 , Pages 46-55 ; 03043975 (ISSN) ; Ghodsi, M ; Jafari, A ; Sharif University of Technology
Elsevier B.V
2018

Abstract

Given a set S of n disjoint line segments in R2, 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 be solved trivially in O(logn) query time using O(n4logn) preprocessing time and O(n4) space. Gudmundsson and Morin (2010) [10] proposed a 2-approximation algorithm for this problem with a tradeoff between the space and the query time. For any constant 0≤α≤1, their algorithm answers any query in Oϵ(m(1−α)/2) time with Oϵ(m1+α) of preprocessing time and space, where ϵ>0 is a constant that can be made arbitrarily small and Oϵ(f(n))=O(f(n)nϵ) and m=O(n2) is a number that depends...

#### Visibility testing and counting for uncertain segments

, Article Theoretical Computer Science ; Volume 779 , 2019 , Pages 1-7 ; 03043975 (ISSN) ; Alipour, S ; Ghodsi, M ; Mahdian, M ; Sharif University of Technology
Elsevier B.V
2019

Abstract

We study two well-known planar visibility problems, namely visibility testing and visibility counting, in a model where there is uncertainty about the input data. The standard versions of these problems are defined as follows: we are given a set S of n segments in R 2 , and we would like to preprocess S so that we can quickly answer queries of the form: is the given query segment s∈S visible from the given query point q∈R 2 (for visibility testing) and how many segments in S are visible from the given query point q∈R 2 (for visibility counting). In our model of uncertainty, each segment may or may not exist, and if it does, it is located in one of finitely many possible locations, given by a...