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#### α-visibility

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7357 LNCS , 2012 , Pages 1-12 ; 03029743 (ISSN) ; 9783642311543 (ISBN) ; Maheshwari, A ; Nouri, M ; Sack, J. R ; Zarrabi Zadeh, H ; Sharif University of Technology
2012

Abstract

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility, weak and complete segment visibility, and the construction of the visibility graph. We also investigate the natural query versions of these problems, when α is either fixed or specified at query time

#### Near optimal line segment queries in simple polygons

, Article Journal of Discrete Algorithms ; Volume 35 , November , 2015 , Pages 51-61 ; 15708667 (ISSN) ; Ghodsi, M ; Sharif University of Technology
Elsevier
2015

Abstract

This paper considers the problem of computing the weak visibility polygon (WVP) of any query line segment pq (or WVP(pq)) inside a given simple polygon P. We present an algorithm that preprocesses P and creates a data structure from which WVP(pq) is efficiently reported in an output sensitive manner. Our algorithm needs O(n2log n) time and O(n2) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(|WVP(pq)|+log2 n+κlog2 (nκ)), where κ is an input and output sensitive parameter of at most |WVP(pq)|. We improve the preprocessing time and space of current results for this problem [11,6] at the expense of more query time

#### Weak visibility queries of line segments in simple polygons and polygonal domains

, Article International Journal of Computer Mathematics ; 2017 , Pages 1-18 ; 00207160 (ISSN) ; Ghodsi, M ; Sharif University of Technology
Taylor and Francis Ltd
2017

Abstract

In this paper we consider the problem of computing the weak visibility polygon of a query line segment pq (or (Formula presented.)) inside a given polygon (Formula presented.). Our first algorithm runs in simple polygons and needs (Formula presented.) time and (Formula presented.) space in the preprocessing phase to report (Formula presented.) of any query line segment pq in time (Formula presented.). We also give an algorithm to compute the weak visibility polygon of a query line segment in a non-simple polygon with (Formula presented.) pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm needs (Formula presented.) time and (Formula presented.) space in the...

#### Weak visibility queries of line segments in simple polygons and polygonal domains

, Article International Journal of Computer Mathematics ; Volume 95, Issue 4 , 2018 , Pages 721-738 ; 00207160 (ISSN) ; Ghodsi, M ; Sharif University of Technology
Taylor and Francis Ltd
2018

Abstract

In this paper we consider the problem of computing the weak visibility polygon of a query line segment pq (or WVP(pq)) inside a given polygon P. Our first algorithm runs in simple polygons and needs O(n3 log n) time and O(n3) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log n + |WVP(pq)|).. We also give an algorithm to compute the weak visibility polygon of a query line segment in a non-simple polygon with h ≥ 1 pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm needs O(n2 log n) time and O(n2) space in the preprocessing phase and WVP(pq) in query time of O(nh’ log n + k), in which h’ is an output sensitive parameter...

#### Weak visibility queries in simple polygons

, Article Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 ; 2011 ; Ghodsi, M ; Sharif University of Technology
Abstract

In this paper, we consider the problem of computing the weak visibility (WV ) of a query line segment in- side a simple polygon. Our algorithm first preprocesses the polygon and creates data structures from which any WV query is answered efficiently in an output sensitive manner. In our solution, the preprocessing is performed in time O(n3 log n) and the size of the constructed data structure is O(n3). It is then possible to report the WV polygon of any query line segment in time O(log n+k), where k is the size of the output. Our algorithm im- proves the current results for this problem

#### Visibility maintenance of a moving segment observer inside polygons with holes

, Article Proceedings of the 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, 9 August 2010 through 11 August 2010, Winnipeg, MB ; 2010 , Pages 117-120 ; Ghodsi, M ; Sharif University of Technology
2010

Abstract

We analyze how to efficiently maintain and update the visibility polygons for a segment observer moving in a polygonal domain. The space and time requirements for preprocessing are O(n2) and after preprocessing, visibil- ity change events for weak and strong visibility can be handled in O(log VP) and O(log(VP1 + VP2)) re- spectively, or O(log n) in which VP is the size of the line segment's visibility polygon and VP 1 and VP2 represent the number of vertices in the visibility poly- gons of the line segment endpoints

#### Visibility of a moving segment

, Article Proceedings of the 2009 International Conference on Computational Science and Its Applications, ICCSA 2009, 29 June 2009 through 2 July 2009, Yongin ; 2009 , Pages 169-176 ; 9780769537016 (ISBN) ; Ghodsi, M ; Sharif University of Technology
2009

Abstract

In this paper we define topological segment visibility, and show how to compute and maintain it as the observer moves in the plane. There are n non-intersecting line segment objects in the plane, and we have a segment observer among them. As the topological visibility of a line segment has not been studied before, we first consider static case of the problem, in which the observer and objects are static, and then we study dynamic case of the problem, in which the observer can move among obstacles

#### α-Visibility

, Article Computational Geometry: Theory and Applications ; Vol. 47, issue. 3 PART A , April , 2014 , pp. 435-446 ; ISSN: 09257721 ; ISBN: 9783642311543 ; Maheshwari, A ; Nouri-Baygim, M ; Sack, J. R ; Zarrabi-Zadeh, H ; Sharif University of Technology
Abstract

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility, weak and complete segment visibility, and the construction of the visibility graph. We also investigate the natural query versions of these problems, when α is either fixed or specified at query time

#### 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

#### Covering orthogonal polygons with sliding k-transmitters

, Article Theoretical Computer Science ; Volume 815 , May , 2020 , Pages 163-181 ; Seddighin, S ; Ghodsi, M ; Sharif University of Technology
Elsevier B. V
2020

Abstract

In this paper, we consider a new variant of covering in an orthogonal art gallery problem where each guard is a sliding k-transmitter. Such a guard can travel back and forth along an orthogonal line segment, say s, inside the polygon. A point p is covered by this guard if there exists a point q∈s such that pq‾ is a line segment normal to s, and has at most k intersections with the boundary walls of the polygon. The objective is to minimize the sum of the lengths of the sliding k-transmitters to cover the entire polygon. In other words, the goal is to find the minimum total length of trajectories on which the guards can travel to cover the entire polygon. We prove that this problem is NP-hard...

#### Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons

, Article Proceedings of the Annual Symposium on Computational Geometry, 13 June 2011 through 15 June 2011 ; June , 2011 , Pages 407-416 ; 9781450306829 (ISBN) ; Aronov, B ; De Berg, M ; Khosravi, A ; Sharif University of Technology
2011

Abstract

Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms. We also study Steiner triangulations of a simple (nonrectilinear) polygon P. Here the stabbing number is defined as the maximum number of triangles that can be stabbed by any line segment inside P. We give an O(1)-approximation algorithm for the problem of computing a Steiner triangulation with minimum stabbing 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...

#### 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...