Volume 55 (2023)
Volume 54 (2022)
Volume 53 (2021)
Volume 52 (2020)
Volume 51 (2019)
Volume 50 (2018)
Volume 49 (2017)
Volume 48 (2016)
Volume 47 (2016)
Volume 46 (2015)
Volume 45 (2014)
Volume 44 (2013)
Volume 43 (2009)
Volume 42 (2008)
Volume 41 (2007)
Approximating the Number of Lattice Points inside a Regular Polygon

Mahdi Imanparast

Volume 54, Issue 1 , June 2022, , Pages 89-98

https://doi.org/10.22059/jac.2022.88337

Abstract
  We study the problem of counting the number of lattice points inside a regular polygon with $n$ sides when its center is at the origin and present an exact algorithm with $\mathcal{O}(k^{2}\log n)$ time and two approximate answers for this problem, where $k$ is the absolute value of side length of the ...  Read More

On Point-inclusion Test in Convex Polygons and Polyhedrons

Mahdi Imanparast; Mehdi Kazemi Torbaghan

Volume 52, Issue 1 , June 2020, , Pages 197-207

https://doi.org/10.22059/jac.2020.77122

Abstract
  A new algorithm for point-inclusion test in convex polygons is introduced. The proposed algorithm answers the point-inclusion test in convex polygons in $\mathcal{O}(\log n)$ time without any preprocessing and with $\mathcal{O}(n)$ space. The proposed algorithm is extended to do the point-inclusion test ...  Read More

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

Mahdi Imanparast; Seyed Naser Hashemi; Ali Mohades

Volume 51, Issue 2 , December 2019, , Pages 47-61

https://doi.org/10.22059/jac.2019.75162

Abstract
  We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \varepsilon\leqslant 1$. We also ...  Read More