Journal Conference

Journal papers

2022

  1. On the plane angle-monotone graphs


    Abstract: Let $P=(p_1,\ldots, p_n)$ be a geometric path in the plane. For a real number $0<\gamma<180^\circ$, $P$ is called an \em angle-monotone path with width $\gamma$ if there exists a closed wedge of angle $\gamma$ such that the vector of every edge $(p_i,p_{i+1})$ of $P$ lies in this wedge. Let $G$ be a geometric graph in the plane. The graph $G$ is called \em angle-monotone with width $\gamma$ if there exists an angle-monotone path with width $\gamma$ between any two vertices. Let $\gamma}_{\min}$ be the smallest width such that every set of points in the plane has a plane angle-monotone graph with width $\gamma_ \min}$. It has been shown that $90^\circ<\gamma_\min}\leq 120^\circ$. In this paper, we show that $\gamma_\min}=120^\circ$. This solves an open problem posed by Bonichon et al. [GD~2016].
    D. Bakhshesh and M. Farshi.
    Computational Geometry: Theory and Applications, 100, 2022.
    DOI 
    @article{Ontheplane,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={On the plane angle-monotone graphs},
  journal={Computational Geometry: Theory and Applications},
  year={2022},
  volume={100},
  doi={https://doi.org/10.1016/j.comgeo.2021.101818},
  eprint={https://doi.org/10.1016/j.comgeo.2021.101818},
  url={https://doi.org/10.1016/j.comgeo.2021.101818}
}

2021

  1. Angle-monotonicity of Delaunay triangulation


    Abstract: Given an angle $\gamma>0$, a geometric path $(v_1,\ldots,v_k)$ is called angle-monotone with width $\gamma$ if, for any two integers $1\leq i,j<$, the angle between the two vectors $\overrightarrow{v_iv_{i+1}}$ and $\overrightarrow{v_jv_{j+1}}$ is at most $\gamma$. Let $S$ be a set of $n$ points in the plane. A geometric graph $G$ with vertex set $S$ is called angle-monotone with width $\gamma$, if there exists an angle-monotone path with width $\gamma$ between every pair of vertices of $G$. In this paper, we show that the Delaunay triangulation of a given point set in the plane is not necessarily angle-monotone with width $\alpha$, for $0<\alpha< 140^\circ$. This gives a negative answer to an open problem posed by Bonichon et al. (Bonichon et al., Gabriel triangulations and angle-monotone graphs: Local routing and recognition, Graph Drawing and Network Visualization, 2016).
    D. Bakhshesh and M. Farshi.
    Computational Geometry: Theory and Applications, 94:101711, 2021.
    DOI ISSN URL 
    @article{BAKHSHESH2021101711,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Angle-monotonicity of {D}elaunay triangulation},
  journal={Computational Geometry: Theory and Applications},
  year={2021},
  volume={94},
  pages={101711},
  issn={0925-7721},
  doi={https://doi.org/10.1016/j.comgeo.2020.101711},
  url={http://www.sciencedirect.com/science/article/pii/S092577212030105X}
}

  2. A quadratic-time algorithm for isolate domination in trees


    Abstract: For a graph $G$ with vertex set $V$, a set $S\subseteq V$ is called a \it dominating set of $G$ if every vertex in $V-S$ has a neighbor in $S$. If the set $S\subseteq V$ is a dominating set of $G$ and the induced subgraph $G[S]$ contains at least one isolated vertex, the set $S$ is called an \it isolate dominating set of $G$. The minimum cardinality of a dominating set of $G$ is called the \it domination number of $G$, denoted by $\gamma(G)$, and the minimum cardinality of an isolate dominating set of $G$ is called the \it isolate domination number of $G$, denoted by $\gamma_0(G)$. It has been proved that the isolate domination problem is NP-complete in general. In this paper, we present a quadratic-time algorithm to compute the isolate domination number of a tree.
    D. Bakhshesh.
    Iranian Journal of Science and Technology, Transactions A: Science, 45:2063–2072, 2021.
    DOI 
    @article{AQuadratic,
  author={Bakhshesh, Davood},
  title={A Quadratic-Time Algorithm for Isolate Domination in Trees},
  journal={Iranian Journal of Science and Technology, Transactions A: Science},
  year={2021},
  volume={45},
  pages={2063--2072},
  doi={https://doi.org/10.1007/s40995-021-01200-6},
  eprint={https://doi.org/10.1007/s40995-021-01200-6},
  url={https://doi.org/10.1007/s40995-021-01200-6}
}

  3. A degree 3 plane 5.19-spanner for points in convex position


    Abstract: Let $S$ be a set of $n$ points in the plane that is in convex position. In this paper, using the well-known path-greedy spanner algorithm, we present an algorithm that constructs a plane $\frac{3+4\pi}{3}$-spanner $G$ of degree 3 on the point set $S$. Recently, Biniaz et al. (\it Towards plane spanners of degree 3, Journal of Computational Geometry, 8 (1), 2017) have proposed an algorithm that constructs a degree 3 plane $\frac{3+4\pi}{3}$-spanner $G’$ for $S$. We show that there is no upper bound with a constant factor on the total weight of $G’$, but the total weight of $G$ is asymptotically equal to the total weight of the minimum spanning tree of $S$.
    D. Bakhshesh and M. Farshi.
    Accepted to Scientia Iranica.
    DOI URL 
    @article{ADegree3,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={A Degree 3 Plane 5.19-Spanner for Points in Convex Position},
  journal={Scientia Iranica},
  year={2021},
  doi={10.24200/sci.2021.56576.4796},
  url={http://scientiairanica.sharif.edu/article_22416.html}
}

  4. K-adjacency domination in graphs (in persian)


    Abstract: Let $G$ be a simple and undirected graph with vertex set $V$. A set $S\subseteq V$ is called a dominating set of $G$ if every vertex outside $S$ is adjacent to at least one vertex of $S$. For any integer $k\geq 1$, a dominating set S is called a $k$-adjacency dominating set of $G$ if the induced subgraph $G[S]$ contains at least one vertex of degree at most $k-1$. The minimum cardinality of a $k$-adjacency dominating set of $G$ is called the $k$-adjacency domination number of $G$ that is denoted by $\gamma_k^a (G).$ In this paper, the study of $k$-adjacency domination in graphs is initiated, and exact values and some bounds on the $k$-adjacency domination number of a given graph are presented. Furthermore, it is shown that there is a polynomial-time algorithm that computes the $k$-adjacency domination number of a given tree. Moreover, it is proven that the decision problem associated to the $k$-adjacency domination is NP-complete for bipartite graphs.
    D. Bakhshesh.
    Accepted to Electronic and Cyber Defense.
    URL 
    @article{Kadjacencydomination,
  author={Bakhshesh, Davood},
  title={K-adjacency domination in graphs (in Persian)},
  journal={Electronic and Cyber Defense},
  year={2021},
  url={https://ecdj.ihu.ac.ir/}
}

  5. Isolate roman domination in graphs


    Abstract: Let $G$ be a graph with the vertex set $V$. A function $f:V\rightarrow {0,1,2}$ is called a Roman dominating function of $G$, if every vertex $v$ with $f(v)=0$ is adjacent to at least one vertex $u$ with $f(u)=2$. The weight of a Roman dominating function~$f$ is equal to $\sum_v\in V(G)f(v)$. The minimum weight of a Roman dominating function of $G$ is called the Roman domination number of $G$, denoted by $\gamma_R(G)$. In this paper, we initiate the study of a variant of Roman dominating functions. A function $f:V(G)\rightarrow {0,1,2}$ is called an isolate Roman dominating function of $G$, if $f$ is a Roman dominating function and there is a vertex $v$ with $f(v)=0$ which is not adjacent to any vertex $u$ with $f(u)=0$. The minimum weight of an isolate Roman dominating function of $G$ is called the isolate Roman domination number of $G$, denoted by $\gamma_IR(G)$. We present some upper bound on the isolate Roman domination number of a graph $G$ in terms of its Roman domination number and its domination number. Moreover, we present some classes of graphs $G$ with $\gamma_IR(G)=\gamma_R(G)$. Finally, we show that the decision problem associated with the isolate Roman dominating functions is NP-complete for bipartite graphs and chordal graphs.
    D. Bakhshesh.
    Accepted to Discrete Mathematics, Algorithms and Applications.
    DOI 
    @article{IsolateRoman,
  author={Bakhshesh, Davood},
  title={Isolate Roman domination in graphs},
  journal={Discrete Mathematics, Algorithms and Applications},
  year={2021},
  doi={https://doi.org/10.1142/S1793830921501317},
  url={https://doi.org/10.1142/S1793830921501317}
}

2020

  1. Characterization of some classes of graphs with equal domination number and isolate domination number


    Abstract: Let $G$ be a simple and undirected graph with vertex set $V$. A set $D\subseteq V$ is called a dominating set of $G$, if every vertex in $V\backslash D$ is adjacent to at least one vertex in $D$. The minimum cardinality of a dominating set of $G$ is called the domination number of $G$, denoted by $\gamma(G)$. A dominating set $D$ of $G$ is called isolate dominating, if the induced subgraph $G[D]$ of $G$ contains at least one isolated vertex. The minimum cardinality of an isolate dominating set of $G$ is called the isolate domination number of $G$, denoted by $\gamma_0(G)$. In this paper, we show that for every proper interval graph $G$, $\gamma_0(G)=\gamma(G)$. Moreover, we provide a constructive characterization for trees with equal domination number and isolate domination number. These solve part of an open problem posed by Hamid and Balamurugan [Isolate domination in graphs, Arab Journal of Mathematical Sciences, 22, 2, 2016, 232-241].
    D. Bakhshesh.
    Discrete Mathematics, Algorithms and Applications, 12(05):2050065, 2020.
    DOI 
    @article{doi:10.1142/S1793830920500652,
  author={Bakhshesh, Davood},
  title={Characterization of some classes of graphs with equal domination number and isolate domination number},
  journal={Discrete Mathematics, Algorithms and Applications},
  year={2020},
  volume={12},
  number={05},
  pages={2050065},
  doi={10.1142/S1793830920500652},
  eprint={https://doi.org/10.1142/S1793830920500652},
  url={https://doi.org/10.1142/S1793830920500652}
}

2019

  1. Fault tolerancy of continuous Yao graph of angle less than 2π/5


    Abstract: Let $S$ be a point set in the plane and $0<\theta\leq 2\pi$ be a real number. The continuous Yao graph $cY(\theta)$ for $S$ is constructed as follows. For each $p,q\in S$, we add the edge $(p,q)$ to $cY(\theta)$, if there exists a cone $C$ with apex at $p$ and aperture $\theta$ such that $q$ is the closest point to $p$ inside $C$. In this paper, we show that for every $\pi/3\leq\theta<2\pi/5$ and for the family of all convex regions in the plane, the continuous Yao graph $cY(\theta)$ is a region-fault tolerant $t$-spanner in which $t$ only depends on $\theta$.
    D. Bakhshesh and M. Farshi.
    Information Processing Letters, 148:13 – 18, 2019.
    DOI ISSN URL 
    @article{BAKHSHESH201913,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Fault tolerancy of continuous {Y}ao graph of angle less than 2π/5},
  journal={Information Processing Letters},
  year={2019},
  volume={148},
  pages={13 - 18},
  issn={0020-0190},
  doi={https://doi.org/10.1016/j.ipl.2019.03.014},
  url={http://www.sciencedirect.com/science/article/pii/S0020019019300717}
}

  2. (Weakly) Self-approaching geometric graphs and spanners


    Abstract: A geometric graph is called self-approaching, if for each (ordered) pair of vertices of the graph, there exists a self-approaching (directed) path between them. A path from a vertex $u$ to a vertex $v$ of the graph is called self-approaching, if for any point (not just vertex) $x$ on the path, the distance between $x$ and any point that starts at $u$ and moves toward $x$ is decreasing. A path is called an increasing-chord, if it is self-approaching from both sides, source to destination and destination to source. A geometric graph is called a self-approaching $t$-spanner, for $t>1$, if for each pair $(u,v)$ of vertices of the graph, there exists a self-approaching path from $u$ to $v$ of length at most $t$ times the Euclidean distance between $u$ and $v$. In 2015, Dehkordi et al. (2015) [16] left the problem of the existence of an increasing-chord planar geometric graph for a set of points that lie along the sides of an acute triangle, as an open problem, but they did not mention anything about the case of an obtuse triangle. In this paper, we show that for each set of points on the boundary of an obtuse triangle, there exists an increasing-chord planar geometric graph. Moreover, we show that for each set of points on the boundary of an acute triangle, there exists an increasing-chord planar geometric graph using at most three Steiner points. We also introduce weakly self-approaching geometric graphs (spanners) as a variation of self-approaching geometric graphs (spanners). A weakly self-approaching path is defined similarly to a self-approaching path, except that when a point $p$ on the path moves from the source to the destination, the Euclidean distance between $p$ and the destination vertex (but not all the points on the path) decreases. A weakly self-approaching geometric graph (spanner) is defined by replacing “self-approaching” by “weakly self-approaching” in the above definition. In this paper, we show that for every point set $S\subseteq \mathbb R^d$, there is a weakly self-approaching planar geometric graph spanning $S$. Furthermore, this study shows how to test in polynomial time, whether a given geometric graph is weakly self-approaching. Notably, the corresponding decision problem in the context of self-approaching geometric graphs in $\mathbb{R}^d$ with $d\geq 3$ is NP-hard. We also propose some algorithms for constructing a weakly self-approaching geometric $t$-spanner for a given point set and a real constant $t>1$. Also, we show that for every point set $S$ on the boundary of any triangle, there exists an increasing-chord $t$-spanner spanning $S$ and a weakly self-approaching $t$-spanner spanning $S$, both with $O(kn)$ edges, in which $k$ depends only on $t$.
    D. Bakhshesh and M. Farshi.
    Computational Geometry: Theory and Applications, 78:20 – 36, 2019.
    DOI ISSN URL 
    @article{BAKHSHESH201920,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={({W}eakly) {S}elf-approaching geometric graphs and spanners},
  journal={Computational Geometry: Theory and Applications},
  year={2019},
  volume={78},
  pages={20 - 36},
  issn={0925-7721},
  doi={https://doi.org/10.1016/j.comgeo.2018.10.002},
  url={http://www.sciencedirect.com/science/article/pii/S0925772118301901}
}

  3. Complexity results for $k$-domination and $\alpha$-domination problems and their variants


    Abstract: Let $G=(V, E)$ be a simple and undirected graph. For some integer $k\geq 1$, a set $D\subseteq V$ is said to be a $k$-dominating set in $G$ if every vertex $v$ of $G$ outside $D$ has at least $k$ neighbors in $D$. Furthermore, for some real number $\alpha$ with $0<\alpha\leq1$, a set $D\subseteq V$ is called an $\alpha$-dominating set in $G$ if every vertex $v$ of $G$ outside $D$ has at least $\alpha\times d_v$ neighbors in $D$, where $d_v$ is the degree of $v$ in $G$. The cardinality of a minimum $k$-dominating set and a minimum $\alpha$-dominating set in $G$ is said to be the $k$-domination number and the $\alpha$-domination number of $G$, respectively. In this paper, we present some approximability and inapproximability results on the problem of finding of $k$-domination number and $\alpha$-domination number of some classes of graphs. Moreover, we introduce a generalization of $\alpha$-dominating set which we call $f$-dominating set. Given a function $f:\mathbb{N}\rightarrow \mathbb{R}$, where $\mathbb{N}={1,2,3,\ldots,}$, a set $D\subseteq V$ is said to be an $f$-dominating set in $G$ if every vertex $v$ of $G$ outside $D$ has at least $f(d_v)$ neighbors in $D$. We prove NP-hardness of the problem of finding of a minimum $f$-dominating set in $G$, for a large family of functions $f$.
    D. Bakhshesh, M. Farshi, and M. Hasheminezhad.
    Ars Combinatoria, 145:11–27, 2019.
    URL 
    @article{Bakhshesh2017ars,
  author={Bakhshesh, Davood and Farshi, Mohammad and Hasheminezhad, Mahdieh},
  title={Complexity results for {$k$}-domination and {$\alpha$}-domination problems and their variants},
  journal={Ars Combinatoria},
  year={2019},
  volume={145},
  pages={11-27},
  url={http://www.combinatorialmath.ca/ArsCombinatoria/Vol145.html}
}

2018

  1. 2-domination number of generalized petersen graphs


    Abstract: Let $G=(V,E)$ be a graph. A subset $S\subseteq V$ is a $k$-dominating set of $G$ if each vertex in $V-S$ is adjacent to at least $k$ vertices in $S$. The $k$-domination number of $G$ is the cardinality of the smallest $k$-dominating set of G. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs $P(5k+1, 2)$ and $P(5k+2, 2)$, for $k>0$, is $4k+2$ and $4k+3$, respectively. This proves two conjectures due to Cheng (Ph.D. thesis, National Chiao Tung University, 2013). Moreover, we determine the exact 2-domination number of generalized Petersen graphs $P(2k, k)$ and $P(5k+4,3)$. Furthermore, we give a good lower and upper bounds on the 2-domination number of generalized Petersen graphs $P(5k+1, 3), P(5k+2,3)$ and $P(5k+3, 3)$.
    D. Bakhshesh, M. Farshi, and M. R. Hooshmandasl.
    Proceedings - Mathematical Sciences, 128(2):17, Apr 2018.
    DOI ISSN 
    @article{Bakhshesh2018,
  author={Bakhshesh, Davood and Farshi, Mohammad and Hooshmandasl, Mohammad Reza},
  title={2-Domination number of generalized Petersen graphs},
  journal={Proceedings - Mathematical Sciences},
  year={2018},
  volume={128},
  number={2},
  pages={17},
  issn={0973-7685},
  month={Apr},
  doi={10.1007/s12044-018-0395-2},
  url={https://doi.org/10.1007/s12044-018-0395-2}
}

  2. Continuous Yao graphs


    Abstract: In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points $S\subset \mathbb{R}^2$ and an angle $0 < \theta \leq 2\pi$, we define the continuous Yao graph $cY(\theta)$ with vertex set $S$ and angle $\theta$ as follows. For each $p,q\in S$, we add an edge from $p$ to $q$ in $cY(\theta)$ if there exists a cone with apex $p$ and aperture $\theta$ such that $q$ is a closest point to $p$ inside this cone. We study the spanning ratio of $cY(\theta)$ for different values of $\theta$. Using a new algebraic technique, we show that $cY(\theta)$ is a spanner when $\theta \leq 2\pi /3$. We believe that this technique may be of independent interest. We also show that $cY(\pi)$ is not a spanner, and that $cY(\theta)$ may be disconnected for $\theta > \pi$, but on the other hand is always connected for $\theta\leq \pi$. Furthermore, we show that $cY(\theta)$ is a region-fault-tolerant geometric spanner for convex fault regions when $\theta<\pi/3$. For half-plane faults, $cY(\theta)$ remains connected if $\theta\leq\pi$. Finally, we show that $cY(\theta)$ is not always self-approaching for any value of $\theta$.
    D. Bakhshesh, L. Barba, P. Bose, J.-L. De Carufel, M. Damian, R. Fagerberg, M. Farshi, A. van Renssen, P. Taslakian, and S. Verdonschot.
    Computational Geometry: Theory and Applications, 67:42–52, 2018.
    DOI 
    @article{continuous-yao-graphs-cgta,
  author={Bakhshesh, Davood and Barba, Luis and Bose, Prosenjit and De Carufel, Jean-Lou and Damian, Mirela and Fagerberg, Rolf and Farshi, Mohammad and van Renssen, Andr\'e and Taslakian, Perouz and Verdonschot, Sander},
  title={Continuous {Y}ao Graphs},
  journal={Computational Geometry: Theory and Applications},
  year={2018},
  volume={67},
  pages={42--52},
  doi={10.1016/j.comgeo.2017.10.002}
}

2017

  1. Improving space and time complexity of the gap-greedy spanner algorithm


    Abstract: Let $S$ be a set of $n$ points in $\mathbb{R}^d$ and $G$ be a geometric graph with vertex set $S$. For a fixed real number $t \geq 1$, $G$ is called a $t$-spanner of $S$ if, for all pairs of vertices $u, v \in S$, the shortest path in $G$ between $u$ and $v$ is no longer than $t|uv|$, where $| uv|$ is the Euclidean distance between $u$ and $v$. One of the interesting geometric spanner is the gap-greedy spanner. It is well known that the edge count and the maximal degree of the gap-greedy spanner are asymptotically optimal and its total weight is $O(\log n)$ times the weight of the minimum spanning tree for the same vertices. To the best of our knowledge, there is one algorithm, denoted by gap-greedy algorithm, to construct the gap-greedy spanner that takes $O(n^3)$ time and $O(n^2)$ space. Note that there is an approximation version of the gap-greedy algorithm, denoted by modified gap-greedy algorithm, that constructs a geometric graph in $O(n\log ^2n)$ time and $O(n\log ^2n)$ space keeping all geometric properties the same as the gap-greedy spanner, but the generated graph is not the same as the gap-greedy spanner. In this paper, we present an algorithm to construct the gap-greedy spanner that takes $O(n^2)$ time and $O(n^2)$ space, and another variant of this algorithm that takes $O(n^3)$ time and $O(n)$ space. We also improve the (theoretical) dilation of the gap-greedy spanner. Moreover, we present some other $O(n^3)$ time algorithms to construct the gap-greedy spanner and compare their time complexity with the gap-greedy algorithm in practice. Furthermore, we experimentally compare the running time and some geometric properties of the gap-greedy spanner with the greedy spanner as a high quality spanner. We hoped that we can find some point sets in the plane such that the geometric properties of the gap-greedy spanner and the greedy spanner of the point sets are almost the same and the running time of computing the gap-greedy spanner is faster than the greedy spanner, but the experiments show that this is not correct.
    D. Bakhshesh and M. Farshi.
    CSI Journal on Computer Science and Engineering, 14(1):6 – 18, 2017.
    URL 
    @article{Bakhshesh2017CSIGap,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Improving space and time complexity of the gap-greedy spanner algorithm},
  journal={CSI Journal on Computer Science and Engineering},
  year={2017},
  volume={14},
  number={1},
  pages={6 - 18},
  url={http://www.jcse.ir/journalcontent.aspx?vol=14&no=1}
}

  2. Angle-constrained spanners with angle at least $\pi/3$


    Abstract: Let $S$ be a set of $n$ points in $\mathbb{R}^d$ and let $t \geq 1$ be a real number. A geometric graph $G$ with vertex set $S$ is called a $t$-spanner for $S$ if for each two points $p$ and $q$ in $S$, there exists a path $Q$ in $G$ between $p$ and $q$ whose length is at most $t$ times $|pq|$, the Euclidean distance between $p$ and $q$. The geometric graph $G$ with vertex set $S$ is called a $\theta$-angle-constrained $t$-spanner if $G$ is a $t$-spanner of $S$ and any two edges ${p,q}$ and ${p,r}$ in $G$ make an angle of at least $\theta$. In this paper, we show that there is a point set $P$ in the plane such that for every $\theta>\pi/3$, there is no $\theta$-angle-constrained $t$-spanner on $P$. Moreover, we show that for $\theta=\pi/3$ and every $t<2/\sqrt{3}$, there is no $\theta$-angle-constrained $t$-spanner on $P$. This solves an open problem posed by Paz Carmi and Michiel Smid (Journal of Computational Geometry, 3(1):196--221, 2012)
    D. Bakhshesh and M. Farshi.
    Information Processing Letters, 120:44 – 46, 2017.
    DOI ISSN URL 
    @article{Bakhshesh201744,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Angle-constrained spanners with angle at least $\pi/3$},
  journal={Information Processing Letters},
  year={2017},
  volume={120},
  pages={44 - 46},
  issn={0020-0190},
  doi={http://dx.doi.org/10.1016/j.ipl.2017.01.002},
  url={http://www.sciencedirect.com/science/article/pii/S0020019017300029}
}

  3. On the effect of inducted negative correlation rate for beta acceptance–rejection algorithms


    Abstract: One of the variance reduction methods in simulation experiments is negative correlation induction, and in particular the use of the antithetic variates. The simultaneous use of antithetic variates and an acceptance–rejection method has been studied in some papers, where the inducted negative correlation has been calculated. In this study, the factors affecting the inducted negative correlation rate are addressed. To do this, the beta distribution is first selected to generate negatively correlated random variates using the acceptance–rejection method. The effects of both the efficiency of the acceptance–rejection method and the initial negative correlation rate on the inducted negative correlation are explored. Results show that both factors have significant effects; therefore, a combination of both can lead to algorithms better able to generate negative correlations.
    H. Moheghi, S. T. A. Niaki, B. Bootaki, and D. Bakhshesh.
    Communications in Statistics - Simulation and Computation, 46(3):2152–2167, 2017.
    DOI 
    @article{Moheghi2017,
  author={Hamidreza Moheghi and Niaki, Seyed Taghi Akhavan and Behrang Bootaki and Bakhshesh, Davood},
  title={On the effect of inducted negative correlation rate for beta acceptance–rejection algorithms},
  journal={Communications in Statistics - Simulation and Computation},
  year={2017},
  volume={46},
  number={3},
  pages={2152-2167},
  doi={10.1080/03610918.2015.1039128},
  eprint={http://dx.doi.org/10.1080/03610918.2015.1039128},
  url={http://dx.doi.org/10.1080/03610918.2015.1039128}
}

2015

  1. Approximating of conic sections by DP curves with endpoint interpolation


    Abstract: Conic sections have many applications in industrial design, however, they cannot be exactly represented in polynomial form. Hence approximating conic sections with polynomials is a challenging problem. In this paper, we use the monomial form of Delgado and Peña (DP) curves and present a matrix representation for them. Using the matrix form and the least squares method, we propose a simple and efficient algorithm for approximating conic sections by DP curves of arbitrary degree with endpoint interpolation. Finally, we test and compare the proposed algorithm on some numerical examples which validates and confirms efficiency of it.
    D. Bakhshesh and M. Davoodi.
    International Journal of Computer Mathematics, 92(1):1–14, 2015.
    DOI 
    @article{doi:10.1080/00207160.2014.889293,
  author={Bakhshesh, Davood and Davoodi, Mansoor},
  title={Approximating of conic sections by {DP} curves with endpoint interpolation},
  journal={International Journal of Computer Mathematics},
  year={2015},
  volume={92},
  number={1},
  pages={1-14},
  doi={10.1080/00207160.2014.889293},
  eprint={http://dx.doi.org/10.1080/00207160.2014.889293},
  url={http://dx.doi.org/10.1080/00207160.2014.889293}
}

2013

  1. A new univariate basis for curve construction and its multi-degree reduction


    Abstract: In this paper, we employ monomial matrices to determine the transformations between Chebyshev and our proposed bases, as well as, the matrices of multi-degree elevation and multi-degree reduction of Chebyshev polynomials. As a result, it will present a simple and efficient method for multi-degree elevation and optimal multi-degree reduction for the new polynomial curves with respect to the weighted $L_2$-norm for the interval $[0, 1]$, using the weight function $w(t) =1/\sqrt{4t-4t^2}$. The error of the degree reduction scheme will be used to evaluate the multi-degree reduction with endpoint interpolations.
    N. Dejdumrong and D. Bakhshesh.
    Advanced Science Letters, 19(5):1495–1499, 2013.
    DOI ISSN URL 
    @article{Dejdumrong:2013:1936-6612:1495,
  author={Dejdumrong, Natasha and Bakhshesh, Davood},
  title={A New Univariate Basis for Curve Construction and Its Multi-Degree Reduction},
  journal={Advanced Science Letters},
  year={2013},
  volume={19},
  number={5},
  pages={1495-1499},
  issn={1936-6612},
  doi={doi:10.1166/asl.2013.4463},
  url={http://www.ingentaconnect.com/content/asp/asl/2013/00000019/00000005/art00055}
}

Conference papers

2019

  1. A plane region-fault tolerant $2.095$-spanner for points in convex position


    D. Bakhshesh and M. Farshi.
    In Proceedings of the 2nd Iranian Conference on Computational Geometry (ICCG 2019), Sharif University of Technology, Tehran, Iran, 2019.
    URL 
    @inproceedings{Bakhshesh2019ICCG,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={A Plane Region-Fault Tolerant $2.095$-Spanner for Points in Convex Position},
  booktitle={Proceedings of the 2nd Iranian Conference on Computational Geometry (ICCG 2019)},
  year={2019},
  address={Sharif University of Technology, Tehran, Iran},
  url={http://iccg.math.sharif.ir//}
}

2018

  1. Fault tolerancy of continuous Yao graph


    D. Bakhshesh and M. Farshi.
    In Proceedings of the 1st Iranian Conference on Computational Geometry (ICCG 2018), Amirkabir University of Technology, Tehran, Iran, 2018.
    URL 
    @inproceedings{Bakhshesh2018cYaofault,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Fault Tolerancy of Continuous {Y}ao Graph},
  booktitle={Proceedings of the 1st Iranian Conference on Computational Geometry (ICCG 2018)},
  year={2018},
  address={Amirkabir University of Technology, Tehran, Iran},
  url={http://iccg.aut.ac.ir/iccg2018/}
}

  2. A new construction of the greedy spanner in linear space


    D. Bakhshesh and M. Farshi.
    In Proceedings of the 1st Iranian Conference on Computational Geometry (ICCG 2018), Amirkabir University of Technology, Tehran, Iran, 2018.
    URL 
    @inproceedings{Bakhshesh2018Greedy,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={A New Construction of the Greedy Spanner in Linear Space},
  booktitle={Proceedings of the 1st Iranian Conference on Computational Geometry (ICCG 2018)},
  year={2018},
  address={Amirkabir University of Technology, Tehran, Iran},
  url={http://iccg.aut.ac.ir/iccg2018/}
}

  3. Increasing-chord planar graphs for points in convex position


    A. Poureidi, D. Bakhshesh, and M. Farshi.
    In Proceedings of the 1st Iranian Conference on Computational Geometry (ICCG 2018), Amirkabir University of Technology, Tehran, Iran, 2018.
    URL 
    @inproceedings{Abolfazl2018Increasing,
  author={Poureidi, Abolfazl and Bakhshesh, Davood and Farshi, Mohammad},
  title={Increasing-Chord Planar Graphs for Points in Convex Position},
  booktitle={Proceedings of the 1st Iranian Conference on Computational Geometry (ICCG 2018)},
  year={2018},
  address={Amirkabir University of Technology, Tehran, Iran},
  url={http://iccg.aut.ac.ir/iccg2018/}
}

2016

  1. Some properties of continuous Yao graph


    D. Bakhshesh and M. Farshi.
    In M. T. Hajiaghayi and M. R. Mousavi, editors, Proceedings of the 1st Topics in Theoretical Computer Science, (TTCS 2015), Lecture Notes in Computer Science, pages 44–55, Cham, 2016.
    DOI ISBN 
    @inproceedings{Bakhshesh2016,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Some Properties of Continuous {Y}ao Graph},
  booktitle={Proceedings of the 1st Topics in Theoretical Computer Science, (TTCS 2015)},
  year={2016},
  editor={Hajiaghayi, Mohammad Taghi and Mousavi, Mohammad Reza},
  series={Lecture Notes in Computer Science},
  address={Cham},
  pages={44--55},
  isbn={978-3-319-28678-5},
  doi={10.1007/978-3-319-28678-5_4},
  url={http://dx.doi.org/10.1007/978-3-319-28678-5_4}
}

  2. Geometric spanners merging and its applications


    D. Bakhshesh and M. Farshi.
    In Proceedings of the 28th Canadian Conference on Computational Geometry (CCCG 2016), Simon Fraser University, Vancouver, Canada, 2016.
    URL 
    @inproceedings{Bakhshesh2016Merging,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={Geometric Spanners Merging and its Applications},
  booktitle={Proceedings of the 28th Canadian Conference on Computational Geometry (CCCG 2016)},
  year={2016},
  address={Simon Fraser University, Vancouver, Canada},
  url={http://www.sfu.ca/~shermer/CCCG2016/}
}

  3. The firm gap property and its applications


    D. Bakhshesh and M. Farshi.
    In Proceedings of the47th Annual Iranian Mathematics Conference (AIMC 47), Kharazmi University, Karaj, Iran., 2016.
    URL 
    @inproceedings{Bakhshesh2016firm,
  author={Bakhshesh, Davood and Farshi, Mohammad},
  title={The Firm Gap Property and Its Applications},
  booktitle={Proceedings of the47th Annual Iranian Mathematics Conference (AIMC 47)},
  year={2016},
  address={Kharazmi University, Karaj, Iran.},
  url={http://aimc47.khu.ac.ir/}
}

2015

  1. A generalization of $\alpha$-dominating set and its complexity


    D. Bakhshesh, M. Farshi, and M. Hasheminezhad.
    In Proceedings of the 46th Annual Iranian Mathematics Conference (AIMC 46), Yazd University, Yazd, Iran, 2015.
    URL 
    @inproceedings{Bakhshesh2015alpha,
  author={Bakhshesh, Davood and Farshi, Mohammad and Hasheminezhad, Mahdieh},
  title={A generalization of {$\alpha$}-dominating set and its complexity},
  booktitle={Proceedings of the 46th Annual Iranian Mathematics Conference (AIMC 46)},
  year={2015},
  address={Yazd University, Yazd, Iran},
  url={http://confs.yazd.ac.ir/AIMC46/}
}

2011

  1. A combination method for image encryption based on hyper-chaos functions and evolutionary operators


    S. A. Esfahani and D. Bakhshesh.
    In Proceedings of the 8th International ISC Conference on Information Security and Cryptology (ISCISC 2011),, Ferdowsi University of Mashhad, Mashhad, Iran, 2011.
    URL 
    @inproceedings{Bakhsheshhamid,
  author={Esfahani, Seyyed Abdolhamid and Bakhshesh, Davood},
  title={A combination method for image encryption based on hyper-chaos functions and evolutionary operators},
  booktitle={Proceedings of the 8th International ISC Conference on Information Security and Cryptology (ISCISC 2011),},
  year={2011},
  address={Ferdowsi University of Mashhad, Mashhad, Iran},
  url={http://www.civilica.com/}
}

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