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#### Kinetic polar diagram

, Article 13th International Computer Society of Iran Computer Conference on Advances in Computer Science and Engineering, CSICC 2008, Kish Island, 9 March 2008 through 11 March 2008 ; Volume 6 CCIS , 2008 , Pages 283-290 ; 18650929 (ISSN); 3540899847 (ISBN); 9783540899846 (ISBN) ; Chitforoush, F ; Yazdandoost, M ; Ghodsi, M ; Sharif University of Technology
2008

Abstract

Polar Diagram [4] is a new locus approach for problems processing angles. The solution to many important problems in Computational Geometry requires some kind of angle processing of the data input. Using the Polar Diagrma as preprocessing, exhaustive searches to find those sites with smallest angle become unnecessary. In this paper, we use the notion of kinetic data structure [1][2] to model the dynamic case of polar diagram, i.e we maintain the polar diagram of a set of continuously moving objects in the scene. We show that our proposed structure meets the main criteria of a good KDS. © 2008 Springer-Verlag

#### Kinetic Euclidean minimum spanning tree in the plane

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7056 LNCS , 2011 , Pages 261-274 ; 03029743 (ISSN) ; 9783642250101 (ISBN) ; Zarei, A ; Sharif University of Technololgy
2011

Abstract

This paper presents the first kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of n moving points in 2-dimensional space. We build a KDS of size O(n) in O(nlogn) preprocessing time by which their EMST is maintained efficiently during the motion. In terms of the KDS performance parameters, our KDS is responsive, local, and compact

#### Web graph compression by edge elimination

, Article Data Compression Conference, DCC 2006, Snowbird, UT, 28 March 2006 through 30 March 2006 ; 2006 , Pages 459- ; 10680314 (ISSN) ; Khalili, H ; Nourbakhsh, E ; Ghodsi, M ; Brandeis University ; Sharif University of Technology
2006

#### Binary Taylor Diagrams: An efficient implementation of Taylor expansion Diagrams

, Article IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005, Kobe, 23 May 2005 through 26 May 2005 ; 2005 , Pages 424-427 ; 02714310 (ISSN) ; Shamshiri, S ; Alisafaee, M ; Lotfi Kamran, P ; Naderi, M ; Navabi, Z ; Alizadeh, B ; Sharif University of Technology
2005

Abstract

This paper presents an efficient way of implementing Taylor expansion Diagrams (TED) that is called Binary Taylor Diagrams (BTD). BTD is based on Taylor series like TED, but uses a binary data structure. So BTD functions are simpler than those of TED. © 2005 IEEE

#### Efficient Data Structures for Spatiotemporal Data

, M.Sc. Thesis Sharif University of Technology ; Zarei, Alireza (Supervisor)
Abstract

With rapid increase of availability of moving object data, especially with help of GPS, need for algorithms which can process spatiotemporal data and data structures capable of storing it efficiently, has been increased. One of spatiotemporal data applications is in wild life, which demands tracking of animal movements through time. One of problems introduced in this application is flock problem. Flock is a group of entities, which move together through time. There is a belief that in bulky data, there are a lot of hidden information and patterns. Hence, we believe that with help of flocks, we can get insight of animal behaviors in environment and to each other. In this thesis we will...

#### Developing an ordering-based renumbering approach for triangular unstructured grids

, Article Engineering with Computers ; Volume 29, Issue 2 , April , 2013 , Pages 225-243 ; 01770667 (ISSN) ; Fouladi, N ; Sharif University of Technology
2013

Abstract

The unstructured grid generation and employment have become very common in computational fluid dynamics applications since a few decades ago. Comparing with the structured grid data, the unstructured grid has a random data structure known as unstructured data structure (USDS). In this work, we develop a new method to convert the USDS of a triangular unstructured grid to a quasi-structured data structure (QSDS) using an ordering-based renumbering approach. In this method, the unstructured grid data is re-ordered in a manner to represent several bands in the original unstructured grid domain. Each band presents one element layer and two node lines. Then, the indices of elements and nodes are...

#### Kinetic Euclidean minimum spanning tree in the plane

, Article Journal of Discrete Algorithms ; Volume 16 , October , 2012 , Pages 2-11 ; 15708667 (ISSN) ; Zarei, A ; Sharif University of Technology
Elsevier
2012

Abstract

This paper presents a kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of moving points in 2-dimensional space. For a set of n points moving in the plane we build a KDS of size O(n) in O(nlogn) preprocessing time by which the EMST is maintained efficiently during the motion. This is done by applying the required changes to the combinatorial structure of the EMST which is changed in discrete timestamps. We assume that the motion of the points, i.e. x and y coordinates of the points, are defined by algebraic functions of constant maximum degree. In terms of the KDS performance parameters, our KDS is responsive, local, and compact. The...

#### A reduced domain strategy for local mesh movement application in unstructured grids

, Article Applied Numerical Mathematics ; Volume 61, Issue 9 , 2011 , Pages 1001-1016 ; 01689274 (ISSN) ; Fouladi, N ; Sharif University of Technology
Abstract

Automatic control of mesh movement is mandatory in many fluid flow and fluid-solid interaction problems. This paper presents a new strategy, called reduced domain strategy (RDS), which enhances the efficiency of node connectivity-based mesh movement methods and moves the unstructured grid locally and effectively. The strategy dramatically reduces the grid computations by dividing the unstructured grid into two active and inactive zones. After any local boundary movement, the grid movement is performed only within the active zone. To enhance the efficiency of our strategy, we also develop an automatic mesh partitioning scheme. This scheme benefits from a new quasi-structured mesh data...

#### Spanning colored points with intervals

, Article CCCG 2013 - 25th Canadian Conference on Computational Geometry ; 2013 , Pages 265-270 ; Mohades, A ; Abam, M. A ; Kazemi, M. R ; Sharif University of Technology
Canadian Conference on Computational Geometry
2013

Abstract

We study a variant of the problem of spanning colored objects where the goal is to span colored objects with two similar regions. We dedicate our attention in this paper to the case where objects are points lying on the real line and regions are intervals. Precisely, the goal is to compute two intervals together spanning all colors. As the main ingredient of our algorithm, we first introduce a kinetic data structure to keep track of minimal intervals spanning all colors. Then we present a novel algorithm using the proposed KDS to compute a pair of intervals which together span all the colors with the property that the largest one is as small as possible. The algorithm runs in O(n2 log n)...

#### 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

#### Polar diagram of moving objects

, Article 20th Annual Canadian Conference on Computational Geometry, CCCG 2008, Montreal, QC, 13 August 2008 through 15 August 2008 ; August , 2008 , Pages 51-54 ; Ghodsi, M ; Sharif University of Technology
2008

Abstract

Many important problems in Computational Geometry needs to perform some kind of angle processing. The Polar Diagram [4] is a locus approach for problems processing angles. Using this structure as preprocessing, one can eliminate exhaustive searches to find objects with smallest angle. Handling data in change is a significant concept in Computer Science. One of the design and analysis tools used in the modeling of moving geometric objects is the kinetic data structure (or KDS) framework Kinetic Data Structure is a framework for maintaining a certain attribute of a set of objects while moving in a continuous manner. In this paper, we use the notion of kinetic data structure to model the...

#### Optimal point removal in closed-2PM labeling

, Article Information Processing Letters ; Volume 105, Issue 3 , 2008 , Pages 108-113 ; 00200190 (ISSN) ; Sadeghi, I ; Ghodsi, M ; Khosravi, R ; Sharif University of Technology
2008

Abstract

An optimal labeling where labels are disjoint axis-parallel equal-size squares is called 2PM labeling if the labels have maximum length each attached to its corresponding point on the middle of one of its horizontal edges. In a closed-2PM labeling, no two edges of labels containing points should intersect. Removing one point and its label, makes free room for its adjacent labels and may cause a global label expansion. In this paper, we construct several data structures in the preprocessing stage, so that any point removal event is handled efficiently. We present an algorithm which decides in O (lg n) amortized time whether a label removal leads to label expansion in which case a new optimal...

#### Optimal strategy for walking in streets with minimum number of turns for a simple robot

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Vol. 8881, issue , 2014 , p. 101-112 ; Ghodsi, M ; Sharif University of Technology
Abstract

We consider the problem of walking a simple robot in an unknown street. The robot that cannot infer any geometric properties of the street traverses the environment to reach a target t, starting from a point s. The robot has a minimal sensing capability that can only report the discontinuities in the depth information (gaps), and location of the target point once it enters in its visibility region. Also, the robot can only move towards the gaps while moving along straight lines is cheap, but rotation is expensive for the robot. We maintain the location of some gaps in a tree data structure of constant size. The tree is dynamically updated during the movement. Using the data structure, we...

#### Kinetic pie delaunay graph and its applications

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7357 LNCS , 2012 , Pages 48-58 ; 03029743 (ISSN) ; 9783642311543 (ISBN) ; Rahmati, Z ; Zarei, A ; Sharif University of Technology
2012

Abstract

We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yao graph and Euclidean minimum spanning tree (EMST). We efficiently maintain the Pie Delaunay graph where the points are moving in the plane. We use the kinetic Pie Delaunay graph to create a kinetic data structure (KDS) for maintenance of the Yao graph and the EMST on a set of n moving points in 2-dimensional space. Assuming x and y coordinates of the points are defined by algebraic functions of at most degree s, the structure uses O(n) space, O(nlogn) preprocessing time, and processes O(n 2 λ 2s∈+∈2(n)β s + 2(n)) events for the Yao graph and O(n 2 λ 2s + 2(n)) events for the...

#### Skiptree: a new scalable distributed data structure on multidimensional data supporting range-queries

, Article Computer Communications ; Volume 33, Issue 1 , 2010 , Pages 73-82 ; 01403664 (ISSN) ; Ghodsi, M ; Toossi, M ; Sharif University of Technology
Abstract

This paper presents a new balanced, distributed data structure for storing data with multidimensional keys in a peer-to-peer network. It supports range queries as well as single point queries which are routed in O (log n) hops. Our structure, called SkipTree, is fully decentralized with each node being connected to O (log n) other nodes. We propose modifications to the structures, so that the memory usage for maintaining the link structure at each node is reduced from the worst case of O (n) to O (log n log log n) on the average and O (log2 n) in the worst case. It is also shown that the load balancing is guaranteed to be within a constant factor. Our experimental results verify our...

#### Efficiently computing the smallest axis-parallel squares spanning all colors

, Article Scientia Iranica ; Volume 24, Issue 3 , 2017 , Pages 1325-1334 ; 10263098 (ISSN) ; Mohades, A ; Abam, M. A ; Kazemi, M. R ; Sedighin, S ; Sharif University of Technology
Sharif University of Technology
2017

Abstract

For a set of colored points, a region is called color-spanning if it contains at least one point of each color. In this paper, we first consider the problem of maintaining the smallest color-spanning interval for a set of n points with k colors on the real line, such that the insertion and deletion of an arbitrary point takes O(log2 n) the worst-case time. Then, we exploit the data structure to show that there is O(n log2 n) time algorithm to compute the smallest color-spanning square for a set of n points with k colors in the plane. This is a new way to improve O(nk log n) time algorithm presented by Abellanas et al. [1] when k = !(log n). We also consider the problem of computing the...

#### Kinetic k-Semi-Yao graph and its applications

, Article Computational Geometry: Theory and Applications ; Volume 77 , 2019 , Pages 10-26 ; 09257721 (ISSN) ; Abam, M. A ; King, V ; Whitesides, S ; Sharif University of Technology
Elsevier B.V
2019

Abstract

This paper introduces a new supergraph, called the k-Semi-Yao graph (k-SYG), of the k-nearest neighbor graph (k-NNG) of a set P of points in Rd. We provide a kinetic data structure (KDS) to maintain the k-SYG on moving points, where the trajectory of each point is a polynomial function whose degree is bounded by some constant. Our technique gives the first KDS for the theta graph (i.e., 1-SYG) in Rd. It generalizes and improves on previous work on maintaining the theta graph in R2. As an application, we use the kinetic k-SYG to provide the first KDS for maintenance of all the k-nearest neighbors in Rd, for any k≥1. Previous works considered the k=1 case only. Our KDS for all the 1-nearest...

#### Conflict-Free Coloring for Moving Objects

, M.Sc. Thesis Sharif University of Technology ; Abam, Mohammad Ali (Supervisor)
Abstract

Let S be a set of n regions of some fixed type (such as discs, axis-parallel rectangles, etc). A conflict-free coloring (CF-coloring) of S is an assignment of colors to each region such that for every point p covered by a non-empty subset of S, there is a region with a unique color among the regions containing p. We try to maintain a CF-coloring as the objects move. Regions are moving, so after an intersection, the coloring might not be conflict-free anymore and we need to recolor some regions. The goal is to recognize the intersections and to minimize both the total number of colors used and the number of recolorings needed. In this thesis we study kinetic CF-coloring for moving...

#### Label updating to avoid point-shaped obstacles in fixed model

, Article Theoretical Computer Science ; Volume 369, Issue 1-3 , 2006 , Pages 197-210 ; 03043975 (ISSN) ; Ghodsi, M ; Sharif University of Technology
2006

Abstract

In this paper, we present efficient algorithms for updating the labeling of a set of n points after the presence of a random obstacle that appears on the map repeatedly. We update the labeling so that the given obstacle does not appear in any of the labels, the new labeling is valid, and the labels are as large as possible (called the optimal labeling). Each point is assumed to have an axis-parallel, square-shaped label of unit size, attached exclusively to that point in the middle of one of its edges. We consider two models: (1) the 2PM model, where each label is attached to its feature only on the middle of one of its horizontal edges, and (2) the r4PM model, where each label is attached...

#### Performance comparison of adaptive routing algorithms in the star interconnection network

, Article 8th International Conference on High-Performance Computing in Asia-Pacific Region, HPC Asia 2005, Beijing, 30 November 2005 through 3 December 2005 ; Volume 2005 , 2005 , Pages 257-264 ; 0769524869 (ISBN); 9780769524863 (ISBN) ; Sarbazi Azad, H ; Rezazad, M. S ; Sharif University of Technology
2005

Abstract

The star graph was introduced as an attractive alternative to the well-known hypercube and its properties have been well studied in the past. Most of these studies have focused on topological properties and algorithmic aspects of this network. In this paper, the performance of nine fully-adaptive routing algorithms in the star network are studied under uniform (with and without locality) and hotspot traffic patterns. The performance factors considered are the average message latency and network utilization. We consider three basic routing algorithms (two hop scheme routing algorithms: positive-hop and negative-hop, and Msic's routing algorithm) and two other improved sets of improved...