Sharif Digital Repository

We focus on two metric clusterings namely r-gather and (r, ?)-gather. The objective of r-gather is to minimize the radius of clustering, such that each cluster has at least r points. (r, ?)-gather is a version of r-gather with the extra condition that at most n? points can be left unclustered (outliers). MapReduce is a model used for processing big data. In each round, it distributes data to multiple servers, then simultaneously processes each server's data. We prove a lower bound 2 on the approximation factor of metric r-gather in the MapReduce model, even if an optimal algorithm for r-gather exists. Then, we give a (4+ δ)-approximation algorithm for r-gather in MapReduce which runs in O(... 

We focus on two metric clusterings namely r-gather and (r, ?)-gather. The objective of r-gather is to minimize the radius of clustering, such that each cluster has at least r points. (r, ?)-gather is a version of r-gather with the extra condition that at most n? points can be left unclustered (outliers). MapReduce is a model used for processing big data. In each round, it distributes data to multiple servers, then simultaneously processes each server's data. We prove a lower bound 2 on the approximation factor of metric r-gather in the MapReduce model, even if an optimal algorithm for r-gather exists. Then, we give a (4+ δ)-approximation algorithm for r-gather in MapReduce which runs in O(... 

A geometric spanner on a point set is a sparse graph that approximates the Euclidean distances between all pairs of points in the point set. Here, we intend to construct a geometric spanner for a massive point set, using a distributed algorithm on parallel machines. In particular, we use the MapReduce model of computation to construct spanners in several rounds with inter-communications in between. An algorithm in this model is called efficient if it uses a sublinear number of machines and runs in a polylogarithmic number of rounds. In this paper, we propose an efficient MapReduce algorithm for constructing a geometric spanner in a constant number of rounds, using linear amount of... 

Given a set of n segments and a query shape Q, the windowing length query asks for finding the sum of the lengths of the parts of the segments that lie inside Q. The popular places problem of a set of curves asks for the subset of the plane where each query shape centered at a point of that region intersects with at least f distinct curves. For square queries, an optimal O(n2) time algorithm and a matching lower bound exist. We solve the length query problem for convex polygons and disks as query shapes, with O(log n+ k) query time and polynomial preprocessing time that depends on the complexity of the query shape. We define a new version of the problem of finding popular places in a set of... 

Given a set of n segments and a query shape Q, the windowing length query asks for finding the sum of the lengths of the parts of the segments that lie inside Q. The popular places problem of a set of curves asks for the subset of the plane where each query shape centered at a point of that region intersects with at least f distinct curves. For square queries, an optimal O(n2) time algorithm and a matching lower bound exist. We solve the length query problem for convex polygons and disks as query shapes, with O(log n+ k) query time and polynomial preprocessing time that depends on the complexity of the query shape. We define a new version of the problem of finding popular places in a set of... 

Given a set of n segments and a query shape Q, the windowing length query asks for finding the sum of the lengths of the parts of the segments that lie inside Q. The popular places problem of a set of curves asks for the subset of the plane where each query shape centered at a point of that region intersects with at least f distinct curves. For square queries, an optimal O(n2) time algorithm and a matching lower bound exist. We solve the length query problem for convex polygons and disks as query shapes, with O(log n+ k) query time and polynomial preprocessing time that depends on the complexity of the query shape. We define a new version of the problem of finding popular places in a set of... 

Packedness is a measure defined for curves as the ratio of maximum curve length inside any disk divided by its radius. Sparsification allows us to reduce the number of candidate disks for maximum packedness to a polynomial amount in terms of the number of vertices of the polygonal curve. This gives an exact algorithm for computing packedness. We prove that using a fat shape, such as a square, instead of a disk gives a constant factor approximation for packedness. Further sparsification using well-separated pair decomposition improves the time complexity at the cost of losing some accuracy. By adjusting the ratio of the separation factor and the size of the query, we improve the approximation... 

Purpose: This paper aims to to simulate the flow and heat transfer during free convection in a square cavity using double-multi-relaxation time (MRT) lattice Boltzmann method. Design/methodology/approach: The double-MRT lattice Boltzmann method is used, and the natural convection fluid flow and heat transfer under influence of different parameters are analyzed. The D2Q5 model and D2Q9 model are used for simulation of temperature field and flow field, respectively. The cavity is filled with CuO-water nanofluid; in addition, the thermo-physical properties of nanofluid and the effect of nanoparticles’ shapes are considered using Koo–Kleinstreuer–Li (KKL) model. On the other hand, the cavity is... 

Learning a foreign language encompasses a process of trial and error that can lead to the progression of the learner's interlanguage, meaning that the learners make use of their language knowledge that receives feedback and brings about progress through diagnosis of the problems and being corrected by the teacher. Therefore, there exists a need to analyze the underlying reasons causing the students to remain taciturn with a low willingness to communicate (WTC) during a language class. There has been much work done investigating the role of the learner's stable personal characteristics (traits) along with their situational changes at a specific time (states) that influence the student's... 

Using 3-D scanned data to analyze and extract pore network plays a vital role in investigation of porous media's characteristics. In this paper, a new simple method is developed to detect pores and throats for analyzing the connectivity and permeability of the network. This automated method utilizes some of the common and well-known image processing functions which are widely accessible by researchers and this has led to an easy algorithm implementation. In this method, after polishing and quality control of images, using city-block distance function and watershed segmentation algorithm, pores and throats are detected and 3-D network is produced. This method can also be applied on 2-D images... 

In this paper, we try to recognize and distinguish different groups of arrhythmia using novel features which have been obtained from the heart rate's phase space in recent years. For this purpose, we used Triangular Phase Space Mapping (TPSM) and Parabolic Phase Space Mapping (PPSM). For recognition, we used three groups of 15 subjects using the Physionet database (Arrhythmia, Congestive Heart Failure (CHF), and Atrial Fibrillation (AF)) with Normal Sinus Rhythm (NSR). The obtained features discriminate arrhythmia from NSR by p