Computational Geometry Column 67

Banyassady, Bahareh; Korman, Matias; Mulzer, Wolfgang

doi:10.1145/3232679.3232692

Cited by 7 publications

(5 citation statements)

References 35 publications

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“…Vehicle speed is represented by s. T is the dwell time within the cell. A chord of a circle is a line of which both endpoints lie on the boundary of the circle [62]. The dwell distance is denoted by a random chord (C) of the coverage circle that passes through points Handover failure (HOF) occurs if a handover process is initiated but not completed [65].…”

Section: Number Of Handoversmentioning

confidence: 99%

An Adaptive Cell Selection Scheme for 5G Heterogeneous Ultra-Dense Networks

Alablani

Arafah

2021

IEEE Access

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Fifth-generation (5G) cellular networks are a promising technology to meet the rapid growth in wireless traffic. Small cells are critical in fulfilling the requirements of 5G networks. A heterogeneous ultra-dense network (HUDN) is an enabling technology consisting of several types of small cells to enhance the performance of 5G networks effectively. A critical issue of HUDN is the cell selection method because the traditional technique for cell selection is inapplicable in such a network. This study proposes a novel adaptive cell selection (ADA-CS) scheme. It adapts to various characteristics of HUDNs and vehicle movements. It performs six phases to select the best base station with which to be associated. Simulation results show that, with low-and medium-speed vehicles, the ADA-CS scheme outperforms the traditional protocol in terms of the average number of handovers by 42.39%. In addition, it is superior to some relevant recent schemes by up to 36.53%. The adaptation feature of the proposed protocol provides additional improvements regarding the average number of handovers with high-speed vehicles. Therefore, it achieves superiority in terms of the average number of handover failures and unnecessary handovers. In addition, the ADA-CS scheme enhances the average achievable downlink data rates and spectral efficiency per vehicle by 3.98% and 2.79% compared with the traditional and the relevant recent schemes.

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Section: Number Of Handoversmentioning

confidence: 99%

An Adaptive Cell Selection Scheme for 5G Heterogeneous Ultra-Dense Networks

Alablani

Arafah

2021

IEEE Access

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“…Following Asano et al [2] and Darwish and Elmasry [11], we refer to this model as the read-only random-access model. Over the years, starting with a seminal paper of Munro and Paterson [35] where a related model was used, the space-time trade-offs in this restricted RAM model have been studied for many problems, including sorting [21,36,39], selection [18,21,36,42], and various geometric problems [1,3,4,12,13]. The practical motivation for some of the previous work has been the appearance of special devices where the size of working space is limited (e.g., mobile devices) and where writing is expensive (e.g., flash memories).…”

Section: Introduction 1problem Areamentioning

confidence: 99%

Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls

Darwish

Elmasry

Katajainen

2021

ACM Trans. Algorithms

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We consider space-bounded computations on a random-access machine, where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and writes but is of limited capacity. The length of the input is N elements, the length of the output is limited by the computation, and the capacity of the workspace is O ( S ) bits for some predetermined parameter S ≥ lg N . We present a state-of-the-art priority queue—called an adjustable navigation pile —for this restricted model. This priority queue supports M inimum in O (1) time, C onstruct in O ( N ) time, and E xtract - min in O ( N / S + lg S ) time for any S ≥ lg N . The priority queue can be further augmented in O ( N ) time to deal with a batch of at most S elements in a specified range of values at a time, and allow to I nsert (activate) or E xtract (deactivate) an element among these elements, such that I nsert and E xtract take O ( N / S + lg S ) time for any S ≥ lg N . We show how to use our data structure to sort N elements and to compute the convex hull of N points in the Euclidean plane in O ( N 2 / S + N lg S ) time for any S ≥ lg N . Following a known lower bound for the space-time product of any branching program for finding unique elements, both our sorting and convex-hull algorithms are optimal. The adjustable navigation pile has turned out to be useful when designing other space-efficient algorithms, and we expect that it will find its way to yet other applications.

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“…In recent years, the constant-workspace model has enjoyed growing popularity in the computational geometry community [6]. Motivated by the increasing deployment of small devices with limited memory capacities, the goal is to develop simple and efficient algorithms for the situation where little workspace is available.…”

Section: Introductionmentioning

confidence: 99%

“…Following the initial work by Asano et al from 2011 [2], numerous results have been published for this model, leading to a solid theoretical foundation for dealing with geometric problems when the working memory is scarce. The recent survey by Banyassady et al [6] gives an overview of the problems that have been considered and of the results that are available for them.…”

Section: Introductionmentioning

confidence: 99%

An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace Model

Cleve

Mulzer

2019

Lecture Notes in Computer Science

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We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed at random. In addition, the algorithm may use a constant number of words for reading and for writing. The constant-workspace model has been studied extensively in recent years, and algorithms for geodesic shortest paths have received particular attention. We have implemented three such algorithms in Python, and we compare them to the classic algorithm by Lee and Preparata that uses linear time and linear space. We also clarify a few implementation details that were missing in the original description of the algorithms. Our experiments show that all algorithms perform as advertised in the original works and according to the theoretical guarantees. However, the constant factors in the running times turn out to be rather large for the algorithms to be fully useful in practice.Keywords: simple polygon · geodesic shortest path · constant workspace · experimental evaluation Supported in part by DFG projects MU/3501-1 and RO/2338-6 and ERC StG 757609.

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Computational Geometry Column 67

Cited by 7 publications

References 35 publications

An Adaptive Cell Selection Scheme for 5G Heterogeneous Ultra-Dense Networks

An Adaptive Cell Selection Scheme for 5G Heterogeneous Ultra-Dense Networks

Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls

An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace Model

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