An exact construction of digital convex polygons with minimal diameter

Matić-Kekić, Snežana; Acketa, Dragan M.; Žunić, Joviša

doi:10.1016/0012-365x(95)00195-3

Cited by 10 publications

(4 citation statements)

References 3 publications

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“…This output of the polynomial is similar with the default output of the fitting polynomial obtained by Mathematica (10), where all the coefficients, except the constant term, have six significant digits. According to Table 4, one can conclude that P = 0.…”

Section: Application Of the Algorithm On The Fitting Polynomial (D < N)mentioning

confidence: 72%

“…Sometimes, we are faced with different mathematical problems which are partially or completely unsolvable without using a PC. For example, it helps us to generate large number (approximately 2000) of new 2-designs [1] or completely solve the problem of optimal construction of digital convex polygons with n vertices, n ∈ N [10,11]. Also, it is well known that the analysis of experimental data must be done by using the software support utilities.…”

Section: Introductionmentioning

confidence: 99%

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Nonsensical Excel and Statistica Default Output and Algorithm for an Adequate Display

Matic-Kekic,

Dedovic,

Mutavdzic

2013

Preprint

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The purpose of this paper is to present an algorithm that determines the necessary and sufficient number of significant digits in the coefficients of polynomial trend in order to achieve a pre-specified precision of polynomial trend. Thus, the obtained coefficients should be presented in the default output when fitting the experimental data by polynomial trend. Namely, in order to find the best fitting function for certain type of data there is a real possibility of making significant errors using default output of Excel 2003Excel , 2007Excel , 2010Excel , 2013 and Statistica for Windows 2007-2012 software packages. Conversely, software package Mathematica (version 6) has shown very good characteristics in dealing with precision problems, although the default output sometimes shows more significant digits than necessary. Also, it turned out that the software packages Excel and Statistica violated the order of operations as defined in mathematics. For example, −1 2 = 1 and −(−3) 2 = 9. This problem always occurs in Excel, while at Statistica during the graphical interpretation of a function.

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Section: Application Of the Algorithm On The Fitting Polynomial (D < N)mentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Nonsensical Excel and Statistica Default Output and Algorithm for an Adequate Display

Matic-Kekic,

Dedovic,

Mutavdzic

2013

Preprint

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“…It has been shown in [19] and [1] that such convex n-gons can be constructed so that they can be inscribed inside a square grid of side-size Θ(n 3/2 ). Therefore, by using such convex n-gon, our senders can be covered, according to the construction above, using ( √ k + O(n 3/2 )) 2 = k + O(n 3/2 √ k + n 3 ) n-gons, hence the schedule requires k + O(n 3/2 √ k + n 3 ) transmission rounds.…”

Section: A General Upper Boundmentioning

confidence: 99%

Broadcast Transmission to Prioritizing Receivers

Alon

Rutenberg²

2017

SIAM J. Discrete Math.

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We consider a broadcast model involving multiple transmitters and receivers. Transmission is performed in rounds, where in each round any transmitter is allowed to broadcast a single message, and each receiver can receive only a single broadcast message, determined by a priority permutation over the transmitters. The message received by receiver R in a given transmission round is the one sent by the first transmitter among all those broadcasting in that round according to the permutation of R. In our model, each pair of transmitter and receiver has a unique message which the transmitter has to send to the receiver. We prove upper and lower bounds on the minimal number of rounds needed for transmitting all the messages to their respective receivers. We also consider the case where the priority permutations are determined geometrically.

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“…(An exact construction of optimal Qi(n) polygons for arbitrary n is given in [6].) [3] Optimal convex lattice polygons 231…”

Section: C\= Ffmentioning

confidence: 99%

The Perimeter of optimal convex lattice polygons in the sense of different metrics

Stojaković¹

2001

Bull. Austral. Math. Soc.

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Classes of convex lattice polygons which have minimal lp-perimeter with respect to the number of their vertices are said to be optimal in the sense of the lp-metric.It is proved that if p and q are arbitrary integers or ∞, the asymptotic expression for the lq-perimeter of these optimal convex lattice polygons Qp(n) as a function of the number of their vertices n is . for arbitrary ɛ > 0, where . and Ap is equal to the area of the planar shape |x|p + |y|p ≤ 1.

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An exact construction of digital convex polygons with minimal diameter

Cited by 10 publications

References 3 publications

Nonsensical Excel and Statistica Default Output and Algorithm for an Adequate Display

Nonsensical Excel and Statistica Default Output and Algorithm for an Adequate Display

Broadcast Transmission to Prioritizing Receivers

The Perimeter of optimal convex lattice polygons in the sense of different metrics

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