ON MAINTAINING THE WIDTH AND DIAMETER OF A PLANAR POINT-SET ONLINE

1993 ◽  
Vol 03 (03) ◽  
pp. 331-344 ◽  
Author(s):  
RAVI JANARDAN
Keyword(s):  
Data Structures ◽  
Online Algorithm ◽  
Greedy Heuristic ◽  
Convex Hulls ◽  
Approximation Formula ◽  
Maximum Weight ◽  
Worst Case ◽  
Planar Point ◽  
Point Set ◽  
The One

Efficient online algorithms are presented for maintaining the (almost-exact) width and diameter of a dynamic planar point-set, S. Let n be the number of points currently in S, let W and D denote the width and diameter of S, respectively, and let α>1 and β≥1 be positive, integer-valued parameters. The algorithm for the width problem uses O(αn) space, supports updates in O(α log 2 n) time, and reports in O(α log 2 n) time an approximation, Ŵ, to the width such that [Formula: see text]. The algorithm for the diameter problem uses O(βn) space, supports updates in O(β log n) time, and reports in O(β) time an approximation, [Formula: see text], to the diameter such that [Formula: see text]. Thus, for instance, even for α as small as 11, Ŵ/W≤1.01, and for β as small as 9, [Formula: see text]. All bounds stated are worst-case. Both algorithms, but especially the one for the diameter problem, use well-understood data structures and should be simple to implement. The diameter result yields a fast implementation of the greedy heuristic for maximum-weight Euclidean matching and an efficient online algorithm to maintain approximate convex hulls in the plane.

On the minimum cardinality of a planar point set containing two disjoint convex polygons

2013 ◽  
Vol 50 (3) ◽  
pp. 331-354
Author(s):  
Liping Wu ◽  
Wanbing Lu
Keyword(s):  
Positive Integer ◽  
Convex Hulls ◽  
Convex Polygons ◽  
Minimum Cardinality ◽  
Planar Point ◽  
Point Set ◽  
Disjoint Convex

Let N(k, l) be the smallest positive integer such that any set of N(k, l) points in the plane, no three collinear, contains both a convex k-gon and a convex l-gon with disjoint convex hulls. In this paper, we prove that N(3, 4) = 7, N(4, 4) = 9, N(3, 5) = 10 and N(4, 5) = 11.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

scholarly journals Analysis of the robustness of a steel frame structure with composite floors subject to multiple fire scenarios

2021 ◽  
pp. 136943322199249
Author(s):  
Riza Suwondo ◽  
Lee Cunningham ◽  
Martin Gillie ◽  
Colin Bailey
Keyword(s):  
Progressive Collapse ◽  
Three Dimensional ◽  
Steel Structure ◽  
Frame Structure ◽  
Worst Case ◽  
Collapse Resistance ◽  
Fire Scenarios ◽  
Element Approach ◽  
The One ◽  
Steel Frame Structure

This study presents robustness analyses of a three-dimensional multi-storey composite steel structure under the action of multiple fire scenarios. The main objective of the work is to improve current understanding of the collapse resistance of this type of building under different fire situations. A finite element approach was adopted with the model being firstly validated against previous studies available in the literature. The modelling approach was then used to investigate the collapse resistance of the structure for the various fire scenarios examined. Different sizes of fire compartment are considered in this study, starting from one bay, three bays and lastly the whole ground floor as the fire compartment. The investigation allows a fundamental understanding of load redistribution paths and member interactions when local failure occurs. It is concluded that the robustness of the focussed building in a fire is considerably affected by the size of fire compartments as well as fire location. The subject building can resist progressive collapse when the fire occurs only in the one-bay compartment. On the other hand, total collapse occurs when fire is located in the edge three-bay case. This shows that more than one fire scenario needs to be taken into consideration to ensure that a structure of this type can survive from collapse in the worst-case situation.

scholarly journals Parallel One-Step Control of Parametrised Boolean Networks

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 560 ◽  
Author(s):  
Luboš Brim ◽  
Samuel Pastva ◽  
David Šafránek ◽  
Eva Šmijáková
Keyword(s):  
Control Problem ◽  
Boolean Networks ◽  
Actual State ◽  
Worst Case ◽  
Symbolic Data ◽  
One Step ◽  
The One ◽  
Step Control ◽  
Symbolic Algorithm ◽  
Naive Approach

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as this model allows leaving some update functions unspecified. In our work, we attack the control problem for ParBNs with asynchronous semantics. While there is an extensive work on controlling BNs without parameters, the problem of control for ParBNs has not been in fact addressed yet. The goal of control is to ensure the stabilisation of a system in a given state using as few interventions as possible. There are many ways to control BN dynamics. Here, we consider the one-step approach in which the system is instantaneously perturbed out of its actual state. A naïve approach to handle control of ParBNs is using parameter scan and solve the control problem for each parameter valuation separately using known techniques for non-parametrised BNs. This approach is however highly inefficient as the parameter space of ParBNs grows doubly exponentially in the worst case. We propose a novel semi-symbolic algorithm for the one-step control problem of ParBNs, that builds on symbolic data structures to avoid scanning individual parameters. We evaluate the performance of our approach on real biological models.

scholarly journals MAINTAINING VISIBILITY INFORMATION OF PLANAR POINT SETS WITH A MOVING VIEWPOINT

2007 ◽  
Vol 17 (04) ◽  
pp. 297-304 ◽  
Author(s):  
OLIVIER DEVILLERS ◽  
VIDA DUJMOVIĆ ◽  
HAZEL EVERETT ◽  
SAMUEL HORNUS ◽  
SUE WHITESIDES ◽  
...  
Keyword(s):  
Linear Space ◽  
Point Sets ◽  
Worst Case ◽  
Planar Point ◽  
Set Of Points

Given a set of n points in the plane, we consider the problem of computing the circular ordering of the points about a viewpoint q and efficiently maintaining this ordering information as q moves. In linear space, and after O(n log n) preprocessing time, our solution maintains the view at a cost of O( log n) amortized time (resp.O( log 2 n) worst case time) for each change. Our algorithm can also be used to maintain the set of points sorted according to their distance to q .

Topology Optimization of Dynamic Systems Under Uncertain Loads: An H∞-Norm-Based Approach

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Paolo Venini
Keyword(s):  
Topology Optimization ◽  
Structural Parameters ◽  
Goal Function ◽  
Dynamic Compliance ◽  
Case Scenario ◽  
Worst Case ◽  
Original Definition ◽  
Optimal Material ◽  
The One ◽  
Definition Of

An innovative approach to topology optimization of dynamic system is introduced that is based on the system transfer-function H∞-norm. As for the structure, the proposed strategy allows to determine the optimal material distribution that ensures the minimization of a suitable goal function, such as (an original definition of) the dynamic compliance. Load uncertainty is accounted for by means of a nonprobabilistic convex-set approach (Ben-Haim and Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam). At each iteration, the worst load is determined as the one that maximizes the current dynamic compliance so that the proposed strategy fits the so-called worst case scenario (WCS) approach. The overall approach consists of the repeated solution of the two steps (minimization of the dynamic compliance with respect to structural parameters and maximization of the dynamic compliance with respect to the acting load) until convergence is achieved. Results from representative numerical studies are eventually presented along with extensions to the proposed approach that are currently under development.

scholarly journals Intelligent design af fokusgrupper - om metodisk design af fokusgrupper og menneskets forskellige intelligenser

2008 ◽  
Vol 24 (45) ◽  
pp. 13
Author(s):  
Lene Heiselberg
Keyword(s):  
Focus Groups ◽  
Intelligent Design ◽  
Verbal Intelligence ◽  
Case Scenario ◽  
Worst Case ◽  
Apparent Lack ◽  
Self Confidence ◽  
Media Research ◽  
The One ◽  
Interviewing Techniques

Når man arbejder professionelt med at gennemføre kvalitative mini- og fokusgruppeanalyser, kan det ikke undgås, at man som moderator indimellem tænker: Hvorfor deltager hun ikke? Hvad kan jeg gøre for at inkludere hende i diskussionen? Ofte skyldes nogle deltageres manglende engagement, at mini- eller fokusgruppens metodiske design favoriserer de deltagere, som har en fremtrædende verbalsproglig intelligens, og samtidig ekskluderes de, der har andre fremtrædende intelligenser, fra at yde det maksimale. En sådan situation er meget uheldig og kan i værste fald give en undersøgelse bias. Derfor har vi i DR Medieforskning arbejdet med en pragmatisk tilgang til problemet, hvor vi har afprøvet et metodisk design, som inkluderer kvalitative interviewteknikker og procesværktøjer, som appellerer til samtlige intelligenser. Som et resultat af en målrettet indsats for at inkludere flere intelligenser i det metodiske design, oplever vi, at deltagerne har mere lyst til at engagere sig og gør det med større selvsikkerhed. Desuden oplever vi i mindre grad fænomenet “cognitive tuning” , og derfor kan vi arbejde med flere og bedre data i analyse- og fortolkningsfasen. Intelligent design of focus groups - article about methodological design of focus groups and the different intelligences When you work professionally with the conducting and moderating of qualitative mini- and focus groups, you can't avoid sometimes thinking: Why isn’t she participating? What can I do to include her in the discussion? A participant's apparent lack of enthusiasm is often caused by the methodological design of the focus group giving preference to participants who have an explicit verbal intelligence, and as a consequence excludes participants with other explicit intelligences from contributing. A situation like the one described above is very undesirable and in a worst-case scenario it can cause a study to be biased. In order to try to solve this problem DR Media Research applied a methodological design which includes qualitative interviewing techniques and processing tools, which appeal to all of the intelligences instead of just one. As a result of this work, we find that the participants are more eager to participate and that they do it with greater self-confidence. In addition we encounter less cognitive tuning, and are therefore able to work with richer data in the phases of analysis and interpretation.

scholarly journals The Synthesis of Stochastic Circuits for Nanoscale Computation

2009 ◽  
Vol 1 (4) ◽  
pp. 39-57 ◽  
Author(s):  
Weikang Qian ◽  
John Backes ◽  
Marc D. Riedel
Keyword(s):  
Data Structures ◽  
Self Assembly ◽  
Logic Synthesis ◽  
Nanowire Arrays ◽  
Stochastic Nature ◽  
Symbolic Data ◽  
The One ◽  
High Degree ◽  
Stochastic Circuits ◽  
General Method

Emerging technologies for nanoscale computation such as self-assembled nanowire arrays present specific challenges for logic synthesis. On the one hand, they provide an unprecedented density of bits with a high degree of parallelism. On the other hand, they are characterized by high defect rates. Also they often exhibit inherent randomness in the interconnects due to the stochastic nature of self-assembly. We describe a general method for synthesizing logic that exploits both the parallelism and the random effects. Our approach is based on stochastic computation with parallel bit streams. Circuits are synthesized through functional decomposition with symbolic data structures called multiplicative binary moment diagrams. Synthesis produces designs with randomized parallel components—and operations and multiplexing—that are readily implemented in nanowire crossbar arrays. Synthesis results for benchmarks circuits show that our technique maps circuit designs onto nanowire arrays effectively.

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