Delaunay Triangulations on the Word RAM: Towards a Practical Worst-Case Optimal Algorithm

2013 ◽  
Author(s):  
Okke Schrijvers ◽  
Frits van Bommel ◽  
Kevin Buchin
Keyword(s):  
Optimal Algorithm ◽  
Worst Case ◽  
Delaunay Triangulations

scholarly journals Efficiency Through Procrastination: Approximately Optimal Algorithm Configuration with Runtime Guarantees

2017 ◽  
Author(s):  
Robert Kleinberg ◽  
Kevin Leyton-Brown ◽  
Brendan Lucier
Keyword(s):  
High Probability ◽  
Optimal Algorithm ◽  
Optimal Performance ◽  
Worst Case ◽  
Running Time ◽  
Performance Guarantees ◽  
Algorithm Configuration ◽  
Time Requirements

Algorithm configuration methods have achieved much practical success, but to date have not been backed by meaningful performance guarantees. We address this gap with a new algorithm configuration framework, Structured Procrastination. With high probability and nearly as quickly as possible in the worst case, our framework finds an algorithm configuration that provably achieves near optimal performance. Moreover, its running time requirements asymptotically dominate those of existing methods.

NUMERICAL STABILITY OF ALGORITHMS FOR 2D DELAUNAY TRIANGULATIONS

1995 ◽  
Vol 05 (01n02) ◽  
pp. 193-213 ◽  
Author(s):  
STEVEN FORTUNE
Keyword(s):  
Delaunay Triangulation ◽  
Floating Point ◽  
Worst Case ◽  
Delaunay Triangulations ◽  
Floating Point Arithmetic ◽  
Circular Arcs ◽  
Stability Of Algorithms ◽  
Forming Angle ◽  
Point Arithmetic ◽  
Floating Point Implementation

We consider the correctness of 2-d Delaunay triangulation algorithms implemented using floating-point arithmetic. The α-pseudocircle through points a, b, c consists of three circular arcs connecting ab, bc, and ac, each arc inside the circumcircle of a, b, c and forming angle α with the circumcircle; a triangulation is α-empty if the α-pseudocircle through the vertices of each triangle is empty. We show that a simple Delaunay triangulation algorithm—the flipping algorithm—can be implemented to produce O(n∈)-empty triangulations, where n is the number of point sites and ∈ is the relative error of floating-point arithmetic; its worst-case running time is O(n2). We also discuss floating-point implementation of other 2-d Delaunay triangulation algorithms.

New Optimal Preemptively Scheduling for Real-Time Reconfigurable Sporadic Tasks Based on Earliest Deadline First Algorithm

2012 ◽  
Vol 4 (2) ◽  
pp. 65-81 ◽  
Author(s):  
Hamza Gharsellaoui ◽  
Mohamed Khalgui ◽  
Samir Ben Ahmed
Keyword(s):  
Response Time ◽  
Real Time ◽  
Dynamic Scheduling ◽  
Optimal Algorithm ◽  
Real Life ◽  
Sporadic Tasks ◽  
Periodic Tasks ◽  
Worst Case ◽  
Utilization Factor ◽  
Earliest Deadline

This paper examines the problem of scheduling the mixed workload of both sporadic (on-line) and periodic (off-line) tasks on uniprocessor in a hard real-time environment. The authors introduce an optimal earliest deadline scheduling algorithm to optimize response time while ensuring that all periodic tasks meet their deadlines and to accept as many sporadic tasks. A necessary and sufficient schedulability test is presented, and an efficient O(n+m) guarantee algorithm is proposed. This optimal algorithm results in dynamic scheduling solutions. They are presented by a proposed intelligent agent-based architecture where a software agent is used to evaluate the response time, to calculate the processor utilization factor and also to verify the satisfaction of real-time deadlines. The agent dynamically provides technical solutions for users where the system becomes unfeasible by sending sporadic tasks to idle times, by modifying the deadlines of tasks, the worst case execution times (WCETs), the activation time, by tolerating some non critical tasks according to the (m, n) firm and a reasonable cost, or in the worst case by removing some non hard (soft) tasks according to predefined heuristic. The authors implement the agent to support these services which are applied to extensive experiments with real-life design examples in order to demonstrate the effectiveness and the excellent performance of the new optimal algorithm in normal and overload conditions.

Constructing Delaunay Triangulations by Merging Buckets in Quad Tree Order

1988 ◽  
Vol 11 (3) ◽  
pp. 275-288
Author(s):  
Jyrki Katajainen ◽  
Markku Koppinen
Keyword(s):  
Delaunay Triangulation ◽  
Slight Modification ◽  
Divide And Conquer ◽  
Worst Case ◽  
Delaunay Triangulations ◽  
Running Time ◽  
Expected Time ◽  
Divide And Conquer Algorithm ◽  
Quad Tree ◽  
Average Running Time

Recently Rex Dwyer [D87] presented an algorithm which constructs a Delaunay triangulation for a planar set of N sites in O(N log log N) expected time and O(N log N) worst-case time. We show that a slight modification of his algorithm preserves the worst-case running time, but has only O(N) average running time. The methcxl is a hybrid which combines the cell technique with the divide-and-conquer algorithm of Guibas & Stolfi [GS85]. First a square grid of size about N by N is placed on the set of sites. The grid forms about N cells (buckets), each of which is implemented as a list of the sites which fall into the corresponding square of the grid. A Delaunay triangulation of the generally rather few sites within each cell is constructed with the Guibas & Stolfi algorithm. Then the triangulations are merged, four by four, in a quadtree-like order.

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