A linear time deterministic algorithm to find a small subset that approximates the centroid

2007 ◽  
Vol 105 (1) ◽  
pp. 17-19
Author(s):  
Pratik Worah ◽  
Sandeep Sen
Keyword(s):  
Linear Time ◽  
Deterministic Algorithm ◽  
Small Subset

On the Euclidean Minimum Spanning Tree Problem

2005 ◽  
Vol 1 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Sanguthevar Rajasekaran
Keyword(s):  
Spanning Tree ◽  
Euclidean Distance ◽  
Minimum Spanning Tree ◽  
Linear Time ◽  
Randomized Algorithm ◽  
Weighted Graph ◽  
Deterministic Algorithm ◽  
Probabilistic Algorithms ◽  
Tree Algorithms ◽  
Minimum Spanning Tree Problem

Given a weighted graph G(V;E), a minimum spanning tree for G can be obtained in linear time using a randomized algorithm or nearly linear time using a deterministic algorithm. Given n points in the plane, we can construct a graph with these points as nodes and an edge between every pair of nodes. The weight on any edge is the Euclidean distance between the two points. Finding a minimum spanning tree for this graph is known as the Euclidean minimum spanning tree problem (EMSTP). The minimum spanning tree algorithms alluded to before will run in time O(n2) (or nearly O(n2)) on this graph. In this note we point out that it is possible to devise simple algorithms for EMSTP in k- dimensions (for any constant k) whose expected run time is O(n), under the assumption that the points are uniformly distributed in the space of interest.CR Categories: F2.2 Nonnumerical Algorithms and Problems; G.3 Probabilistic Algorithms

scholarly journals ADAPTIVE SUB-LINEAR TIME FOURIER ALGORITHMS

2013 ◽  
Vol 05 (01) ◽  
pp. 1350003 ◽  
Author(s):  
DAVID LAWLOR ◽  
YANG WANG ◽  
ANDREW CHRISTLIEB
Keyword(s):  
Fourier Transform ◽  
Fourier Coefficients ◽  
Linear Time ◽  
Input Function ◽  
Deterministic Algorithm ◽  
Average Case ◽  
Deterministic Algorithms

We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k ≪ N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic runtime scaling, while our algorithm scales linearly with k in the average case. Underlying our algorithm are a few simple observations relating the Fourier coefficients of time-shifted samples to unshifted samples of the input function. This allows us to detect when aliasing between two or more frequencies has occurred, as well as to determine the value of unaliased frequencies. We show that empirically our algorithm is orders of magnitude faster than competing algorithms.

scholarly journals A Reduction Algorithm for Large-Base Primitive Permutation Groups

2006 ◽  
Vol 9 ◽  
pp. 159-173 ◽  
Author(s):  
Maska Law ◽  
Alice C. Niemeyer ◽  
Cheryl E. Praeger ◽  
Ákos Seress
Keyword(s):  
Permutation Group ◽  
Las Vegas ◽  
Linear Time ◽  
Symmetric Groups ◽  
Deterministic Algorithm ◽  
Primitive Permutation Group ◽  
Reduction Algorithm ◽  
Product Action ◽  
Speed Up ◽  
Las Vegas Algorithm

AbstractThe authors present a nearly linear-time Las Vegas algorithm that, given a large-base primitive permutation group, constructs its natural imprimitive representation. A large-base primitive permutation group is a subgroup of a wreath product of symmetric groups Sn and Sr in product action on r-tuples of k-element subsets of {1, …, n}, containing Anr. The algorithm is a randomised speed-up of a deterministic algorithm of Babai, Luks, and Seress.

scholarly journals Selection Algorithms with Small Groups

2020 ◽  
Vol 31 (03) ◽  
pp. 355-369
Author(s):  
Ke Chen ◽  
Adrian Dumitrescu
Keyword(s):  
Small Groups ◽  
Linear Time ◽  
Deterministic Algorithm ◽  
Worst Case ◽  
Running Time ◽  
Original Algorithm ◽  
Will Force ◽  
Time Fall ◽  
Step Algorithm ◽  
Selection Algorithms

We revisit the selection problem, namely that of computing the [Formula: see text]th order statistic of [Formula: see text] given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973). Whereas the original algorithm uses groups of odd size at least [Formula: see text] and runs in linear time, it has been perpetuated in the literature that using smaller group sizes will force the worst-case running time to become superlinear, namely [Formula: see text]. We first point out that the usual arguments found in the literature justifying the superlinear worst-case running time fall short of proving this claim. We further prove that it is possible to use group size smaller than [Formula: see text] while maintaining the worst case linear running time. To this end we introduce three simple variants of the classic algorithm, the repeated step algorithm, the shifting target algorithm, and the hyperpair algorithm, all running in linear time.

A Real Time Control Architecture for Continuously Managing Patients in a Care Unit

1995 ◽  
Vol 34 (05) ◽  
pp. 475-488
Author(s):  
B. Seroussi ◽  
J. F. Boisvieux ◽  
V. Morice
Keyword(s):  
Real Time ◽  
Linear Time ◽  
Treatment Plan ◽  
Control Architecture ◽  
Real Time Control ◽  
Time Representation ◽  
Time Control ◽  
Continuous Support ◽  
Definition Of ◽  
Computerized System

Abstract:The monitoring and treatment of patients in a care unit is a complex task in which even the most experienced clinicians can make errors. A hemato-oncology department in which patients undergo chemotherapy asked for a computerized system able to provide intelligent and continuous support in this task. One issue in building such a system is the definition of a control architecture able to manage, in real time, a treatment plan containing prescriptions and protocols in which temporal constraints are expressed in various ways, that is, which supervises the treatment, including controlling the timely execution of prescriptions and suggesting modifications to the plan according to the patient’s evolving condition. The system to solve these issues, called SEPIA, has to manage the dynamic, processes involved in patient care. Its role is to generate, in real time, commands for the patient’s care (execution of tests, administration of drugs) from a plan, and to monitor the patient’s state so that it may propose actions updating the plan. The necessity of an explicit time representation is shown. We propose using a linear time structure towards the past, with precise and absolute dates, open towards the future, and with imprecise and relative dates. Temporal relative scales are introduced to facilitate knowledge representation and access.

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