On the Time-Space Complexity of Geometric Elimination Procedures

2001 ◽  
Vol 11 (4) ◽  
pp. 239-296 ◽  
Author(s):  
Joos Heintz ◽  
Guillermo Matera ◽  
Ariel Waissbein
Keyword(s):  
Space Complexity ◽  
Time Space

How significant are the known collision and element distinctness quantum algorithms?

2004 ◽  
Vol 4 (3) ◽  
pp. 201-206
Author(s):  
L. Grover ◽  
T. Rudolph
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithms ◽  
Search Space ◽  
Space Complexity ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Space ◽  
Simple Quantum ◽  
Structured Problems ◽  
Better Than

Quantum search is a technique for searching $N$ possibilities for a desired target in $O(\sqrt{N})$ steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires $O(S)$ hardware should be considered significant if it produces a speedup of better than $O\left(\sqrt{S}\right)$ over a simple quantum search algorithm. This is because a speedup of $O\left(\sqrt{S}\right)$ can be trivially obtained by dividing the search space into $S$ separate parts and handing the problem to $S$ independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.

A PARALLEL ALGORITHM FOR ANALYZING CONNECTED COMPONENTS IN BINARY IMAGES

1992 ◽  
Vol 06 (02n03) ◽  
pp. 315-333 ◽  
Author(s):  
FRANCO CHIAVETTA ◽  
VITO DI GESÙ ◽  
ROSALIA RENDA
Keyword(s):  
Parallel Algorithm ◽  
Parallel Implementation ◽  
Discrete Space ◽  
Space Complexity ◽  
Connected Components ◽  
Two Dimensional ◽  
Binary Images ◽  
Cylindrical Algebraic Decomposition ◽  
Time Space ◽  
Connectivity Degree

In this paper, a parallel algorithm for analyzing connected components in binary images is described. It is based on the extension of the Cylindrical Algebraic Decomposition (CAD) to a two-dimensional (2D) discrete space. This extension allows us to find the number of connected components, to determine their connectivity degree, and to solve the visibility problem. The parallel implementation of the algorithm is outlined and its time/space complexity is given.

DYNAMIC GRAPH MERGING FOR IMAGE SEGMENTATION

2013 ◽  
Vol 11 (06) ◽  
pp. 1350051
Author(s):  
JIANPING GU ◽  
LI ZHANG ◽  
CUN CHENG
Keyword(s):  
Image Segmentation ◽  
Elastic Energy ◽  
Linear Time ◽  
Space Complexity ◽  
Variational Model ◽  
Dynamic Graph ◽  
3D Images ◽  
Time Space ◽  
New Energy ◽  
Merging Process

A new algorithm named dynamic graph merging (DGM) for automatic image segmentation is explored. Firstly a novel variational model for multi-section cut is introduced by decomposing the traditional cut into two parts, the harmonic cut and the elastic energy of the boundary. The new energy is called the continuous combined cut. Secondly a new algorithm that removes those edges with higher energy and synchronously merges their starting and ending vertices in an ordered manner is proposed. The continual merging process would iteratively contract the graph, merge those homogeneous vertices into bigger and bigger super-pixels, and fuse the remainder edges into longer and longer boundaries. So we call this algorithm dynamic graph merging. Merging criterions based on the continuous combined cut model are also discussed, which will be used to determine whether a given edge should collapse. Since the merging condition should be highly related to the image content, we present different predicates for structure images and texture images respectively. This algorithm whose efficiency is showed by experiments has a linear time/space complexity, and can efficiently segment gray/color and 2D/3D images.

scholarly journals Time-space complexity and the opening hours of commerce: a study of four European cities

2017 ◽  
pp. 153-177 ◽  
Author(s):  
Mattias Kärrholm ◽  
Teresa Barata-Salgueiro ◽  
Jean Soumagne ◽  
José Fernandes ◽  
Pedro Chamusca
Keyword(s):  
Space Complexity ◽  
European Cities ◽  
Time Space

scholarly journals CPT+: Decreasing the Time/Space Complexity of the Compact Prediction Tree

2015 ◽  
pp. 625-636 ◽  
Author(s):  
Ted Gueniche ◽  
Philippe Fournier-Viger ◽  
Rajeev Raman ◽  
Vincent S. Tseng
Keyword(s):  
Space Complexity ◽  
Time Space
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