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.

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.

TWO TOPICS CONCERNING TWO-DIMENSIONAL AUTOMATA OPERATING IN PARALLEL

1992 ◽  
Vol 06 (02n03) ◽  
pp. 211-225 ◽  
Author(s):  
KATSUSHI INOUE ◽  
ITSUO SAKURAMOTO ◽  
MAKOTO SAKAMOTO ◽  
ITSUO TAKANAMI
Keyword(s):  
Turing Machine ◽  
Finite Automata ◽  
Space Complexity ◽  
Two Dimensional ◽  
Turing Machines ◽  
Small Space ◽  
Bottom Up ◽  
Constructible Function ◽  
Deterministic Turing Machine ◽  
Alternating Turing Machines

This paper deals with two topics concerning two-dimensional automata operating in parallel. We first investigate a relationship between the accepting powers of two-dimensional alternating finite automata (2-AFAs) and nondeterministic bottom-up pyramid cellular acceptors (NUPCAs), and show that Ω ( diameter × log diameter ) time is necessary for NUPCAs to simulate 2-AFAs. We then investigate space complexity of two-dimensional alternating Turing machines (2-ATMs) operating in small space, and show that if L (n) is a two-dimensionally space-constructible function such that lim n → ∞ L (n)/ loglog n > 1 and L (n) ≤ log n, and L′ (n) is a function satisfying L′ (n) =o (L(n)), then there exists a set accepted by some strongly L (n) space-bounded two-dimensional deterministic Turing machine, but not accepted by any weakly L′ (n) space-bounded 2-ATM, and thus there exists a rich space hierarchy for weakly S (n) space-bounded 2-ATMs with loglog n ≤ S (n) ≤ log n.

scholarly journals A Probabilistic Statistical Method for the Determination of Void Morphology with CFD-DEM Approach

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4041
Author(s):  
Yuanxiang Lu ◽  
Sihan Liu ◽  
Xinru Zhang ◽  
Zeyi Jiang ◽  
Dianyu E
Keyword(s):  
Probabilistic Method ◽  
Gas Injection ◽  
Morphological Characteristics ◽  
Packed Bed ◽  
Two Dimensional ◽  
Two Phase ◽  
Binary Images ◽  
Void Shape ◽  
Shape And Size

Voids that are formed by gas injection in a packed bed play an important role in metallurgical and chemical furnaces. Herein, two-phase gas–solid flow in a two-dimensional packed bed during blast injection was simulated numerically. The results indicate that the void stability was dynamic, and the void shape and size fluctuated within a certain range. To determine the void morphology quantitatively, a probabilistic method was proposed. By statistically analyzing the white probability of each pixel in binary images at multiple times, the void boundaries that correspond to different probability ranges were obtained. The boundary that was most appropriate with the simulation result was selected and defined as the well-matched void boundary. Based on this method, the morphologies of voids that formed at different gas velocities were simulated and compared. The method can help us to express the morphological characteristics of the dynamically stable voids in a numerical simulation.

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