scholarly journals Recursively Divided Pancake Graphs with a Small Network Cost

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 844
Author(s):  
Jung-Hyun Seo ◽  
Hyeong-Ok Lee
Keyword(s):  
Computer Science ◽  
Sorting Algorithm ◽  
Topological Properties ◽  
Signed Permutation ◽  
Permutation Graphs ◽  
Sorting Problem ◽  
Network Cost

Graphs are often used as models to solve problems in computer science, mathematics, and biology. A pancake sorting problem is modeled using a pancake graph whose classes include burnt pancake graphs, signed permutation graphs, and restricted pancake graphs. The network cost is degree × diameter. Finding a graph with a small network cost is like finding a good sorting algorithm. We propose a novel recursively divided pancake (RDP) graph that has a smaller network cost than other pancake-like graphs. In the pancake graph Pn, the number of nodes is n!, the degree is n − 1, and the network cost is O(n2). In an RDPn, the number of nodes is n!, the degree is 2log2n − 1, and the network cost is O(n(log2n)3). Because O(n(log2n)3) < O(n2), the RDP is superior to other pancake-like graphs. In this paper, we propose an RDPn and analyze its basic topological properties. Second, we show that the RDPn is recursive and symmetric. Third, a sorting algorithm is proposed, and the degree and diameter are derived. Finally, the network cost is compared between the RDP graph and other classes of pancake graphs.

scholarly journals Design and Analysis of a Symmetric Log Star Graph with a Smaller Network Cost Than Star Graphs

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 981
Author(s):  
Jung-Hyun Seo ◽  
Hyeong-Ok Lee
Keyword(s):  
Parallel Computing ◽  
Computer Science ◽  
Regular Graph ◽  
Connected Graph ◽  
Routing Algorithm ◽  
Star Graph ◽  
Topological Properties ◽  
Star Graphs ◽  
Network Cost ◽  
Network Costs

Graphs are used as models to solve problems in fields such as mathematics, computer science, physics, and chemistry. In particular, torus, hypercube, and star graphs are popular when modeling the connection structure of processors in parallel computing because they are symmetric and have a low network cost. Whereas a hypercube has a substantially smaller diameter than a torus, star graphs have been presented as an alternative to hypercubes because of their lower network cost. We propose a novel log star (LS) that is symmetric and has a lower network cost than a star graph. The LS is an undirected, recursive, and regular graph. In LSn, the number of nodes is n! while the degree is 2log2n − 1 and the diameter is 0.5n(log2n)2 + 0.75nlog2n. In this study, we analyze the basic topological properties of LS. We prove that LSn is a symmetrical connected graph and analyzed its subgraph characteristics. Then, we propose a routing algorithm and derive the diameter and network cost. Finally, the network costs of the LS and star graph-like networks are compared.

scholarly journals AVERAGE-CASE ANALYSIS OF PERFECT SORTING BY REVERSALS

2011 ◽  
Vol 03 (03) ◽  
pp. 369-392 ◽  
Author(s):  
MATHILDE BOUVEL ◽  
CEDRIC CHAUVE ◽  
MARNI MISHNA ◽  
DOMINIQUE ROSSIN
Keyword(s):  
Average Length ◽  
Algorithm Analysis ◽  
Sorting Algorithm ◽  
Average Case Analysis ◽  
Signed Permutation ◽  
Average Case ◽  
Combinatorial Properties ◽  
Sorting By Reversals ◽  
Identity Permutation ◽  
Interval Trees

Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any common interval. Bérard et al. (2007) make use of strong interval trees to describe an algorithm for sorting signed permutations by reversals. Combinatorial properties of this family of trees are essential to the algorithm analysis. Here, we use the expected value of certain tree parameters to prove that the average run-time of the algorithm is at worst, polynomial, and additionally, for sufficiently long permutations, the sorting algorithm runs in polynomial time with probability one. Furthermore, our analysis of the subclass of commuting scenarios yields precise results on the average length of a reversal, and the average number of reversals.

scholarly journals Large-Scale Storage/Retrieval Requests Sorting Algorithm for Multi-I/O Depots Automated Storage/Retrieval Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yu Bo Song ◽  
Hai Bo Mu
Keyword(s):  
Large Scale ◽  
Special Kind ◽  
Minimum Cost ◽  
Sorting Algorithm ◽  
Optimal Sequence ◽  
Sorting Problem ◽  
Retrieval Systems ◽  
Multiple Input ◽  
Sorting Process ◽  
Automated Storage

This paper addresses the sequence sorting problem of large-scale storage/retrieval (S/R) requests in multiple Input/Output (multi-I/O) depots automated storage/retrieval systems (AS/RS), in which the cargoes can enter/leave the system through multi-I/O depots, the stacker can load only one cargo, and the load travel time of stacker is fixed. The problem is to find an optimal sequence for a certain S/R requests sequence, and it is a special kind of traveling salesman problem. In this paper, a heuristic algorithm based on assignment is proposed. In order to eliminate the subloops emerged in the sorting process, the equivalent merging and minimum cost merging methods of subloops are considered, and the proposed algorithm is modified. Experimental results indicate the effectiveness of the proposed algorithm.

Four-Layer Grapheme Model for Computational Paleography

2016 ◽  
Vol 9 (4) ◽  
pp. 64-82 ◽  
Author(s):  
Raymond E.I. Pardede ◽  
Loránd L. Tóth ◽  
György A. Jeney ◽  
Ferenc Kovács ◽  
Gábor Hosszú
Keyword(s):  
Mathematical Model ◽  
Computer Science ◽  
Supervised Learning ◽  
Logical Relation ◽  
Learning Method ◽  
Topological Properties ◽  
Logical Relationship ◽  
Visual Identity ◽  
Applied Computer Science ◽  
Semantic Layer

This article proposes a novel mathematical model of logical relationship among glyphs belonging to the same grapheme. Its research belongs to the computational paleography that is a field in the applied computer science. The proposed grapheme model is presented in four logical layers from bottom to up namely as Topology, Visual Identity, Phonetic, and Semantic Layer. In the Topology Layer, a unique glyph is defined by a set of topological properties. When trying to describe the logical relation of various glyphs, their topological properties must be examined in a higher layer framework so called Visual Identity Layer. In that layer, the glyphs of a single grapheme share some topological attributes in common. These common topological attributes form a main identity of a grapheme, which is called Common Identity template that is obtained by means of Supervised Learning method. The Phonetic Layer gives the sound values associated to the grapheme, and the Semantic Layer describes the usage of the grapheme in texts. Some potential implementations of the grapheme model are also presented.

A CONSTANT TIME SORTING ALGORITHM FOR A THREE DIMENSIONAL RECONFIGURABLE MESH AND RECONFIGURABLE NETWORK

1995 ◽  
Vol 05 (03) ◽  
pp. 401-412 ◽  
Author(s):  
MARK S. MERRY ◽  
JOHNNIE BAKER
Keyword(s):  
Computer Science ◽  
Real Number ◽  
Three Dimensional ◽  
Time Algorithm ◽  
Constant Time ◽  
Sorting Algorithm ◽  
Compression Algorithms ◽  
Reconfigurable Mesh ◽  
Integer Sorting ◽  
Time Selection

Sorting techniques have numerous applications in computer science. Current real number and integer sorting techniques for the reconfigurable mesh operate in constant time using a reconfigurable mesh of size n × n to sort n numbers. This paper presents a constant time algorithm to sort n items on a reconfigurable network with [Formula: see text] switches and [Formula: see text] processors. Also, new constant time selection and compression algorithms are given. All results may also be implemented on the 3-D reconfigurable mesh.

Algorithm for TDOA Sorting Based on Clustering

2014 ◽  
Vol 1049-1050 ◽  
pp. 1308-1311 ◽  
Author(s):  
Ting Jun Li ◽  
You Ming Liu ◽  
Zhi Yu Che ◽  
Chang Wen Qu ◽  
Yang Zhang
Keyword(s):  
Detection System ◽  
Time Difference ◽  
Sorting Algorithm ◽  
Histogram Method ◽  
One Dimensional ◽  
Pulse Trains ◽  
Passive Detection ◽  
Sorting Problem ◽  
Key Technologies ◽  
Grid Division

Correctly sorting the staggered pulse trains each station received is one of the key technologies in the location effect of multi-station time difference passive detection system. According to the problem of straight grid division and the difficulty in sorting two emitters with the same one-dimensional time difference in the histogram method, a time difference sorting algorithm based on natural clustering is proposed. Simulation results show that the algorithm can overcome the defects of histogram method above, and solve the pulse miss-sorting problem, offering better sorting results.

scholarly journals A New Characterization of Tree Medians with Applications to Distributed Algorithms

1991 ◽  
Vol 20 (364) ◽  
Author(s):  
O. Gerstel ◽  
Shmuel Zaks
Keyword(s):  
Lower Bound ◽  
Sorting Algorithm ◽  
Message Complexity ◽  
Ranking Problem ◽  
Worst Case ◽  
Sorting Problem ◽  
Vertex Set ◽  
Pass Through ◽  
Case Number

A new characterization of tree medians is presented: we show that a vertex <em>m</em> is a median of a tree <em>T</em> with <em>n</em> vertices iff there exists a partition of the vertex set into [<em>n</em>/2] disjoint pairs (excluding m when <em>n</em> is odd), such that all the paths connecting the two vertices in any of the pairs pass through <em>m</em>. We show that in this case this sum is the largest possible among all such partitions, and we use this fact to discuss lower bounds on the message complexity of the distributed sorting problem. This lower bound implies that, given a network of a tree topology, choosing a median and then route all the information through it is the best possible strategy, in terms of worst-case number of messages sent during any execution of any distributed sorting algorithm. We also discuss the implications for networks of a general topology and for the distributed ranking problem.

scholarly journals Comparison of sort algorithms in Hadoop and PCJ

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Marek Nowicki
Keyword(s):  
Parallel Computing ◽  
Computer Science ◽  
Wide Spectrum ◽  
Performance Comparison ◽  
Sorting Algorithm ◽  
Address Space ◽  
Partitioned Global Address Space ◽  
Apache Hadoop ◽  
Sorting Algorithms ◽  
Application Codes

AbstractSorting algorithms are among the most commonly used algorithms in computer science and modern software. Having efficient implementation of sorting is necessary for a wide spectrum of scientific applications. This paper describes the sorting algorithm written using the partitioned global address space (PGAS) model, implemented using the Parallel Computing in Java (PCJ) library. The iterative implementation description is used to outline the possible performance issues and provide means to resolve them. The key idea of the implementation is to have an efficient building block that can be easily integrated into many application codes. This paper also presents the performance comparison of the PCJ implementation with the MapReduce approach, using Apache Hadoop TeraSort implementation. The comparison serves to show that the performance of the implementation is good enough, as the PCJ implementation shows similar efficiency to the Hadoop implementation.

Electron Microscopy of Nucleic Acids

1974 ◽  
Vol 32 ◽  
pp. 302-303
Author(s):  
Norman Davidson
Keyword(s):  
Electron Microscopy ◽  
Nucleic Acids ◽  
Basic Protein ◽  
Molecular Biologist ◽  
Topological Properties ◽  
Protein Film ◽  
Polynucleotide Chain

The basic protein film technique for mounting nucleic acids for electron microscopy has proven to be a general and powerful tool for the working molecular biologist in characterizing different nucleic acids. It i s possible to measure molecular lengths of duplex and single-stranded DNAs and RNAs. In particular, it is thus possible to as certain whether or not the nucleic acids extracted from a particular source are or are not homogeneous in length. The topological properties of the polynucleotide chain (linear or circular, relaxed or supercoiled circles, interlocked circles, etc. ) can also be as certained.

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