Allowed Boundary Sequences for Fused Polycyclic Patches and Related Algorithmic Problems

2001 ◽  
Vol 41 (2) ◽  
pp. 300-308 ◽  
Author(s):  
Michel Deza ◽  
Patrick W. Fowler ◽  
Viatcheslav Grishukhin
Keyword(s):  
Algorithmic Problems

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

scholarly journals Conjugacy Problem in the Fundamental Groups of High-Dimensional Graph Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1330
Author(s):  
Raeyong Kim
Keyword(s):  
Group Structure ◽  
Conjugacy Problem ◽  
High Dimensional ◽  
Fundamental Groups ◽  
Graph Manifold ◽  
Solvable Word Problem ◽  
Algorithmic Problems ◽  
Graph Manifolds ◽  
Dimensional Graph ◽  
Solvable Word

The conjugacy problem for a group G is one of the important algorithmic problems deciding whether or not two elements in G are conjugate to each other. In this paper, we analyze the graph of group structure for the fundamental group of a high-dimensional graph manifold and study the conjugacy problem. We also provide a new proof for the solvable word problem.

Some algorithmic problems of plotting codes for unstructured grids

1989 ◽  
Author(s):  
RAINALD LOEHNER ◽  
PARESH PARIKH ◽  
CLYDE GUMBERT
Keyword(s):  
Unstructured Grids ◽  
Algorithmic Problems

Aqueous Solutions of Algorithmic Problems: Emphasizing Knights on a 3 × 3

2002 ◽  
pp. 191-202 ◽  
Author(s):  
Tom Head ◽  
Xia Chen ◽  
Matthew J. Nichols ◽  
Masayuki Yamamura ◽  
Susannah Gal
Keyword(s):  
Aqueous Solutions ◽  
Algorithmic Problems

scholarly journals Daisy: Data analysis integrated software system for X-ray experiments

2021 ◽  
Vol 251 ◽  
pp. 04020
Author(s):  
Yu Hu ◽  
Ling Li ◽  
Haolai Tian ◽  
Zhibing Liu ◽  
Qiulan Huang ◽  
...  
Keyword(s):  
Data Analysis ◽  
High Energy ◽  
Software System ◽  
Energy Photon ◽  
X Ray ◽  
High Throughput Data ◽  
Extensive Range ◽  
Algorithmic Problems ◽  
Integrated Software ◽  
Photon Source

Daisy (Data Analysis Integrated Software System) has been designed for the analysis and visualisation of X-ray experiments. To address the requirements of the Chinese radiation facilities community, spanning an extensive range from purely algorithmic problems to scientific computing infrastructure, Daisy sets up a cloud-native platform to support on-site data analysis services with fast feedback and interaction. Furthermore, the plug-in based application is convenient to process the expected high throughput data flow in parallel at next-generation facilities such as the High Energy Photon Source (HEPS). The objectives, functionality and architecture of Daisy are described in this article.

scholarly journals Ranking top-k trees in tree-based phylogenetic networks

2019 ◽  
Author(s):  
Momoko Hayamizu ◽  
Kazuhisa Makino
Keyword(s):  
Optimal Algorithm ◽  
Linear Time ◽  
Fundamental Problem ◽  
Phylogenetic Network ◽  
Reticulate Evolution ◽  
Interesting Property ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Linear Delay ◽  
Algorithmic Problems

Abstract 'Tree-based' phylogenetic networks provide a mathematically-tractable model for representing reticulate evolution in biology. Such networks consist of an underlying 'support tree' together with arcs between the edges of this tree. However, a tree-based network can have several such support trees, and this leads to a variety of algorithmic problems that are relevant to the analysis of biological data. Recently, Hayamizu (arXiv:1811.05849 [math.CO]) proved a structure theorem for tree-based phylogenetic networks and obtained linear-time and linear-delay algorithms for many basic problems on support trees, such as counting, optimisation, and enumeration. In the present paper, we consider the following fundamental problem in statistical data analysis: given a tree-based phylogenetic network $N$ whose arcs are associated with probability, create the top-$k$ support tree ranking for $N$ by their likelihood values. We provide a linear-delay (and hence optimal) algorithm for the problem and thus reveal the interesting property of tree-based phylogenetic networks that ranking top-$k$ support trees is as computationally easy as picking $k$ arbitrary support trees.

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