Discrete Mathematics and its Applications

离散数学及其应用

• 批准号: 18J23484
• 负责人: AZAM NAVEED AHMED
• 金额: $ 1.79万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2018
• 资助国家: 日本
• 起止时间: 2018-04-25 至 2021-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18J23484/
• 关键词: Subsitution box; Elliptic curve; Image encryption; PCG; Chemical graphs; Linear programming; Neural networks; Graph enumeration; Substitution box

We developed efficient algorithms to solve some practical problems related to informatics. We proposed efficient algorithms to generate a substitution box for modern block ciphers in two papers accepted to be published. In a published paper, we proposed a new fast and efficient image encryption scheme that is independent of point computation over elliptic curves. In chemi-informatics, we proposed a model to infer chemical graphs with given property based on artificial neural network and integer linear programming and produced three papers. Then, we proposed algorithms based on dynamic programming to count and generate tree-like graphs with a given cycle rank. Finally, we characterized pairwise compatibility graphs based on which proposed algorithms to enumerate these graphs efficiently.

我们开发了有效的算法来解决与信息学有关的一些实际问题。我们提出了有效的算法，以在接受发表的两篇论文中为现代块密码生成一个替代盒。在发表的论文中，我们提出了一种新的快速有效的图像加密方案，该方案独立于椭圆曲线上的点计算。在化学信息学中，我们提出了一个模型，以基于人工神经网络和整数线性编程来推断具有给定特性的化学图，并产生了三篇论文。然后，我们根据动态编程提出了算法，以计数并生成具有给定周期等级的树状图。最后，我们根据提出的算法有效地枚举这些图表来表征成对兼容图。

项目成果

Enumerating all pairwise compatibility graphs with a given number of vertices using linear programming

使用线性规划枚举具有给定数量顶点的所有成对兼容性图

• 发表时间: 2019
• 作者: Masaki Waga;Ichiro Hasuo;Kohei Suenaga;糸数温子;Naveed Ahmed Azam
• 通讯作者: Naveed Ahmed Azam

An Improved Integer Programming Formulation for Inferring Chemical Compounds with Prescribed Topological Structures

一种改进的整数规划公式，用于推断具有指定拓扑结构的化合物

• 发表时间: 2021
• 作者: J. Zhu;N. A. Azam;K. Haraguchi;L. Zhao;H. Nagamochi;T. Akutsu
• 通讯作者: T. Akutsu

Counting tree-like graphs with a given number of vertices and self-loops

计算具有给定数量的顶点和自循环的树状图

• 发表时间: 2019
• 作者: Masaki Waga;Etienne Andre;Atsuko ITOKAZU;Naveed Ahmed Azam
• 通讯作者: Naveed Ahmed Azam

Experimental results of a dynamic programming algorithm for generating chemical isomers based on frequency vectors

基于频率向量生成化学异构体的动态规划算法的实验结果

• 发表时间: 2020
• 作者: Naveed Ahmed Azam;Jianshen Zhu;Ryota Ido;Hiroshi Nagamochi,Tatsuya Akutsu
• 通讯作者: Hiroshi Nagamochi,Tatsuya Akutsu

On the enumeration of minimal non-pairwise compatibility graphs

• DOI: 10.1007/s10878-021-00799-x
• 发表时间: 2021-09-01
• 期刊: JOURNAL OF COMBINATORIAL OPTIMIZATION
• 影响因子: 1
• 作者: Azam，Naveed Ahmed;Shurbevski，Aleksandar;Nagamochi，Hiroshi
• 通讯作者: Nagamochi，Hiroshi