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一些与信息学相关的实际问题。我们在两篇即将发表的论文中提出了为现代分组密码生成替换框的有效算法。在一篇发表的论文中，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。在化学信息学方面，我们提出了一种基于人工神经网络和整数线性规划来推断具有给定性质的化学图的模型，并发表了三篇论文。然后，我们提出了基于动态规划的算法来计数并生成具有给定循环等级的树状图。最后，我们基于所提出的算法来描述成对兼容性图，以有效地枚举这些图。

项目成果

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

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

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

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

A novel method for the inverse QSAR/QSPR based on artificial neural networks and mixed integer linear programming with guaranteed admissibility

基于人工神经网络和混合整数线性规划的保证可接受性的逆QSAR/QSPR新方法

• 发表时间: 2019
• 作者: Masaki Waga;Eienne Andre;Atsuko ITOKAZU;Rachaya Chiewvanichakorn
• 通讯作者: Rachaya Chiewvanichakorn