A Sampling-Based Method to Estimate the Volume of Solution Space for Linear Arithmetic Constraints

被引：0
|
作者：
Xie, Yan-Feng [1 ,2 ]
Yuan, Chun-Ming [1 ,2 ]
Jing, Rui-Juan [3 ]
机构：
[1] Chinese Acad Sci, KLMM, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Jiangsu Univ, Sch Math Sci, Zhenjiang 212023, Peoples R China
来源：
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2024年
基金：
中国国家自然科学基金;
关键词：
Linear arithmetic constraints; oblique cones; polytope; volume estimation;
D O I：
10.1007/s11424-024-3425-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The linear arithmetic constraints play important roles in many research fields. Estimating the volume of their solution spaces has specific applications, such as programming verification, linear programming, polyhedral optimization, and so on. In this paper, the authors provide an efficient estimation for the volume of the solution space for linear arithmetic constraints. This method sums up the estimations for volumes of oblique cones centered along randomly generated rays. The error analysis is provided to improve the accuracy.
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收藏
页数：23
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