A Sampling-Based Method to Estimate the Volume of Solution Space for Linear Arithmetic Constraints
作者机构：KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences School of Mathematical Sciences Jiangsu University
出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报(英文版))
年 卷 期：2024年
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：supported by the National Natural Science Foundation of China under Grant Nos.12101267 and 12271516 the funding for scientific research startup of Jiangsu University under Grant No.19JDG035
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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