The paper concerns the elimination of a set of variables from a system of linear inequalities. We employ the widely used Fourier–Motzkin elimination method extended with the Chernikov rules. A straightforward implementation of the algorithm results in extensive enumeration during the most computationally demanding stage. We propose a new way of checking Chernikov rules using bit pattern trees as an accelerating data structure to avoid extensive enumeration. The bit pattern tree is a data structure based on k-d tree used to accelerate the double description method. First we describe an adaptation of that approach to check the second Chernikov rule in Fourier–Motzkin elimination. We also propose a new algorithm that employs bit pattern trees to accelerate both Chernikov rules. Presented results of computational evaluation prove competitiveness of the proposed algorithms.

本文涉及从线性不等式系统中消除一组变量。我们采用切尔尼科夫规则扩展的，广泛使用的傅里叶-莫茨金消除方法。该算法的直接实现会导致在计算要求最高的阶段进行大量枚举。我们提出了一种使用位模式树作为加速数据结构来检查Chernikov规则的新方法，以避免进行大量枚举。位模式树是基于k的数据结构-d树用于加速双重描述方法。首先，我们描述该方法的一种适应方法，以检查傅立叶-莫兹金消除算法中的第二切尔尼科夫规则。我们还提出了一种新的算法，该算法采用位模式树来加速两个Chernikov规则。提出的计算评估结果证明了所提算法的竞争力。