Neighborhood Persistency of the Linear Optimization Relaxation of Integer Linear Optimization
Neighborhood Persistency of the Linear Optimization Relaxation of Integer Linear Optimization
复制标题
线性优化的邻域持续性整数线性优化的松弛
DOI：
10.1007/978-3-031-18530-4_23
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kotaro Nakayama
中科院分区：
文献类型：
--
作者：
Kei Kimura;Kotaro Nakayama
对于整数线性优化（ILO）问题，其线性优化（LO）松弛的持久性是指：对于将整数值赋给某些变量的松弛的每个最优解，存在ILO问题的最优解，其中这些变量保持相同的值。虽然persistence已被用来开发启发式，近似和固定参数的算法，特殊情况下的劳工组织，其适用性仍然未知的文献。本文提出了一个更强的性质--邻域持久性，并证明了单位双变量不等式（UTVPI）系统上的ILO松弛是ILO松弛具有邻域持久性的极大类.我们关于邻域持久性的结果推广了Nemhauser和Trotter，Hochbaum等人，和Fiorini等人，在目标函数和变量均为非负的情况下，UTVPI系统的ILO具有固定参数易处理性和两个可逼近性。
For an integer linear optimization (ILO) problem, persistency of its linear optimization (LO) relaxation is a property that for every optimal solution of the relaxation that assigns integer values to some variables, there exists an optimal solution of the ILO problem in which these variables retain the same values. Although persistency has been used to develop heuristic, approximation, and fixed-parameter algorithms for special cases of ILO, its applicability remains unknown in the literature. In this paper, we propose a stronger property calledneighborhood persistencyand show that the LO relaxation of ILO on unit-two-variable-per-inequality (UTVPI) systems is a maximal class of ILO such that its LO relaxation has (neighborhood) persistency. Our result on neighborhood persistency generalizes the previous results of Nemhauser and Trotter, Hochbaum et al., and Fiorini et al., and implies fixed-parameter tractability and two-approximability for ILO on UTVPI systems where the objective function and the variables are non-negative.