Neighborhood persistency of the linear optimization relaxation of integer linear optimization
研究了整数线性优化问题的线性规划松弛的持久性，揭示了在单位双变量每不等式系统上该性质成立且是最大的子类，并提出了更强的邻域持久性，用于设计固定参数和2近似算法。
Abstract 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 reveal a maximal subclass of ILO such that its LO relaxation has persistency. Specifically, we show that the LO relaxation of ILO on unit-two-variable-per-inequality (UTVPI) systems has persistency and is (in a certain sense) maximal among such ILO. Our result generalizes the persistency results by Nemhauser and Trotter, Hochbaum et al., and Fiorini et al. Even more, we propose a stronger property called neighborhood persistency and show that the LO relaxation of ILO on UTVPI systems in general has this property. Using this stronger result, we obtain a fixed-parameter algorithm (where the parameter is the optimal value) and another proof of 2-approximability for ILO on UTVPI systems where objective functions and variables are non-negative.