Exact expectations for random graphs and assignments

周期为2的山谷分配在2×2k地图上的精确标记层序分类

Exact Labelled Layer-Order Classification for Period-2 Mountain--Valley Assignments on 2 x 2k Maps

本文分类了周期为2的山谷分配下2×2k地图的标记层序，给出可实现枢轴对的充要条件及状态计数，并单独处理k=1的特殊情形。

关于多样化稳定匹配的研究

On diversifying stable assignments

本研究针对带边容量与顶点配额、偏好由多样化选择函数定义的稳定匹配问题，证明其任意输入均存在唯一稳定匹配，并提出了求解的多项式时间算法。

Exact and heuristic solutions for the assembly line balancing problem with hierarchical worker assignment

This paper proposes new algorithms for the assembly line balancing problem with hierarchical worker assignment (ALBHW). The ALBHW appears in real industrial contexts where companies deal with a multi-skilled workforce. It considers task execution times that vary depending on the worker type to whom the task is assigned. Qualification levels among workers are ranked hierarchically, where a lower qualified worker costs less but requires larger execution times. The aim is to assign workers and tasks to the stations of an assembly line, in such a way that cycle time and precedence constraints are …

具有恰好k个解的CNF和DNF

CNFs and DNFs with Exactly $k$ Solutions

研究确定构造具有恰好k个满足赋值的DNF或CNF所需的最小术语或子句数，提出上界和下界，改进了模型计数算法的效率。

非线性 Hamilton 圈的精确阈值与极限分布

Exact threshold and limiting distribution for non-linear Hamilton cycles

本文研究 Erdős–Rényi 随机超图中 Hamilton $\ell$-圈数量的极限行为，按 $\ell\geq3$ 与 $\ell=2$ 给出集中、Poisson、对数正态及混合分布，并确定非线性 Hamilton 圈的精确出现阈值。

一种Θ(m^9)的三元最小成本网络流LP模型用于分配问题的多面体及其在难解组合优化问题中的应用

A Θ(m^9) ternary minimum-cost network flow LP model of the Assignment Problem polytope with applications to hard combinatorial optimization problems

本文提出一种大规模三元网络流LP模型，用于将NP难问题转化为多项式规模的线性规划问题，通过简单变换成本函数，实现精确求解，适用于物流等实际应用。