摘要： 利用制服型号数有限这一特征，对制服调换(UE)问题和以物易物的制服调换(BUE)问题各给出一个快速的线性时间算法。在常量阶有向图上，将BUE转化为一个顶点容量约束的整值最大环流问题，提出其整数线性规划表示，论证其可行域的整性。证明BUE的最优解必为对应UE的一个最优解子图。实验结果表明，UE和BUE的渐进最优值相同。

关键词: 制服调换, 路圈子图, 圈包装, 环流, 线性规划松弛

Abstract: Utilizing the finiteness of the uniform type number, this paper presents faster linear time algorithms for the Uniform Exchange(UE) problem and the Barter Uniform Exchange(BUE) problem. BUE is Transfered into a vertex constraint integer value maximum circulation problem on a constant order digraph, and the integrality of the feasible region of BUE’s integer linear programming formulation is proved. It is demonstrated that any optimal solution to BUE must be a subgraph of some optimal solution to the corresponding UE, and experimental results show that the two problems share a same asymptotical optimal values.

Key words: Uniform Exchange(UE), path-cycle subgraph, cycle packing, circulation, linear programming relaxation

中图分类号: 

• TP39