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:
王刚, 骆志刚. 制服调换问题中的路圈子图与圈包装研究[J]. 计算机工程, 2013, 39(4): 305-308.
WANG Gang, JIA Zhi-Gang. Study of Path-cycle Subgraph and Cycle Packing in Uniform Exchange Problem[J]. Computer Engineering, 2013, 39(4): 305-308.