AI 中文总结
该研究针对带颜色约束的组合优化问题，提出平均情形模型，通过限制结构中红色边数量，分析其对最小代价生成树、最短路径等四类问题最小代价的影响。
AI 中文摘要
我们提出了带颜色约束的组合优化经典问题的平均情形模型。所有情形中，我们都要寻找完全图的某个（生成）子结构，使其代价最小；边被随机染为红色或蓝色，我们对结构中允许的红色边数量设置了一个界限，该界限在高概率下会低于无区分时的情况。我们研究这种偏向对所需结构最小代价的影响，考虑了最小代价生成树、最短路径、最小代价完美匹配以及非对称旅行商问题。
英文摘要
We present an average case model of classical problems in combinatorial optimization where there are color constraints. In all cases we seek some (spanning) sub-structure of a complete graph of minimum cost. The edges are randomly colored either red or blue. We bias against the red edges by placing a bound on the number of them that are allowed in our structure. This bound will be lower w.h.p. than what would occur without discrimination. We examine the effect of this bias on the minimum cost of a desired structure. We consider minimum cost spanning trees, shortest paths, minimum cost perfect matchings and the asymmetric traveling salesperson problem.
