组合优化中的矩生成函数：二分图匹配
Moment generating functions in combinatorial optimization: Bipartite matching
AI总结：
本文研究了二分图匹配中矩生成函数的性质，提出零点模的猜想，并探讨其在指派问题中的高斯缩放极限意义。
摘要：
在基于指数分布边权的随机最小成本二分图匹配模型中，我们展示了最优解成本分布可以高效计算。该分布由其矩生成函数表示，此模型中该函数始终为有理函数。这些函数的复零点值得关注，因为原点附近缺乏零点表明分布的某种规律性。我们提出一个猜想，即这些矩生成函数的复零点模不会小于其第一个极点。对于最小成本完美匹配，即指派问题，这样的零点自由盘将意味着高斯缩放极限。
英文摘要：
In a random model of minimum cost bipartite matching based on exponentially distributed edge costs, we show that the distribution of the cost of the optimal solution can be computed efficiently. The distribution is represented by its moment generating function, which in this model is always a rational function. The complex zeros of this function are of interest as the lack of zeros near the origin indicates a certain regularity of the distribution. We propose a conjecture according to which these moment generating functions never have complex zeros of smaller modulus than their first pole. For minimum cost perfect matching, also known as the assignment problem, such a zero-free disk would imply a Gaussian scaling limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
