对于具有Toeplitz结构的Robinson矩阵，二次指派问题是一个简单的问题
The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure
摘要：
本文给出了Koopmans-Beckman形式$QAP(A,B)$的二次指派问题的一个新的多项式可解情形，证明了当$A$和$B$分别是Robinson相似和相异矩阵，且$A$或$B$之一是Toeplitz矩阵时，单位置换是最优的. Robinson相似矩阵是一个对称矩阵，它的元素沿行和列从对角线方向单调递减，这种矩阵出现在经典的序列化问题中。
英文摘要：
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form $QAP(A,B)$, by showing that the identity permutation is optimal when $A$ and $B$ are respectively a Robinson similarity and dissimilarity matrix and one of $A$ or $B$ is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along rows and columns when moving away from the diagonal, and such matrices arise in the classical seriation problem.
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。
