Circlet不等式：TSP的一个新的基于循环的面定义不等式
The Circlet Inequalities: A New, Circulant-Based Facet-Defining Inequality for the TSP
摘要：
对称流动推销员问题（TSP）多面体的面定义不等式在多面体TSP研究和最新的TSP求解器中都起着重要的作用。本文引入了一类新的定义面的不等式--\emph{circlet inequalities} .这些不等式在Gutekunst和Williamson \cite{Gut19b}研究循环TSP时首次提出，它们在多面体TSP研究和哈密顿圈的数论研究之间架起了一座桥梁，该研究源于Marco Buratti在2017年提出的一个猜想。圆环不等式表现出循环对称性放置在一个给定的长度的所有边缘相同的重量，我们的主要证明利用这种对称性来证明圆环不等式的有效性。然后，我们表明，圆环不等式的小面定义和计算其强度以下Goemans \cite{Goe95b}，他们实现了相同的最坏情况下的强度类似循环冠Naddef和Rinaldi不等式\cite{Nad92}，但一般更强。
英文摘要：
Facet-defining inequalities of the symmetric Traveling Salesman Problem (TSP) polytope play a prominent role in both polyhedral TSP research and state-of-the-art TSP solvers. In this paper, we introduce a new class of facet-defining inequalities, the \emph{circlet inequalities}. These inequalities were first conjectured in Gutekunst and Williamson \cite{Gut19b} when studying Circulant TSP, and they provide a bridge between polyhedral TSP research and number-theoretic investigations of Hamiltonian cycles stemming from a conjecture due to Marco Buratti in 2017. The circlet inequalities exhibit circulant symmetry by placing the same weight on all edges of a given length; our main proof exploits this symmetry to prove the validity of the circlet inequalities. We then show that the circlet inequalities are facet-defining and compute their strength following Goemans \cite{Goe95b}; they achieve the same worst-case strength as the similarly circulant crown inequalities of Naddef and Rinaldi \cite{Nad92}, but are generally stronger.
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