On an Algorithm of Frieze

球形饰带

Spherical friezes

本文解决球面距离几何中从 $O(n)$ 个测量值恢复 2-球面上 $n$ 元点组的基本问题，提出仅用四则运算的递归算法，并将输出数据排列成具有滑动对称性和 Laurent 现象的新型饰带模式。

多维Farey求和算法的几何与带状图案

Geometry of multidimensional Farey summation algorithm and frieze patterns

该研究提出高维减法连分数算法的新几何方法，引入推广Klein多面体的Farey多面体及其帆，用棱柱图分类，得到多维Conway-Coxeter带状图案并证明其满足推广托勒密关系。

H-admissible permutations and the HCP

This version is similar to math.CO/0210113. We've changed Conjectures 1.1 and 1.2 so that they cover arbitrary graphs(digraphs). Let G be an arbitrary graph(digraph). Then - in polynomial time - either an algorithm obtains a hamilton circuit(cycle)or else the algorithm points to at least one vertex that cannot belong to any hamilton circuit(cycle) of G. We give criteria for determining which vertices should be examined.

A fast new algorithm for weak graph regularity

We provide a deterministic algorithm that finds, in $ε^{-O(1)} n^2$ time, an $ε$-regular Frieze-Kannan partition of a graph on $n$ vertices. The algorithm outputs an approximation of a given graph as a weighted sum of $ε^{-O(1)}$ many complete bipartite graphs. As a corollary, we give a deterministic algorithm for estimating the number of copies of $H$ in an $n$-vertex graph $G$ up to an additive error of at most $εn^{v(H)}$, in time $ε^{-O_H(1)}n^2$.

Finding tight Hamilton cycles in random hypergraphs faster

In an $r$-uniform hypergraph on $n$ vertices a tight Hamilton cycle consists of $n$ edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of $r$ vertices. We provide a first deterministic polynomial time algorithm, which finds a.a.s. tight Hamilton cycles in random $r$-uniform hypergraphs with edge probability at least $C \log^3n/n$. Our result partially answers a question of Dudek and Frieze [Random Structures & Algorithms 42 (2013), 374-385] who proved that tight Hamilton cycles exists already for $p=ω(1/n)$ for $r=3$ and $p=(e + o(…

可积阿拉克-格林函数在度量图上的计算

Computation of Admissible Arakelov-Green Functions on Metrized Graphs

本文提出一种算法，用于计算度量图上的可积阿拉克-格林函数，扩展了Cinkir的公式，并通过实例展示了算法的实现。