当前位置: X-MOL 学术Random Struct. Algorithms › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Randomized greedy algorithm for independent sets in regular uniform hypergraphs with large girth
Random Structures and Algorithms ( IF 1 ) Pub Date : 2021-01-19 , DOI: 10.1002/rsa.20994
Jiaxi Nie 1 , Jacques Verstraëte 1
Affiliation  

In this paper, we consider a randomized greedy algorithm for independent sets in r-uniform d-regular hypergraphs G on n vertices with girth g. By analyzing the expected size of the independent sets generated by this algorithm, we show that urn:x-wiley:rsa:media:rsa20994:rsa20994-math-0001, where urn:x-wiley:rsa:media:rsa20994:rsa20994-math-0002 converges to 0 as g →  for fixed d and r, and f(d, r) is determined by a differential equation. This extends earlier results of Garmarnik and Goldberg for graphs [8]. We also prove that when applying this algorithm to uniform linear hypergraphs with bounded degree, the size of the independent sets generated by this algorithm concentrate around the mean asymptotically almost surely.

中文翻译:

大周长规则均匀超图中独立集的随机贪婪算法

在本文中,我们考虑了一种随机贪婪算法,用于在周长为g 的n个顶点上的r均匀d正则超图G 中的独立集合。通过分析由该算法产生的独立组的预期大小,我们表明,其中收敛到0 →交通 固定d- [R ,和˚Fd,  - [Rurn:x-wiley:rsa:media:rsa20994:rsa20994-math-0001urn:x-wiley:rsa:media:rsa20994:rsa20994-math-0002) 由微分方程确定。这扩展了 Garmarnik 和 Goldberg 早期的图形结果 [8]。我们还证明,当将该算法应用于具有有界度的均匀线性超图时,该算法生成的独立集的大小几乎可以肯定地渐近地集中在均值附近。
更新日期:2021-01-19
down
wechat
bug