IF 1.8 4区物理与天体物理

Spin Pub Date : 2023-05-05 DOI: 10.48550/arXiv.2305.03381

Josefine Foos, S. Held, Yannik Kyle Dustin Spitzley

{"title":"Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem","authors":"Josefine Foos, S. Held, Yannik Kyle Dustin Spitzley","doi":"10.48550/arXiv.2305.03381","DOIUrl":"https://doi.org/10.48550/arXiv.2305.03381","url":null,"abstract":"Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or telecommunication networks. They are a special case of general cost-distance Steiner trees, where different distance functions are used for total length and path lengths. We improve the best published approximation factor for the uniform cost-distance Steiner tree problem from 2.39 to 2.05. If we can approximate the minimum-length Steiner tree problem arbitrarily well, our algorithm achieves an approximation factor arbitrarily close to $ 1 + frac{1}{sqrt{2}} $. This bound is tight in the following sense. We also prove the gap $ 1 + frac{1}{sqrt{2}} $ between optimum solutions and the lower bound which we and all previous approximation algorithms for this problem use. Similarly to previous approaches, we start with an approximate minimum-length Steiner tree and split it into subtrees that are later re-connected. To improve the approximation factor, we split it into components more carefully, taking the cost structure into account, and we significantly enhance the analysis.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"20 1","pages":"19:1-19:16"},"PeriodicalIF":1.8,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82604709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Connectivity in Random Graph Models with Limited Dependencies 有限依赖随机图模型的连通性

IF 1.8 4区物理与天体物理

Spin Pub Date : 2023-05-04 DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.30

J. Lengler, A. Martinsson, Kalina Petrova, P. Schnider, R. Steiner, Simon Weber, E. Welzl

{"title":"On Connectivity in Random Graph Models with Limited Dependencies","authors":"J. Lengler, A. Martinsson, Kalina Petrova, P. Schnider, R. Steiner, Simon Weber, E. Welzl","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.30","url":null,"abstract":"For any positive edge density $p$, a random graph in the ErdH{o}s-Renyi $G_{n,p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider random graph models in which edges that do not share endpoints are independent while incident edges may be dependent and ask: what is the minimum probability $rho(n)$, such that for any distribution $mathcal{G}$ (in this model) on graphs with $n$ vertices in which each potential edge has a marginal probability of being present at least $rho(n)$, a graph drawn from $mathcal{G}$ is connected with non-zero probability? As it turns out, the condition ``edges that do not share endpoints are independent'' needs to be clarified and the answer to the question above is sensitive to the specification. In fact, we formalize this intuitive description into a strict hierarchy of five independence conditions, which we show to have at least three different behaviors for the threshold $rho(n)$. For each condition, we provide upper and lower bounds for $rho(n)$. In the strongest condition, the coloring model (which includes, e.g., random geometric graphs), we show that $rho(n)rightarrow 2-phiapprox 0.38$ for $nrightarrowinfty$, proving a conjecture by Badakhshian, Falgas-Ravry, and Sharifzadeh. This separates the coloring models from the weaker independence conditions we consider, as there we prove that $rho(n)>0.5-o(n)$. In stark contrast to the coloring model, for our weakest independence condition -- pairwise independence of non-adjacent edges -- we show that $rho(n)$ lies within $O(1/n^2)$ of the threshold $1-2/n$ for completely arbitrary distributions.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"35 1","pages":"30:1-30:22"},"PeriodicalIF":1.8,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72782250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Experimental Design for Any p-Norm 任意p-范数的实验设计

IF 1.8 4区物理与天体物理

Spin Pub Date : 2023-05-03 DOI: 10.48550/arXiv.2305.01942

L. Lau, Robert Wang, Hong Zhou

引用次数: 0

Investigating the impact of temperature on magnetic-field behavior of thin-film three-layer systems Co/Cu/Co and Co/Gd/Co 研究了温度对Co/Cu/Co和Co/Gd/Co薄膜三层体系磁场行为的影响

IF 1.8 4区物理与天体物理

Spin Pub Date : 2023-04-26 DOI: 10.1142/s2010324723400106

A. Makarov, E. Shalygina

引用次数: 0

Towards Nonvolatile Spintronic Quaternary Flip-Flop and Register Design 非易失性自旋电子四进制触发器及寄存器设计