Pub Date : 2023-05-05DOI: 10.48550/arXiv.2305.03381
Josefine Foos, S. Held, Yannik Kyle Dustin Spitzley
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.
{"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}
Pub Date : 2023-05-04DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.30
J. Lengler, A. Martinsson, Kalina Petrova, P. Schnider, R. Steiner, Simon Weber, E. Welzl
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.
{"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}
Pub Date : 2023-05-03DOI: 10.48550/arXiv.2305.01942
L. Lau, Robert Wang, Hong Zhou
We consider a general $p$-norm objective for experimental design problems that captures some well-studied objectives (D/A/E-design) as special cases. We prove that a randomized local search approach provides a unified algorithm to solve this problem for all $p$. This provides the first approximation algorithm for the general $p$-norm objective, and a nice interpolation of the best known bounds of the special cases.
对于实验设计问题，我们考虑一个通用的p规范目标，它捕获了一些经过充分研究的目标(D/ a / e设计)作为特殊情况。我们证明了一种随机局部搜索方法提供了一种统一的算法来解决所有p的问题。这为一般的$p$范数目标提供了第一个近似算法，并很好地插值了特殊情况的已知边界。
{"title":"Experimental Design for Any p-Norm","authors":"L. Lau, Robert Wang, Hong Zhou","doi":"10.48550/arXiv.2305.01942","DOIUrl":"https://doi.org/10.48550/arXiv.2305.01942","url":null,"abstract":"We consider a general $p$-norm objective for experimental design problems that captures some well-studied objectives (D/A/E-design) as special cases. We prove that a randomized local search approach provides a unified algorithm to solve this problem for all $p$. This provides the first approximation algorithm for the general $p$-norm objective, and a nice interpolation of the best known bounds of the special cases.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"2015 1","pages":"4:1-4:21"},"PeriodicalIF":1.8,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73318940","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}
Pub Date : 2023-04-26DOI: 10.1142/s2010324723400106
A. Makarov, E. Shalygina
{"title":"Investigating the impact of temperature on magnetic-field behavior of thin-film three-layer systems Co/Cu/Co and Co/Gd/Co","authors":"A. Makarov, E. Shalygina","doi":"10.1142/s2010324723400106","DOIUrl":"https://doi.org/10.1142/s2010324723400106","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47136522","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}
Pub Date : 2023-04-26DOI: 10.1142/s2010324723500157
Motahareh BahmanAbadi, Abdolah Amirany, M. H. Moaiyeri, K. Jafari
{"title":"Towards Nonvolatile Spintronic Quaternary Flip-Flop and Register Design","authors":"Motahareh BahmanAbadi, Abdolah Amirany, M. H. Moaiyeri, K. Jafari","doi":"10.1142/s2010324723500157","DOIUrl":"https://doi.org/10.1142/s2010324723500157","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43932035","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}
Pub Date : 2023-04-21DOI: 10.1142/s201032472340009x
Y. A. Qahoom, R. Aharrouch, K. E. Kihel, M. Madani, N. Hachem, M. E. Bouziani
{"title":"Critical and Compensation Behaviors of a Ferrimagnetic Multilayer System","authors":"Y. A. Qahoom, R. Aharrouch, K. E. Kihel, M. Madani, N. Hachem, M. E. Bouziani","doi":"10.1142/s201032472340009x","DOIUrl":"https://doi.org/10.1142/s201032472340009x","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44414446","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}
Pub Date : 2023-04-07DOI: 10.1142/s2010324723400088
S. Bharadwaj, Y. Kalyana Lakshmi, K. Ramya, Ch. Venkata Koti Reddy, S. Pola
{"title":"A Study of Magnetic and Dielectric Properties for iron ion Variation in Cobalt Ferrite","authors":"S. Bharadwaj, Y. Kalyana Lakshmi, K. Ramya, Ch. Venkata Koti Reddy, S. Pola","doi":"10.1142/s2010324723400088","DOIUrl":"https://doi.org/10.1142/s2010324723400088","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43111593","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}
Pub Date : 2023-03-31DOI: 10.1142/s2010324723920017
L. S. Ferreira, L. N. Jorge, C. DaSilva, Minos A. Neto, A. A. Caparica
{"title":"Erratum: Unveiling Phase Transitions in 1D Systems with Short-Range Interactions","authors":"L. S. Ferreira, L. N. Jorge, C. DaSilva, Minos A. Neto, A. A. Caparica","doi":"10.1142/s2010324723920017","DOIUrl":"https://doi.org/10.1142/s2010324723920017","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44275196","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}
Pub Date : 2023-03-31DOI: 10.1142/s2010324723400076
{"title":"High Curie temperature in epitaxial D022-Mn3-xGa ultrathin films","authors":"","doi":"10.1142/s2010324723400076","DOIUrl":"https://doi.org/10.1142/s2010324723400076","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46897828","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}
Pub Date : 2023-03-23DOI: 10.1142/s2010324723500145
H. Bouchama, N. Benayad, M. Djermouni, S. Kacimi, A. Zaoui
{"title":"Oxygen nonstoichiometry as a source of ferromagnetism in GdCoO3: first-principle investigation","authors":"H. Bouchama, N. Benayad, M. Djermouni, S. Kacimi, A. Zaoui","doi":"10.1142/s2010324723500145","DOIUrl":"https://doi.org/10.1142/s2010324723500145","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49386044","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}
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