Pub Date : 2023-06-02DOI: 10.1137/1.9781611977585.ch6
Emmett Breen, Renee Mirka, Zichen Wang, David P. Williamson
This paper revisits the 2-approximation algorithm for $k$-MST presented by Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul et al. extend Garg's primal-dual subroutine to improve the approximation ratios for the budgeted prize-collecting traveling salesman and minimum spanning tree problems. We follow their algorithm and analysis to provide a cleaner version of Garg's result. Additionally, we introduce the novel concept of a kernel which allows an easier visualization of the stages of the algorithm and a clearer understanding of the pruning phase. Other notable updates include presenting a linear programming formulation of the $k$-MST problem, including pseudocode, replacing the coloring scheme used by Garg with the simpler concept of neutral sets, and providing an explicit potential function.
{"title":"Revisiting Garg's 2-Approximation Algorithm for the k-MST Problem in Graphs","authors":"Emmett Breen, Renee Mirka, Zichen Wang, David P. Williamson","doi":"10.1137/1.9781611977585.ch6","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch6","url":null,"abstract":"This paper revisits the 2-approximation algorithm for $k$-MST presented by Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul et al. extend Garg's primal-dual subroutine to improve the approximation ratios for the budgeted prize-collecting traveling salesman and minimum spanning tree problems. We follow their algorithm and analysis to provide a cleaner version of Garg's result. Additionally, we introduce the novel concept of a kernel which allows an easier visualization of the stages of the algorithm and a clearer understanding of the pruning phase. Other notable updates include presenting a linear programming formulation of the $k$-MST problem, including pseudocode, replacing the coloring scheme used by Garg with the simpler concept of neutral sets, and providing an explicit potential function.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"9 1","pages":"56-68"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74324869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-10DOI: 10.48550/arXiv.2301.03931
V. Cevher, G. Piliouras, Ryann Sim, Stratis Skoulakis
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent approach of Piliouras et al. in normal form games, our work is based on the fact that the update rule of the Proximal Point method (PP) can be approximated up to accuracy $epsilon$ with only $O(log 1/epsilon)$ additional gradient-calls through the iterations of a contraction map. Then combining the analysis of (PP) method with an error-propagation analysis we establish that the resulting first order method, called Clairvoyant Extra Gradient, admits near-optimal time-average convergence for general domains and last-iterate convergence in the unconstrained case.
本文给出了一种一阶方法，该方法允许凸/凹最小-最大问题的近似最优收敛速率，同时需要简单直观的分析。与Nemirovski的开创性工作和Piliouras等人最近在正常形式游戏中的方法类似，我们的工作是基于这样一个事实，即Proximal Point method (PP)的更新规则可以通过收缩地图的迭代仅$O(log 1/epsilon)$额外的梯度调用来近似达到$epsilon$的精度。然后将(PP)方法的分析与误差传播分析相结合，证明了所得到的一阶方法Clairvoyant Extra Gradient在一般情况下具有近似最优的时间平均收敛性，在无约束情况下具有最后迭代收敛性。
{"title":"Min-Max Optimization Made Simple: Approximating the Proximal Point Method via Contraction Maps","authors":"V. Cevher, G. Piliouras, Ryann Sim, Stratis Skoulakis","doi":"10.48550/arXiv.2301.03931","DOIUrl":"https://doi.org/10.48550/arXiv.2301.03931","url":null,"abstract":"In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent approach of Piliouras et al. in normal form games, our work is based on the fact that the update rule of the Proximal Point method (PP) can be approximated up to accuracy $epsilon$ with only $O(log 1/epsilon)$ additional gradient-calls through the iterations of a contraction map. Then combining the analysis of (PP) method with an error-propagation analysis we establish that the resulting first order method, called Clairvoyant Extra Gradient, admits near-optimal time-average convergence for general domains and last-iterate convergence in the unconstrained case.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"136 1","pages":"192-206"},"PeriodicalIF":0.0,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73274911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-06DOI: 10.48550/arXiv.2301.02421
Meike Hatzel, Konrad Majewski, Michal Pilipczuk, Marek Sokolowski
In the directed detour problem one is given a digraph $G$ and a pair of vertices $s$ and~$t$, and the task is to decide whether there is a directed simple path from $s$ to $t$ in $G$ whose length is larger than $mathsf{dist}_{G}(s,t)$. The more general parameterized variant, directed long detour, asks for a simple $s$-to-$t$ path of length at least $mathsf{dist}_{G}(s,t)+k$, for a given parameter $k$. Surprisingly, it is still unknown whether directed detour is polynomial-time solvable on general digraphs. However, for planar digraphs, Wu and Wang~[Networks, '15] proposed an $mathcal{O}(n^3)$-time algorithm for directed detour, while Fomin et al.~[STACS 2022] gave a $2^{mathcal{O}(k)}cdot n^{mathcal{O}(1)}$-time fpt algorithm for directed long detour. The algorithm of Wu and Wang relies on a nontrivial analysis of how short detours may look like in a plane embedding, while the algorithm of Fomin et al.~is based on a reduction to the ${S}$-disjoint paths problem on planar digraphs. This latter problem is solvable in polynomial time using the algebraic machinery of Schrijver~[SIAM~J.~Comp.,~'94], but the degree of the obtained polynomial factor is huge. In this paper we propose two simple algorithms: we show how to solve, in planar digraphs, directed detour in time $mathcal{O}(n^2)$ and directed long detour in time $2^{mathcal{O}(k)}cdot n^4 log n$. In both cases, the idea is to reduce to the $2$-disjoint paths problem in a planar digraph, and to observe that the obtained instances of this problem have a certain topological structure that makes them amenable to a direct greedy strategy.
在有向绕路问题中，给定一个有向图$G$和一对顶点$s$和~$t$，任务是确定$G$中是否存在一条从$s$到$t$的有向简单路径，其长度大于$mathsf{dist}_{G}(s,t)$。对于给定的参数$k$，更一般的参数化变体，定向长迂回，要求一个简单的$s$到$t$的路径，其长度至少为$mathsf{dist}_{G}(s,t)+k$。令人惊讶的是，在一般有向图上，定向绕行是否多项式时间可解仍然是未知的。然而，对于平面有向图，Wu和Wang~[Networks， '15]提出了$mathcal{O}(n^3)$ time算法用于有向绕路，而Fomin等人~[STACS 2022]给出了$2^{mathcal{O}(k)}cdot n^{mathcal{O}(1)}$ time fpt算法用于有向长绕路。Wu和Wang的算法依赖于对平面嵌入中的短弯路的非平凡分析，而Fomin等人的算法是基于对平面有向图上的${S}$-不相交路径问题的简化。用Schrijver~[SIAM~J.~Comp]的代数机制在多项式时间内求解后一个问题。，~'94]，但得到的多项式因子的程度是巨大的。本文提出了两种简单的算法:我们展示了如何求解平面有向图中时间$mathcal{O}(n^2)$的有向绕路和时间$2^{mathcal{O}(k)}cdot n^4 log n$的有向长绕路。在这两种情况下，思想都是将其简化为平面有向图中的$2$-不相交路径问题，并观察该问题的实例具有一定的拓扑结构，使其适用于直接贪婪策略。
{"title":"Simpler and faster algorithms for detours in planar digraphs","authors":"Meike Hatzel, Konrad Majewski, Michal Pilipczuk, Marek Sokolowski","doi":"10.48550/arXiv.2301.02421","DOIUrl":"https://doi.org/10.48550/arXiv.2301.02421","url":null,"abstract":"In the directed detour problem one is given a digraph $G$ and a pair of vertices $s$ and~$t$, and the task is to decide whether there is a directed simple path from $s$ to $t$ in $G$ whose length is larger than $mathsf{dist}_{G}(s,t)$. The more general parameterized variant, directed long detour, asks for a simple $s$-to-$t$ path of length at least $mathsf{dist}_{G}(s,t)+k$, for a given parameter $k$. Surprisingly, it is still unknown whether directed detour is polynomial-time solvable on general digraphs. However, for planar digraphs, Wu and Wang~[Networks, '15] proposed an $mathcal{O}(n^3)$-time algorithm for directed detour, while Fomin et al.~[STACS 2022] gave a $2^{mathcal{O}(k)}cdot n^{mathcal{O}(1)}$-time fpt algorithm for directed long detour. The algorithm of Wu and Wang relies on a nontrivial analysis of how short detours may look like in a plane embedding, while the algorithm of Fomin et al.~is based on a reduction to the ${S}$-disjoint paths problem on planar digraphs. This latter problem is solvable in polynomial time using the algebraic machinery of Schrijver~[SIAM~J.~Comp.,~'94], but the degree of the obtained polynomial factor is huge. In this paper we propose two simple algorithms: we show how to solve, in planar digraphs, directed detour in time $mathcal{O}(n^2)$ and directed long detour in time $2^{mathcal{O}(k)}cdot n^4 log n$. In both cases, the idea is to reduce to the $2$-disjoint paths problem in a planar digraph, and to observe that the obtained instances of this problem have a certain topological structure that makes them amenable to a direct greedy strategy.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"80 1","pages":"156-165"},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80387200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1137/1.9781611977585.ch33
Maxime Larcher, Robert Meier, A. Steger
{"title":"A Simple Optimal Algorithm for the 2-Arm Bandit Problem","authors":"Maxime Larcher, Robert Meier, A. Steger","doi":"10.1137/1.9781611977585.ch33","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch33","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"1 1","pages":"365-372"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78471605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1137/1.9781611977585.ch3
Dor Katzelnick, Roy Schwartz
{"title":"A Simple Algorithm for Submodular Minimum Linear Ordering","authors":"Dor Katzelnick, Roy Schwartz","doi":"10.1137/1.9781611977585.ch3","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch3","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"14 1","pages":"28-35"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83217421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1137/1.9781611977585.ch29
Oliver A. Chubet, Parth Parikh, Don Sheehy, S. Sheth
{"title":"Proximity Search in the Greedy Tree","authors":"Oliver A. Chubet, Parth Parikh, Don Sheehy, S. Sheth","doi":"10.1137/1.9781611977585.ch29","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch29","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"11 1","pages":"332-342"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88735900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1137/1.9781611977585.ch14
Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, Pasin Manurangsi
{"title":"On the Fine-Grained Complexity of Approximating k-Center in Sparse Graphs","authors":"Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, Pasin Manurangsi","doi":"10.1137/1.9781611977585.ch14","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch14","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"26 1","pages":"145-155"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87939977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1137/1.9781611977585.ch34
Lucas Gretta, Eric Price
{"title":"An Improved Online Reduction from PAC Learning to Mistake-Bounded Learning","authors":"Lucas Gretta, Eric Price","doi":"10.1137/1.9781611977585.ch34","DOIUrl":"https://doi.org/10.1137/1.9781611977585.ch34","url":null,"abstract":"","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"2 1","pages":"373-380"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86871049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-28DOI: 10.48550/arXiv.2211.15146
Richard Santiago, I. Sergeev, R. Zenklusen
Random order online contention resolution schemes (ROCRS) are structured online rounding algorithms with numerous applications and links to other well-known online selection problems, like the matroid secretary conjecture. We are interested in ROCRS subject to a matroid constraint, which is among the most studied constraint families. Previous ROCRS required to know upfront the full fractional point to be rounded as well as the matroid. It is unclear to what extent this is necessary. Fu, Lu, Tang, Turkieltaub, Wu, Wu, and Zhang (SOSA 2022) shed some light on this question by proving that no strong (constant-selectable) online or even offline contention resolution scheme exists if the fractional point is unknown, not even for graphic matroids. In contrast, we show, in a setting with slightly more knowledge and where the fractional point reveals one by one, that there is hope to obtain strong ROCRS by providing a simple constant-selectable ROCRS for graphic matroids that only requires to know the size of the ground set in advance. Moreover, our procedure holds in the more general adversarial order with a sample setting, where, after sampling a random constant fraction of the elements, all remaining (non-sampled) elements may come in adversarial order.
{"title":"Simple Random Order Contention Resolution for Graphic Matroids with Almost no Prior Information","authors":"Richard Santiago, I. Sergeev, R. Zenklusen","doi":"10.48550/arXiv.2211.15146","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15146","url":null,"abstract":"Random order online contention resolution schemes (ROCRS) are structured online rounding algorithms with numerous applications and links to other well-known online selection problems, like the matroid secretary conjecture. We are interested in ROCRS subject to a matroid constraint, which is among the most studied constraint families. Previous ROCRS required to know upfront the full fractional point to be rounded as well as the matroid. It is unclear to what extent this is necessary. Fu, Lu, Tang, Turkieltaub, Wu, Wu, and Zhang (SOSA 2022) shed some light on this question by proving that no strong (constant-selectable) online or even offline contention resolution scheme exists if the fractional point is unknown, not even for graphic matroids. In contrast, we show, in a setting with slightly more knowledge and where the fractional point reveals one by one, that there is hope to obtain strong ROCRS by providing a simple constant-selectable ROCRS for graphic matroids that only requires to know the size of the ground set in advance. Moreover, our procedure holds in the more general adversarial order with a sample setting, where, after sampling a random constant fraction of the elements, all remaining (non-sampled) elements may come in adversarial order.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"273 1","pages":"84-95"},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79969833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-20DOI: 10.48550/arXiv.2211.11009
R. Tarjan, Uri Zwick
A emph{resizable array} is an array that can emph{grow} and emph{shrink} by the addition or removal of items from its end, or both its ends, while still supporting constant-time emph{access} to each item stored in the array given its emph{index}. Since the size of an array, i.e., the number of items in it, varies over time, space-efficient maintenance of a resizable array requires dynamic memory management. A standard doubling technique allows the maintenance of an array of size~$N$ using only $O(N)$ space, with $O(1)$ amortized time, or even $O(1)$ worst-case time, per operation. Sitarski and Brodnik et al. describe much better solutions that maintain a resizable array of size~$N$ using only $N+O(sqrt{N})$ space, still with $O(1)$ time per operation. Brodnik et al. give a simple proof that this is best possible. We distinguish between the space needed for emph{storing} a resizable array, and accessing its items, and the emph{temporary} space that may be needed while growing or shrinking the array. For every integer $rge 2$, we show that $N+O(N^{1/r})$ space is sufficient for storing and accessing an array of size~$N$, if $N+O(N^{1-1/r})$ space can be used briefly during grow and shrink operations. Accessing an item by index takes $O(1)$ worst-case time while grow and shrink operations take $O(r)$ amortized time. Using an exact analysis of a emph{growth game}, we show that for any data structure from a wide class of data structures that uses only $N+O(N^{1/r})$ space to store the array, the amortized cost of grow is $Omega(r)$, even if only grow and access operations are allowed. The time for grow and shrink operations cannot be made worst-case, unless $r=2$.
{"title":"Optimal resizable arrays","authors":"R. Tarjan, Uri Zwick","doi":"10.48550/arXiv.2211.11009","DOIUrl":"https://doi.org/10.48550/arXiv.2211.11009","url":null,"abstract":"A emph{resizable array} is an array that can emph{grow} and emph{shrink} by the addition or removal of items from its end, or both its ends, while still supporting constant-time emph{access} to each item stored in the array given its emph{index}. Since the size of an array, i.e., the number of items in it, varies over time, space-efficient maintenance of a resizable array requires dynamic memory management. A standard doubling technique allows the maintenance of an array of size~$N$ using only $O(N)$ space, with $O(1)$ amortized time, or even $O(1)$ worst-case time, per operation. Sitarski and Brodnik et al. describe much better solutions that maintain a resizable array of size~$N$ using only $N+O(sqrt{N})$ space, still with $O(1)$ time per operation. Brodnik et al. give a simple proof that this is best possible. We distinguish between the space needed for emph{storing} a resizable array, and accessing its items, and the emph{temporary} space that may be needed while growing or shrinking the array. For every integer $rge 2$, we show that $N+O(N^{1/r})$ space is sufficient for storing and accessing an array of size~$N$, if $N+O(N^{1-1/r})$ space can be used briefly during grow and shrink operations. Accessing an item by index takes $O(1)$ worst-case time while grow and shrink operations take $O(r)$ amortized time. Using an exact analysis of a emph{growth game}, we show that for any data structure from a wide class of data structures that uses only $N+O(N^{1/r})$ space to store the array, the amortized cost of grow is $Omega(r)$, even if only grow and access operations are allowed. The time for grow and shrink operations cannot be made worst-case, unless $r=2$.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"4 1","pages":"285-304"},"PeriodicalIF":0.0,"publicationDate":"2022-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91247570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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