Algorithmica最新文献

{"title":"Algorithms for Matrix Multiplication via Sampling and Opportunistic Matrix Multiplication","authors":"David G. Harris","doi":"10.1007/s00453-024-01247-y","DOIUrl":"10.1007/s00453-024-01247-y","url":null,"abstract":"<div><p>As proposed by Karppa and Kaski (in: Proceedings 30th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2019) a novel “broken\" or \"opportunistic\" matrix multiplication algorithm, based on a variant of Strassen’s algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks. Their algorithm can compute Boolean matrix multiplication in <span>(O(n^{2.778}))</span> time. While asymptotically faster matrix multiplication algorithms exist, most such algorithms are infeasible for practical problems. We describe an alternative way to use the broken multiplication algorithm to approximately compute matrix multiplication, either for real-valued or Boolean matrices. In brief, instead of running multiple iterations of the broken algorithm on the original input matrix, we form a new larger matrix by sampling and run a single iteration of the broken algorithm on it. Asymptotically, our algorithm has runtime <span>(O(n^{2.763}))</span>, a slight improvement over the Karppa–Kaski algorithm. Since the goal is to obtain new practical matrix-multiplication algorithms, we also estimate the concrete runtime for our algorithm for some large-scale sample problems. It appears that for these parameters, further optimizations are still needed to make our algorithm competitive.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 9","pages":"2822 - 2844"},"PeriodicalIF":0.9,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Online Unit Profit Knapsack with Predictions","authors":"Joan Boyar,&nbsp;Lene M. Favrholdt,&nbsp;Kim S. Larsen","doi":"10.1007/s00453-024-01239-y","DOIUrl":"10.1007/s00453-024-01239-y","url":null,"abstract":"<div><p>A variant of the online knapsack problem is considered in the setting of predictions. In Unit Profit Knapsack, the items have unit profit, i.e., the goal is to pack as many items as possible. For Online Unit Profit Knapsack, the competitive ratio is unbounded. In contrast, it is easy to find an optimal solution offline: Pack as many of the smallest items as possible into the knapsack. The prediction available to the online algorithm is the average size of those smallest items that fit in the knapsack. For the prediction error in this hard online problem, we use the ratio <span>(r=frac{a}{hat{a}})</span> where <i>a</i> is the actual value for this average size and <span>(hat{a})</span> is the prediction. We give an algorithm which is <span>(frac{e-1}{e})</span>-competitive, if <span>(r=1)</span>, and this is best possible among online algorithms knowing <i>a</i> and nothing else. More generally, the algorithm has a competitive ratio of <span>(frac{e-1}{e}r)</span>, if <span>(r le 1)</span>, and <span>(frac{e-r}{e}r)</span>, if <span>(1 le r &lt; e)</span>. Any algorithm with a better competitive ratio for some <span>(r&lt;1)</span> will have a worse competitive ratio for some <span>(r&gt;1)</span>. To obtain a positive competitive ratio for all <i>r</i>, we adjust the algorithm, resulting in a competitive ratio of <span>(frac{1}{2r})</span> for <span>(rge 1)</span> and <span>(frac{r}{2})</span> for <span>(rle 1)</span>. We show that improving the result for any <span>(r&lt; 1)</span> leads to a worse result for some <span>(r&gt;1)</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 9","pages":"2786 - 2821"},"PeriodicalIF":0.9,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01239-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximate and Randomized Algorithms for Computing a Second Hamiltonian Cycle","authors":"Argyrios Deligkas,&nbsp;George B. Mertzios,&nbsp;Paul G. Spirakis,&nbsp;Viktor Zamaraev","doi":"10.1007/s00453-024-01238-z","DOIUrl":"10.1007/s00453-024-01238-z","url":null,"abstract":"<div><p>In this paper we consider the following problem: Given a Hamiltonian graph <i>G</i>, and a Hamiltonian cycle <i>C</i> of <i>G</i>, can we compute a second Hamiltonian cycle <span>(C^{prime } ne C)</span> of <i>G</i>, and if yes, how quickly? If the input graph <i>G</i> satisfies certain conditions (e.g. if every vertex of <i>G</i> is odd, or if the minimum degree is large enough), it is known that such a second Hamiltonian cycle always exists. Despite substantial efforts, no subexponential-time algorithm is known for this problem. In this paper we relax the problem of computing a second Hamiltonian cycle in two ways. First, we consider <i>approximating</i> the length of a second longest cycle on <i>n</i>-vertex graphs with minimum degree <span>(delta )</span> and maximum degree <span>(Delta )</span>. We provide a linear-time algorithm for computing a cycle <span>(C^{prime } ne C)</span> of length at least <span>(n-4alpha (sqrt{n}+2alpha )+8)</span>, where <span>(alpha = frac{Delta -2}{delta -2})</span>. This results provides a constructive proof of a recent result by Girão, Kittipassorn, and Narayanan in the regime of <span>(frac{Delta }{delta } = o(sqrt{n}))</span>. Our second relaxation of the problem is probabilistic. We propose a randomized algorithm which computes a second Hamiltonian cycle <i>with high probability</i>, given that the input graph <i>G</i> has a large enough minimum degree. More specifically, we prove that for every <span>(0&lt;ple 0.02)</span>, if the minimum degree of <i>G</i> is at least <span>(frac{8}{p} log sqrt{8}n + 4)</span>, then a second Hamiltonian cycle can be computed with probability at least <span>(1 - frac{1}{n}left( frac{50}{p^4} + 1 right) )</span> in <span>(poly(n) cdot 2^{4pn})</span> time. This result implies that, when the minimum degree <span>(delta )</span> is sufficiently large, we can compute with high probability a second Hamiltonian cycle faster than any known deterministic algorithm. In particular, when <span>(delta = omega (log n))</span>, our probabilistic algorithm works in <span>(2^{o(n)})</span> time.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 9","pages":"2766 - 2785"},"PeriodicalIF":0.9,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01238-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141351753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Online Geometric Covering and Piercing","authors":"Minati De,&nbsp;Saksham Jain,&nbsp;Sarat Varma Kallepalli,&nbsp;Satyam Singh","doi":"10.1007/s00453-024-01244-1","DOIUrl":"10.1007/s00453-024-01244-1","url":null,"abstract":"<div><p>We consider the online version of the piercing set problem, where geometric objects arrive one by one, and the online algorithm must maintain a valid piercing set for the already arrived objects by making irrevocable decisions. It is easy to observe that any deterministic algorithm solving this problem for intervals in <span>(mathbb {R})</span> has a competitive ratio of at least <span>(Omega (n))</span>. This paper considers the piercing set problem for similarly sized objects. We propose a deterministic online algorithm for similarly sized fat objects in <span>(mathbb {R}^d)</span>. For homothetic hypercubes in <span>(mathbb {R}^d)</span> with side length in the range [1, <i>k</i>], we propose a deterministic algorithm having a competitive ratio of at most <span>(3^dlceil log _2 krceil +2^d)</span>. In the end, we show deterministic lower bounds of the competitive ratio for similarly sized <span>(alpha )</span>-fat objects in <span>(mathbb {R}^2)</span> and homothetic hypercubes in <span>(mathbb {R}^d)</span>. Note that piercing translated copies of a convex object is equivalent to the unit covering problem, which is well-studied in the online setup. Surprisingly, no upper bound of the competitive ratio was known for the unit covering problem when the corresponding object is anything other than a ball or a hypercube. Our result yields an upper bound of the competitive ratio for the unit covering problem when the corresponding object is any convex object in <span>(mathbb {R}^d)</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 9","pages":"2739 - 2765"},"PeriodicalIF":0.9,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Slim Tree-Cut Width","authors":"Robert Ganian,&nbsp;Viktoriia Korchemna","doi":"10.1007/s00453-024-01241-4","DOIUrl":"10.1007/s00453-024-01241-4","url":null,"abstract":"<div><p>Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it turned out that tree-cut width falls short as an edge-cut based alternative to treewidth in algorithmic aspects. This has led to the very recent introduction of a simple edge-based parameter called edge-cut width [WG 2022], which has precisely the algorithmic applications one would expect from an analogue of treewidth for edge cuts, but does not have the desired structural properties. In this paper, we study a variant of tree-cut width obtained by changing the threshold for so-called thin nodes in tree-cut decompositions from 2 to 1. We show that this “slim tree-cut width” satisfies all the requirements of an edge-cut based analogue of treewidth, both structural and algorithmic, while being less restrictive than edge-cut width. Our results also include an alternative characterization of slim tree-cut width via an easy-to-use spanning-tree decomposition akin to the one used for edge-cut width, a characterization of slim tree-cut width in terms of forbidden immersions as well as approximation algorithm for computing the parameter.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 8","pages":"2714 - 2738"},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01241-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximating Long Cycle Above Dirac’s Guarantee","authors":"Fedor V. Fomin,&nbsp;Petr A. Golovach,&nbsp;Danil Sagunov,&nbsp;Kirill Simonov","doi":"10.1007/s00453-024-01240-5","DOIUrl":"10.1007/s00453-024-01240-5","url":null,"abstract":"<div><p>Parameterization above (or below) a guarantee is a successful concept in parameterized algorithms. The idea is that many computational problems admit “natural” guarantees bringing to algorithmic questions whether a better solution (above the guarantee) could be obtained efficiently. For example, for every boolean CNF formula on <i>m</i> clauses, there is an assignment that satisfies at least <i>m</i>/2 clauses. How difficult is it to decide whether there is an assignment satisfying more than <span>(m/2 +k)</span> clauses? Or, if an <i>n</i>-vertex graph has a perfect matching, then its vertex cover is at least <i>n</i>/2. Is there a vertex cover of size at least <span>(n/2 +k)</span> for some <span>(kge 1)</span> and how difficult is it to find such a vertex cover? The above guarantee paradigm has led to several exciting discoveries in the areas of parameterized algorithms and kernelization. We argue that this paradigm could bring forth fresh perspectives on well-studied problems in approximation algorithms. Our example is the longest cycle problem. One of the oldest results in extremal combinatorics is the celebrated Dirac’s theorem from 1952. Dirac’s theorem provides the following guarantee on the length of the longest cycle: for every 2-connected <i>n</i>-vertex graph <i>G</i> with minimum degree <span>(delta (G)le n/2)</span>, the length of a longest cycle <i>L</i> is at least <span>(2delta (G))</span>. Thus the “essential” part in finding the longest cycle is in approximating the “offset” <span>(k = L - 2 delta (G))</span>. The main result of this paper is the above-guarantee approximation theorem for <i>k</i>. Informally, the theorem says that approximating the offset <i>k</i> is not harder than approximating the total length <i>L</i> of a cycle. In other words, for any (reasonably well-behaved) function <i>f</i>, a polynomial time algorithm constructing a cycle of length <i>f</i>(<i>L</i>) in an undirected graph with a cycle of length <i>L</i>, yields a polynomial time algorithm constructing a cycle of length <span>(2delta (G)+Omega (f(k)))</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 8","pages":"2676 - 2713"},"PeriodicalIF":0.9,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01240-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Algorithms for Steiner Tree Reoptimization","authors":"Davide Bilò","doi":"10.1007/s00453-024-01243-2","DOIUrl":"10.1007/s00453-024-01243-2","url":null,"abstract":"<div><p><i>Reoptimization</i> is a setting in which we are given a good approximate solution of an optimization problem instance and a local modification that slightly changes the instance. The main goal is that of finding a good approximate solution of the modified instance. We investigate one of the most studied scenarios in reoptimization known as <i>Steiner tree reoptimization</i>. Steiner tree reoptimization is a collection of strongly <span>(textsf {NP})</span>-hard optimization problems that are defined on top of the classical Steiner tree problem and for which several constant-factor approximation algorithms have been designed in the last decades. In this paper we improve upon all these results by developing a novel technique that allows us to design <i>polynomial-time approximation schemes</i>. Remarkably, prior to this paper, no approximation algorithm better than recomputing a solution from scratch was known for the elusive scenario in which the cost of a single edge decreases. Our results are best possible since none of the problems addressed in this paper admits a fully polynomial-time approximation scheme, unless <span>(textsf {P}=textsf {NP})</span></p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 8","pages":"2652 - 2675"},"PeriodicalIF":0.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01243-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation Algorithms for Covering Vertices by Long Paths","authors":"Mingyang Gong,&nbsp;Brett Edgar,&nbsp;Jing Fan,&nbsp;Guohui Lin,&nbsp;Eiji Miyano","doi":"10.1007/s00453-024-01242-3","DOIUrl":"10.1007/s00453-024-01242-3","url":null,"abstract":"<div><p>Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seems to escape from the literature. A path containing at least <i>k</i> vertices is considered long. When <span>(k le 3)</span>, the problem is polynomial time solvable; when <i>k</i> is the total number of vertices, the problem reduces to the Hamiltonian path problem, which is NP-complete. For a fixed <span>(k ge 4)</span>, the problem is NP-hard and the best known approximation algorithm for the weighted set packing problem implies a <i>k</i>-approximation algorithm. To the best of our knowledge, there is no approximation algorithm directly designed for the general problem; when <span>(k = 4)</span>, the problem admits a 4-approximation algorithm which was presented recently. We propose the first <span>((0.4394 k + O(1)))</span>-approximation algorithm for the general problem and an improved 2-approximation algorithm when <span>(k = 4)</span>. Both algorithms are based on local improvement, and their theoretical performance analyses are done via amortization and their practical performance is examined through simulation studies.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 8","pages":"2625 - 2651"},"PeriodicalIF":0.9,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parity Permutation Pattern Matching","authors":"Virginia Ardévol Martínez,&nbsp;Florian Sikora,&nbsp;Stéphane Vialette","doi":"10.1007/s00453-024-01237-0","DOIUrl":"10.1007/s00453-024-01237-0","url":null,"abstract":"<div><p>Given two permutations, a pattern <span>(sigma )</span> and a text <span>(pi )</span>, <span>Parity Permutation Pattern Matching</span> asks whether there exists a parity and order preserving embedding of <span>(sigma )</span> into <span>(pi )</span>. While it is known that <span>Permutation Pattern Matching</span> is in <span>(textsc {FPT})</span>, we show that adding the parity constraint to the problem makes it <span>(textsc {W}[1])</span>-hard, even for alternating permutations or for 4321-avoiding patterns. However, the problem remains in <span>(textsc {FPT})</span> if <span>(pi )</span> avoids a fixed permutation, thanks to a recent meta-theorem on twin-width. On the other hand, as for the classical version, <span>Parity Permutation Pattern Matching</span> remains polynomial-time solvable when the pattern is separable, or if both permutations are 321-avoiding, but <span>NP</span>-hard if <span>(sigma )</span> is 321-avoiding and <span>(pi )</span> is 4321-avoiding.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 8","pages":"2605 - 2624"},"PeriodicalIF":0.9,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions","authors":"Ishan Bansal,&nbsp;Joseph Cheriyan,&nbsp;Logan Grout,&nbsp;Sharat Ibrahimpur","doi":"10.1007/s00453-024-01235-2","DOIUrl":"10.1007/s00453-024-01235-2","url":null,"abstract":"<div><p>We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for problems in network design via the primal-dual method (Williamson et al. in Combinatorica 15(3):435–454, 1995. https://doi.org/10.1007/BF01299747). Williamson et al. prove an approximation ratio of two for connectivity augmentation problems where the connectivity requirements can be specified by uncrossable functions. They state: “Extending our algorithm to handle non-uncrossable functions remains a challenging open problem. The key feature of uncrossable functions is that there exists an optimal dual solution which is laminar ... A larger open issue is to explore further the power of the primal-dual approach for obtaining approximation algorithms for other combinatorial optimization problems.” Our main result proves that the primal-dual algorithm of Williamson et al. achieves an approximation ratio of <span>(16)</span> for a class of functions that generalizes the notion of an uncrossable function. There exist instances that can be handled by our methods where none of the optimal dual solutions has a laminar support. We present three applications of our main result to problems in the area of network design. (1)  A <span>(16)</span>-approximation algorithm for augmenting a family of small cuts of a graph <i>G</i>. The previous best approximation ratio was <span>(O(log {|V(G)|}))</span>. (2)  A <span>(16cdot {lceil k/u_{min} rceil })</span>-approximation algorithm for the Cap-<i>k</i>-ECSS problem which is as follows: Given an undirected graph <span>(G = (V,E))</span> with edge costs <span>(c in {mathbb {Q}}_{ge 0}^E)</span> and edge capacities <span>(u in {mathbb {Z}}_{ge 0}^E)</span>, find a minimum-cost subset of the edges <span>(Fsubseteq E)</span> such that the capacity of any cut in (<i>V</i>, <i>F</i>) is at least <i>k</i>; <span>(u_{min})</span> (respectively, <span>(u_{max})</span>) denotes the minimum (respectively, maximum) capacity of an edge in <i>E</i>, and w.l.o.g. <span>(u_{max} le k)</span>. The previous best approximation ratio was <span>(min (O(log {|V|}), k, 2u_{max}))</span>. (3)  A <span>(20)</span>-approximation algorithm for the model of (<i>p</i>, 2)-Flexible Graph Connectivity. The previous best approximation ratio was <span>(O(log {|V(G)|}))</span>, where <i>G</i> denotes the input graph.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 8","pages":"2575 - 2604"},"PeriodicalIF":0.9,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}