Computational Geometry-Theory and Applications最新文献

{"title":"Algorithms for radius-optimally augmenting trees in a metric space","authors":"Joachim Gudmundsson ,&nbsp;Yuan Sha","doi":"10.1016/j.comgeo.2023.102018","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102018","url":null,"abstract":"<div><p>Let <em>T</em> be a tree with <em>n</em> vertices in a metric space. We consider the problem of adding one shortcut edge to <em>T</em> to minimize the radius of the resulting graph.</p><p>For the <em>continuous</em> version of the problem where a center may be a point in the interior of an edge of the graph we give a linear time algorithm. In the case when the center is restricted to lie on a vertex, the <em>discrete</em> version, we give an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> expected time algorithm.</p><p>Previously linear-time algorithms were known for the special case when the input graph is a path.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49790333","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":"The constant of point–line incidence constructions","authors":"Martin Balko ,&nbsp;Adam Sheffer ,&nbsp;Ruiwen Tang","doi":"10.1016/j.comgeo.2023.102009","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102009","url":null,"abstract":"<div><p>We study a lower bound for the constant of the Szemerédi–Trotter theorem. In particular, we show that a recent infinite family of point-line configurations satisfies <span><math><mi>I</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>L</mi><mo>)</mo><mo>≥</mo><mo>(</mo><mi>c</mi><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>|</mo><mi>P</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>|</mo><mi>L</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></math></span>, with <span><math><mi>c</mi><mo>≈</mo><mn>1.27</mn></math></span>. Our technique is based on studying a variety of properties of Euler's totient function. We also improve the current best constant for Elekes's construction from 1 to about 1.27. From an expository perspective, this is the first full analysis of the constant of Erdős's construction.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49790332","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":"Simple linear time algorithms for piercing pairwise intersecting disks","authors":"Ahmad Biniaz ,&nbsp;Prosenjit Bose ,&nbsp;Yunkai Wang","doi":"10.1016/j.comgeo.2023.102011","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102011","url":null,"abstract":"<div><p>A set <span><math><mi>D</mi></math></span> of disks in the plane is said to be pierced by a point set <em>P</em> if each disk in <span><math><mi>D</mi></math></span> contains a point of <em>P</em>. Any set of pairwise intersecting unit disks can be pierced by 3 points (Hadwiger and Debrunner (1955) <span>[7]</span>). Stachó and independently Danzer established that any set of pairwise intersecting arbitrary disks can be pierced by 4 points (Stachó (1981–1984) <span>[16]</span>. Danzer (1986) <span>[4]</span><span>). Existing linear-time algorithms for finding a set of 4 or 5 points that pierce pairwise intersecting disks of arbitrary radius use the LP-type problem as a subroutine. We present simple linear-time algorithms for finding 3 points for piercing pairwise intersecting unit disks, and 5 points for piercing pairwise intersecting disks of arbitrary radius. Our algorithms use simple geometric transformations and avoid heavy machinery. We also show that 3 points are sometimes necessary for piercing pairwise intersecting unit disks.</span></p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49790335","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":"Cut locus realizations on convex polyhedra","authors":"Joseph O'Rourke ,&nbsp;Costin Vîlcu","doi":"10.1016/j.comgeo.2023.102010","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102010","url":null,"abstract":"<div><p>We prove that every positively weighted tree <em>T</em> can be realized as the cut locus <span><math><mi>C</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> of a point <em>x</em><span> on a convex polyhedron </span><em>P</em>, with <em>T</em> edge weights matching <span><math><mi>C</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> edge lengths. If <em>T</em> has <em>n</em> leaves, <em>P</em> has (in general) <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span><span> vertices. We show there is in fact a continuum of polyhedra </span><em>P</em> each realizing <em>T</em> for some <span><math><mi>x</mi><mo>∈</mo><mi>P</mi></math></span>. Three main tools in the proof are properties of the star unfolding of <em>P</em>, Alexandrov's gluing theorem, and a new cut-locus partition lemma. The construction of <em>P</em> from <em>T</em> is surprisingly simple.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49790334","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":"Multi-robot motion planning for unit discs with revolving areas","authors":"Pankaj K. Agarwal ,&nbsp;Tzvika Geft ,&nbsp;Dan Halperin ,&nbsp;Erin Taylor","doi":"10.1016/j.comgeo.2023.102019","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102019","url":null,"abstract":"<div><p>We study the problem of motion planning for a collection of <em>n</em> labeled unit disc robots in a polygonal environment. We assume that the robots have <em>revolving areas</em> around their start and final positions: that each start and each final is contained in a radius 2 disc lying in the free space, not necessarily concentric with the start or final position, which is free from other start or final positions. This assumption allows a <em>weakly-monotone</em> motion plan, in which robots move according to an ordering as follows: during the turn of a robot <em>R</em> in the ordering, it moves fully from its start to final position, while other robots do not leave their revolving areas. As <em>R</em> passes through a revolving area, a robot <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> that is inside this area may move within the revolving area to avoid a collision. Notwithstanding the existence of a motion plan, we show that minimizing the total traveled distance in this setting, specifically even when the motion plan is restricted to be weakly-monotone, is APX-hard, ruling out any polynomial-time <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span>-approximation algorithm.</p><p><span>On the positive side, we present the first constant-factor approximation algorithm for computing a feasible weakly-monotone motion plan. The total distance traveled by the robots is within an </span><span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span><span> factor of that of the optimal motion plan, which need not be weakly monotone. Our algorithm extends to an online setting in which the polygonal environment is fixed but the initial and final positions of robots are specified in an online manner. Finally, we observe that the overhead in the overall cost that we add while editing the paths to avoid robot-robot collision can vary significantly depending on the ordering we chose. Finding the best ordering in this respect is known to be NP-hard, and we provide a polynomial time </span><span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>-approximation algorithm for this problem.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49830655","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":"On reverse shortest paths in geometric proximity graphs","authors":"Pankaj K. Agarwal ,&nbsp;Matthew J. Katz ,&nbsp;Micha Sharir","doi":"10.1016/j.comgeo.2023.102053","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102053","url":null,"abstract":"<div><p>Let <em>S</em> be a set of <em>n</em><span> geometric objects of constant complexity (e.g., points, line segments, disks, ellipses) in </span><span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and let <span><math><mi>ϱ</mi><mo>:</mo><mi>S</mi><mo>×</mo><mi>S</mi><mo>→</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>≥</mo><mn>0</mn></mrow></msub></math></span> be a <em>distance function</em> on <em>S</em>. For a parameter <span><math><mi>r</mi><mo>≥</mo><mn>0</mn></math></span>, we define the <em>proximity graph</em> <span><math><mi>G</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>S</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> where <span><math><mi>E</mi><mo>=</mo><mo>{</mo><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>∈</mo><mi>S</mi><mo>×</mo><mi>S</mi><mo>|</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≠</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mspace></mspace><mi>ϱ</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>≤</mo><mi>r</mi><mo>}</mo></math></span>. Given <em>S</em>, <span><math><mi>s</mi><mo>,</mo><mi>t</mi><mo>∈</mo><mi>S</mi></math></span>, and an integer <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>, the <em>reverse-shortest-path</em> (RSP) problem asks for computing the smallest value <span><math><msup><mrow><mi>r</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>≥</mo><mn>0</mn></math></span> such that <span><math><mi>G</mi><mo>(</mo><msup><mrow><mi>r</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math></span> contains a path from <em>s</em> to <em>t</em> of length at most <em>k</em>.</p><p>In this paper we present a general randomized technique that solves the RSP problem efficiently for a large family of geometric objects and distance functions. Using standard, and sometimes more involved, semi-algebraic range-searching techniques, we first give an efficient algorithm for the decision problem, namely, given a value <span><math><mi>r</mi><mo>≥</mo><mn>0</mn></math></span>, determine whether <span><math><mi>G</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></span> contains a path from <em>s</em> to <em>t</em> of length at most <em>k</em>. Next, we adapt our decision algorithm and combine it with a random-sampling method to compute <span><math><msup><mrow><mi>r</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, by efficiently performing a binary search over an implicit set of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> candidate ‘critical’ values that contains <span><math><msup><mrow><mi>r</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>.</p><p>We illustrate the versatility of our general technique by applying it to a variety of g","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49799333","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":"Clustering with faulty centers","authors":"Emily Fox ,&nbsp;Hongyao Huang ,&nbsp;Benjamin Raichel","doi":"10.1016/j.comgeo.2023.102052","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102052","url":null,"abstract":"<div><p>In this paper we introduce and formally study the problem of <em>k</em>-clustering with faulty centers. Specifically, we study the faulty versions of <em>k</em>-center, <em>k</em>-median, and <em>k</em><span>-means clustering, where centers have some probability<span> of not existing, as opposed to prior work where clients had some probability of not existing. For all three problems we provide fixed parameter tractable algorithms, in the parameters </span></span><em>k</em>, <em>d</em>, and <em>ε</em>, that <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span>-approximate the minimum expected cost solutions for points in <em>d</em><span> dimensional Euclidean space. For Faulty </span><em>k</em><span>-center we additionally provide a 5-approximation for general metrics. Significantly, all of our algorithms have only a linear dependence on </span><em>n</em>.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49841451","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":"On algorithmic complexity of imprecise spanners","authors":"Abolfazl Poureidi ,&nbsp;Mohammad Farshi","doi":"10.1016/j.comgeo.2023.102051","DOIUrl":"10.1016/j.comgeo.2023.102051","url":null,"abstract":"<div><p>Let <span><math><mi>t</mi><mo>&gt;</mo><mn>1</mn></math></span> be a real number. A geometric <em>t</em><span>-spanner is a geometric graph for a point set in </span><span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span><span> with straight line segments between vertices such that the ratio of the shortest-path distance between every pair of vertices in the graph (with Euclidean edge lengths) to their actual Euclidean distance is at most </span><em>t</em>.</p><p>An imprecise point set is modeled by a set <em>R</em> of regions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. If one chooses a point inside each region of <em>R</em>, then the resulting point set is called a precise instance from <em>R</em>. An imprecise <em>t</em>-spanner for an imprecise point set <em>R</em> is a graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>R</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> such that for each precise instance <em>S</em> from <em>R</em>, graph <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>=</mo><mo>(</mo><mi>S</mi><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span> is the set of edges corresponding to <em>E</em> and <em>S</em>, is a <em>t</em>-spanner.</p><p>In this paper, we show an imprecise point set <em>R</em> of <em>n</em> straight-line segments in the plane such that any imprecise <em>t</em>-spanner for <em>R</em> has <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> edges. Then, we give an algorithm that computes an imprecise <em>t</em>-spanner for a set of <em>n</em><span> pairwise disjoint </span><em>d</em>-dimensional balls with arbitrary sizes. This imprecise <em>t</em>-spanner has <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>/</mo><msup><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> edges and can be computed in <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>/</mo><msup><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> time. Finally, we show that given an imprecise spanner, finding a precise instance such that its corresponding precise spanner has minimum dilation between all possible precise instances of the imprecise spanner is NP-hard, no matter if crossing edges are allowed or not.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47292577","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":"Augmenting graphs to minimize the radius","authors":"Joachim Gudmundsson ,&nbsp;Yuan Sha","doi":"10.1016/j.comgeo.2023.101996","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.101996","url":null,"abstract":"<div><p>We study the problem of augmenting a metric graph by adding <em>k</em> edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time <span><math><mo>(</mo><mn>5</mn><mo>/</mo><mn>3</mn><mo>−</mo><mi>ϵ</mi><mo>)</mo></math></span>-approximation algorithm, for any <span><math><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></math></span>, unless <span><math><mi>P</mi><mo>=</mo><mi>N</mi><mi>P</mi></math></span>.</p><p>We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49845789","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":"Keep your distance: Land division with separation","authors":"Edith Elkind ,&nbsp;Erel Segal-Halevi ,&nbsp;Warut Suksompong","doi":"10.1016/j.comgeo.2023.102006","DOIUrl":"https://doi.org/10.1016/j.comgeo.2023.102006","url":null,"abstract":"<div><p>This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each agent should receive a plot of a usable geometric shape, and (2) plots of different agents must be physically separated. With these requirements, the classic fairness notion of <em>proportionality</em> is impractical, since it may be impossible to attain any multiplicative approximation of it. In contrast, the <em>ordinal maximin share approximation</em>, introduced by Budish in 2011, provides meaningful fairness guarantees. We prove upper and lower bounds on achievable maximin share guarantees when the usable shapes are squares, fat rectangles, or arbitrary axis-aligned rectangles, and explore the algorithmic and query complexity of finding fair partitions in this setting. Our work makes use of tools and concepts from computational geometry such as independent sets of rectangles and guillotine partitions.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49845790","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}