Theoretical Computer Science最新文献

{"title":"Broadening the applicability of local completeness analysis with intensional and extensional guarantees","authors":"Flavio Ascari ,&nbsp;Roberto Bruni ,&nbsp;Roberta Gori","doi":"10.1016/j.tcs.2025.115452","DOIUrl":"10.1016/j.tcs.2025.115452","url":null,"abstract":"<div><div>Local Completeness Logic (LCL) is a proof system for program analysis rooted in abstract interpretation. The program semantics is under-approximated by any provable postcondition, like incorrectness logic does, but it is also over-approximated by a (locally) <em>complete</em> abstraction of such a postcondition, like Hoare logic does. Therefore, <em>any derivable triple</em> will either prove the program to be correct or unveil true bugs. While the completeness of a program's function with respect to an abstract domain is inherently <em>extensional</em>, LCL's rules demand the preservation of local completeness throughout the abstract interpreter's computations. This characteristic renders LCL analysis <em>intensional</em>, meaning it depends on the way the program is written. Consequently, LCL proof system may not derive all the valid triples. This paper addresses this discrepancy by: 1) designing new rules that allow one to perform part of the intensional analysis in different (complete) abstract domains whenever necessary; and 2) to compare their expressiveness. Notably, some of these new rules enable the derivation of all extensionally valid triples, thereby decoupling the set of provable properties from the way the program is written.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115452"},"PeriodicalIF":0.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632959","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":"Partial permutations comparison, maintenance and applications","authors":"Avivit Levy ,&nbsp;Ely Porat ,&nbsp;B. Riva Shalom","doi":"10.1016/j.tcs.2025.115433","DOIUrl":"10.1016/j.tcs.2025.115433","url":null,"abstract":"<div><div>This paper studies <em>partial permutations</em> and their use in algorithmic tasks. A <em>partial permutation</em> over Σ is a bijection <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>p</mi><mi>a</mi><mi>r</mi></mrow></msub><mo>:</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>↦</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> mapping a subset <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊂</mo><mi>Σ</mi></math></span> to a subset <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊂</mo><mi>Σ</mi></math></span>, where <span><math><mo>|</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>=</mo><mo>|</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo></math></span> (<span><math><mo>|</mo><mi>Σ</mi><mo>|</mo></math></span> denotes the size of a set Σ). Intuitively, two partial permutations <em>agree</em> if their mapping pairs do not form <em>conflicts</em>. We formally define this notion enabling a consistent as well as informatively rich comparison between partial permutations. We define the <em>Partial Permutations Agreement</em> problem (PPA), as follows. Given two sets <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of partial permutations over alphabet Σ, each of size <em>n</em>, output a pair (<span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> <em>agrees</em> with <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>, if exists. We study the existence of a data structure for efficiently maintaining a dynamic set of partial permutations enabling to retrieve agreement of partial permutations giving both negative and positive results. As applications we point out: (1) fruitful/futile methods for efficient genes sequences comparison in database, (2) an automatic color transformation data augmentation technique for image processing through neural networks, (3) negatively answer a recently posed open question on the strict parameterized dictionary matching with one gap (PDMOG) problem over general dictionary alphabets.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115433"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596499","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":"Bit-array-based alternatives to HyperLogLog","authors":"Svante Janson ,&nbsp;Jérémie Lumbroso ,&nbsp;Robert Sedgewick","doi":"10.1016/j.tcs.2025.115450","DOIUrl":"10.1016/j.tcs.2025.115450","url":null,"abstract":"<div><div>We present a family of algorithms for the problem of estimating the number of distinct items in an input stream that are simple to implement and are appropriate for practical applications. Our algorithms are a logical extension of the series of algorithms developed by Flajolet and his coauthors starting in 1983 that culminated in the widely used <span>HyperLogLog</span> algorithm. These algorithms divide the input stream into <em>M</em> substreams and lead to a time-accuracy tradeoff where a small number of bits per substream are saved to achieve a relative accuracy proportional to <span><math><mn>1</mn><mo>/</mo><msqrt><mrow><mi>M</mi></mrow></msqrt></math></span>. Our algorithms use just one or two bits per substream. Their effectiveness is demonstrated by a proof of approximate normality, with explicit expressions for standard errors that inform parameter settings and allow proper quantitative comparisons with other methods. Performance hypotheses are validated through experiments using a realistic input stream, with the general conclusion that our algorithms are significantly more accurate than <span>HyperLogLog</span> when using the same amount of memory, and they use significantly less memory than <span>HyperLogLog</span> to achieve a given accuracy.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115450"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596498","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":"Algorithms for Shortest Path Tour Problem","authors":"Yucen Gao ,&nbsp;Zhuoran Li ,&nbsp;Jingyu He ,&nbsp;Jun Fang ,&nbsp;Hui Gao ,&nbsp;Xiaofeng Gao ,&nbsp;Guihai Chen","doi":"10.1016/j.tcs.2025.115428","DOIUrl":"10.1016/j.tcs.2025.115428","url":null,"abstract":"<div><div>Carpooling route planning becomes an important problem with the growth of low-carbon traffic systems. When each passenger has multiple potential pick-up/drop-off locations, the problem will be more challenging. In the paper, we discussed a simplified carpooling route planning problem, namely the Shortest Path Tour Problem (SPTP), whose aim is to find a single-origin single-destination shortest path through an ordered sequence of disjoint node subsets. We propose Stage Dijkstra and Global Dijkstra algorithms to find the optimal shortest path, with the time complexity of <span><math><mi>O</mi><mo>(</mo><mi>l</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><mi>l</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>l</mi><mi>n</mi><mo>)</mo><mo>)</mo></math></span> respectively, where <em>l</em> represents the number of node subsets. To the best of our knowledge, <span><math><mi>O</mi><mo>(</mo><mi>l</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> is the best time complexity of the exact algorithms for SPTP. Besides, the Stage Dijkstra and Global Dijkstra algorithms both have the linear space complexity, which is highly suitable for resource-constrained environments. Experiments conducted on large-scale road networks and synthetic datasets demonstrate the effectiveness and efficiency of our proposed algorithms in terms of running time and memory consumption.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115428"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596497","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":"Joint bidding in ad auctions","authors":"Yuchao Ma ,&nbsp;Weian Li ,&nbsp;Wanzhi Zhang ,&nbsp;Yahui Lei ,&nbsp;Zhicheng Zhang ,&nbsp;Qi Qi ,&nbsp;Qiang Liu ,&nbsp;Xingxing Wang","doi":"10.1016/j.tcs.2025.115449","DOIUrl":"10.1016/j.tcs.2025.115449","url":null,"abstract":"<div><div>In traditional advertising auctions, commodity suppliers as advertisers compete for adverting positions to display commodities. As e-commerce platforms become more prevalent, offline retailers are also opening online virtual shops, and retailers are starting to pay a fee for extra exposure of their shops. This has led to situations where a single commodity may be sponsored by both the retailer and the supplier, offering opportunities for more profit. In order to explore this novel advertising pattern, we propose a new model called the joint advertising system (JAS), where retailers and suppliers jointly bid for advertising positions. In the context of this realistic scenario, conventional mechanisms such as GFP, GSP and Myerson auction cannot be applied directly. Besides, the VCG mechanism results in negative revenue in JAS. To solve this issue, we modify the payment rule of VCG to create a revised VCG mechanism that guarantees incentive compatible, individually rational and weakly budget-balanced. Additionally, we leverage the structure of the affine maximizer auction (AMA) and the technique of automated mechanism design to train joint AMA. Finally, we conduct several experiments to demonstrate the performance of the joint AMA. It turns out that our mechanism maintains good economic properties and outperforms other mechanisms in various settings.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115449"},"PeriodicalIF":0.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614658","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":"Reconfiguration and enumeration of optimal cyclic ladder lotteries","authors":"Yuta Nozaki ,&nbsp;Kunihiro Wasa ,&nbsp;Katsuhisa Yamanaka","doi":"10.1016/j.tcs.2025.115434","DOIUrl":"10.1016/j.tcs.2025.115434","url":null,"abstract":"<div><div>A <em>ladder lottery</em>, known as “Amidakuji” in Japan, is a common way to decide an assignment at random. In this paper, we investigate reconfiguration and enumeration problems of cyclic ladder lotteries. First, when a permutation <em>π</em> and an optimal displacement vector <strong><em>x</em></strong> are given, we investigate the reconfiguration and enumeration problems of the “optimal” cyclic ladder lotteries of <em>π</em> and <strong><em>x</em></strong>. Next, for a given permutation <em>π</em> we consider reconfiguration and enumeration problems of the optimal displacement vectors of <em>π</em>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115434"},"PeriodicalIF":0.9,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580065","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":"Bike-assisted evacuation of robots on a line with asymmetric S/R communication","authors":"Khaled Jawhar ,&nbsp;Evangelos Kranakis","doi":"10.1016/j.tcs.2025.115438","DOIUrl":"10.1016/j.tcs.2025.115438","url":null,"abstract":"<div><div>Two autonomous mobile robots and a non-autonomous one, also called bike, are placed at the origin of an infinite line. The autonomous robots can travel with maximum speed 1. When a robot rides the bike its speed increases to <span><math><mi>v</mi><mo>&gt;</mo><mn>1</mn></math></span>. Exactly one robot at a time can ride the bike, moreover the bike is non-autonomous in that it cannot move on its own. An Exit is placed on the line at a location which is unknown to the robots and at distance <em>d</em> from the origin. The robots have limited communication behavior; one robot is a sender (denoted by S) in that it can send information wirelessly at any distance and receive messages only in F2F (Face-to-Face), while the other robot is a receiver (denoted by R) in that it can receive information wirelessly but can send information only F2F. The bike has no communication capabilities of its own. We refer to the resulting communication model of the ensemble of the two autonomous robots and the bike as S/R.</div><div>Our general goal is to understand the impact of the non-autonomous robot in assisting the evacuation of two communication-limited autonomous robots. Our main contribution is to provide a new evacuation algorithm that enables both robots to evacuate from the unknown Exit in the S/R model. We also analyze the resulting evacuation time as a function of the bike's speed <em>v</em> and give upper and lower bounds on the competitive ratio of the resulting algorithm for the entire range of possible values of <em>v</em>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115438"},"PeriodicalIF":0.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571081","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":"Harmonious colourings of temporal matchings","authors":"Duncan Adamson","doi":"10.1016/j.tcs.2025.115437","DOIUrl":"10.1016/j.tcs.2025.115437","url":null,"abstract":"<div><div>Graph colouring is a fundamental problem in computer science, with a large body of research dedicated to both the general colouring problem and restricted cases. <em>Harmonious colourings</em> are one such restriction, where each edge must contain a globally unique pair of colours, i.e. if an edge connects a vertex coloured <em>x</em> with a vertex coloured <em>y</em>, then no other pair of connected vertices can be coloured <em>x</em> and <em>y</em>. Finding such a colouring in the traditional graph setting is known to be NP-hard, even in trees. This paper considers the generalisation of harmonious colourings to <em>Temporal Graphs</em>, specifically <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span><em>-Temporal matchings</em>, a class of temporal graphs where the underlying graph is a matching (a collection of disconnected components containing pairs of vertices), each edge can appear in at most <em>t</em> timesteps, and each timestep can contain at most <em>k</em> other edges. We provide a complete overview of the complexity landscape of finding <em>temporal harmonious colourings</em> for <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span>-matchings. We show that finding a <em>Temporal Harmonious Colouring</em>, a colouring that is harmonious in each timestep, is NP-hard for <em>(k,t)-Temporal Matchings</em> when <span><math><mi>k</mi><mo>≥</mo><mn>2</mn><mo>,</mo><mi>t</mi><mo>≥</mo><mn>4</mn></math></span>, or when <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mi>t</mi><mo>≥</mo><mn>2</mn></math></span>. We further show that this problem is inapproximable for <span><math><mi>t</mi><mo>≥</mo><mn>2</mn></math></span> and an unbounded value of <em>k</em>, and that the problem of determining the temporal harmonious chromatic number of a <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span>-temporal matching can be determined in linear time. Finally, we strengthen this result by a set of upper and lower bounds of the temporal harmonious chromatic number both for individual temporal matchings and for the classes of <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span>-temporal matchings, paths, and cycles.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115437"},"PeriodicalIF":0.9,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549637","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":"Channel allocation revisited through 1-extendability of graphs","authors":"Anthony Busson,&nbsp;Malory Marin,&nbsp;Rémi Watrigant","doi":"10.1016/j.tcs.2025.115436","DOIUrl":"10.1016/j.tcs.2025.115436","url":null,"abstract":"<div><div>We revisit the classical problem of channel allocation for Wi-Fi access points (AP). Using mechanisms such as the CSMA/CA protocol, Wi-Fi access points which are in conflict within a same channel are still able to communicate to terminals. In graph theoretical terms, it means that it is not mandatory for the channel allocation to correspond to a proper coloring of the conflict graph. However, recent studies suggest that the structure–rather than the number–of conflicts plays a crucial role in the performance of each AP. More precisely, the graph induced by each channel must satisfy the so-called 1-extendability property, which requires each vertex to be contained in an independent set of maximum cardinality. In this paper we introduce the 1-extendable chromatic number, which is the minimum size of a partition of the vertex set of a graph such that each part induces a 1-extendable graph. We study this parameter and the related optimization problem through different perspectives: algorithms and complexity, structure, and extremal properties. We first show how to compute this number using modular decompositions of graphs, and analyze the running time with respect to the modular width of the input graph. We also focus on the special case of cographs, and prove that the 1-extendable chromatic number can be computed in quasi-polynomial time in this class. Concerning extremal results, we show that the 1-extendable chromatic number of a graph with <em>n</em> vertices is at most <span><math><mn>2</mn><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>, whereas the classical chromatic number can be as large as <em>n</em>. We are also able to construct graphs whose 1-extendable chromatic number is at least logarithmic in the number of vertices.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115436"},"PeriodicalIF":0.9,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580066","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 the exponential growth of geometric shapes","authors":"Nada Almalki ,&nbsp;Siddharth Gupta ,&nbsp;Othon Michail","doi":"10.1016/j.tcs.2025.115439","DOIUrl":"10.1016/j.tcs.2025.115439","url":null,"abstract":"<div><div>In this paper, we explore the exponential growth of geometric structures starting from a single node, focusing on centralized growth operations. We identify a parameter <em>k</em>, representing the number of turning points within specific parts of a shape. We prove that, if edges can only be formed between a newly generated node and the node that created it and cannot be deleted, trees having at most <em>k</em> turning points on every root-to-leaf path can be grown in <span><math><mi>O</mi><mo>(</mo><mi>k</mi><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>+</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time steps and spirals with <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> turning points can be grown in <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time steps, <em>n</em> being the size of the final shape. For this model, we also show that the maximum number of turning points in a root-to-leaf path of a tree is a lower bound on the number of time steps to grow the tree and that there exists a class of paths such that any path in the class with <em>k</em> turning points requires <span><math><mi>Ω</mi><mo>(</mo><mi>k</mi><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></math></span> time steps to be grown. If nodes can additionally be connected as soon as they become adjacent, we prove that if a shape <em>S</em> has a spanning tree with at most <em>k</em> turning points on every root-to-leaf path, then the adjacency closure of <em>S</em> can be grown in <span><math><mi>O</mi><mo>(</mo><mi>k</mi><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>+</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time steps. In the strongest version of the model, where, additionally, edges can be deleted and neighbors handed over to new nodes, we present a universal algorithm for growing any shape <em>S</em> exponentially fast.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115439"},"PeriodicalIF":0.9,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144556910","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}