Algorithmica最新文献

{"title":"Strict Self-Assembly of Discrete Self-Similar Fractals in the Abstract Tile Assembly Model","authors":"Florent Becker,&nbsp;Daniel Hader,&nbsp;Matthew Patitz","doi":"10.1007/s00453-025-01340-w","DOIUrl":"10.1007/s00453-025-01340-w","url":null,"abstract":"<div><p>This paper answers a long-standing open question in tile-assembly theory, namely that it is possible to strictly assemble discrete self-similar fractals (DSSFs) in the abstract Tile-Assembly Model (aTAM). We prove this in 2 separate ways, each taking advantage of a novel set of tools. One of our constructions shows that specializing the notion of a <i>quine</i>, a program which prints its own output, to the language of tile-assembly naturally induces a fractal structure. The other construction introduces <i>self-describing circuits</i> as a means to abstractly represent the information flow through a tile-assembly construction and shows that such circuits may be constructed for a relative of the Sierpinski carpet, and indeed many other DSSFs, through a process of fixed-point iteration. This later result, or more specifically the machinery used in its construction, further enable us to provide a polynomial time procedure for deciding whether any given subset of <span>(mathbb {Z}^2)</span> will generate an aTAM producible DSSF. To this end, we also introduce the <i>Tree Pump Theorem</i>, a result analogous to the important <i>Window Movie Lemma</i>, but with requirements on the set of productions rather than on the self-assembling system itself. This paper is an extension of a version that appeared in the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’25).</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01340-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930555","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":"Plus Strategies are Exponentially Slower for Planted Optima of Random Height","authors":"Johannes Lengler,&nbsp;Leon Schiller,&nbsp;Oliver Sieberling","doi":"10.1007/s00453-025-01352-6","DOIUrl":"10.1007/s00453-025-01352-6","url":null,"abstract":"<div><p>We compare the <span>((1, lambda ))</span>-EA and the <span>((1 + lambda ))</span>-EA on the recently introduced benchmark <span>(textsc {DisOM})</span>, which is the <span>OneMax</span> function with randomly planted local optima. Previous work showed that if all local optima have the same relative height, then the plus strategy never loses more than a factor <span>(O(nlog n))</span> compared to the comma strategy. Here we show that even small random fluctuations in the heights of the local optima have a devastating effect for the plus strategy and lead to superpolynomial time to achieve a prescribed fitness target. On the other hand, due to their ability to escape local optima, comma strategies are unaffected by the height of the local optima and remain efficient. Our results hold for a broad class of possible distortions and show that the plus strategy, but not the comma strategy, is generally deceived by sparse unstructured fluctuations of a smooth landscape.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01352-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930744","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":"Maximum Independent Set when Excluding an Induced Minor: (K_1 + tK_2) and (tC_3 uplus C_4)","authors":"Édouard Bonnet,&nbsp;Julien Duron,&nbsp;Colin Geniet,&nbsp;Stéphan Thomassé,&nbsp;Alexandra Wesolek","doi":"10.1007/s00453-025-01356-2","DOIUrl":"10.1007/s00453-025-01356-2","url":null,"abstract":"<div><p>Dallard, Milanič, and Štorgel [arXiv ’22] ask if, for every class excluding a fixed planar graph <i>H</i> as an induced minor, <span>Maximum Independent Set</span> can be solved in polynomial time, and show that this is indeed the case when <i>H</i> is any planar complete bipartite graph, or the 5-vertex clique minus one edge, or minus two disjoint edges. A positive answer would constitute a far-reaching generalization of the state-of-the-art, when we currently do not know if a polynomial-time algorithm exists when <i>H</i> is the 7-vertex path. Relaxing tractability to the existence of a quasipolynomial-time algorithm, we know substantially more. Indeed, quasipolynomial-time algorithms were recently obtained for the <i>t</i>-vertex cycle, <span>(C_t)</span> [Gartland et al., STOC ’21], and the disjoint union of <i>t</i> triangles, <span>(tC_3)</span> [Bonamy et al., SODA ’23]. We give, for every integer <i>t</i>, a polynomial-time algorithm running in <span>(n^{O(t^5)})</span> when <i>H</i> is the friendship graph <span>(K_1 + tK_2)</span> (<i>t</i> disjoint edges plus a vertex fully adjacent to them), and a quasipolynomial-time algorithm running in <span>(n^{O(t^2 log n)+f(t)})</span>, with <i>f</i> a single-exponential function, when <i>H</i> is <span>(tC_3 uplus C_4)</span> (the disjoint union of <i>t</i> triangles and a 4-vertex cycle). The former generalizes the algorithm readily obtained from Alekseev’s structural result on graphs excluding <span>(tK_2)</span> as an induced subgraph [Alekseev, DAM ’07], while the latter extends Bonamy et al.’s result.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831446","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 of Time-Respecting Arborescences","authors":"Takehiro Ito,&nbsp;Yuni Iwamasa,&nbsp;Naoyuki Kamiyama,&nbsp;Yasuaki Kobayashi,&nbsp;Yusuke Kobayashi,&nbsp;Shun-ichi Maezawa,&nbsp;Akira Suzuki","doi":"10.1007/s00453-025-01365-1","DOIUrl":"10.1007/s00453-025-01365-1","url":null,"abstract":"<div><p>An arborescence, which is a directed analogue of a spanning tree in an undirected graph, is one of the most fundamental combinatorial objects in a digraph. In this paper, we study arborescences in digraphs from the viewpoint of combinatorial reconfiguration, which is the field where we study reachability between two configurations of some combinatorial objects via some specified operations. Especially, we consider reconfiguration problems for time-respecting arborescences, which were introduced by Kempe, Kleinberg, and Kumar. We first prove that if the roots of the initial and target time-respecting arborescences are the same, then the target arborescence is always reachable from the initial one and we can find a shortest reconfiguration sequence in polynomial time. Furthermore, we show if the roots are not the same, then the target arborescence may not be reachable from the initial one. On the other hand, we show that we can determine whether the target arborescence is reachable from the initial one in polynomial time. Finally, we prove that it is NP-hard to find a shortest reconfiguration sequence in the case where the roots are not the same. Our results show an interesting contrast to the previous results for (ordinary) arborescences reconfiguration problems.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831149","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":"Oriented Spanners","authors":"Kevin Buchin,&nbsp;Joachim Gudmundsson,&nbsp;Antonia Kalb,&nbsp;Aleksandr Popov,&nbsp;Carolin Rehs,&nbsp;André van Renssen,&nbsp;Sampson Wong","doi":"10.1007/s00453-025-01342-8","DOIUrl":"10.1007/s00453-025-01342-8","url":null,"abstract":"<div><p>Given a point set <i>P</i> in the Euclidean plane and a parameter <i>t</i>, we define an <i>oriented </i><i>t</i><i>-spanner</i> <i>G</i> as an oriented subgraph of the complete bi-directed graph such that for every pair of points, the shortest closed walk in <i>G</i> through those points is at most a factor <i>t</i> longer than the shortest cycle in the complete graph on <i>P</i>. We investigate the problem of computing sparse graphs with small oriented dilation. As we can show that minimising oriented dilation for a given number of edges is NP-hard in the plane, we first consider one-dimensional point sets. While obtaining a 1-spanner in this setting is straightforward, already for five points such a spanner has no plane embedding with the leftmost and rightmost point on the outer face. This leads to restricting to oriented graphs with a one-page book embedding on the one-dimensional point set. For this case we present a dynamic program to compute the graph of minimum oriented dilation that runs in <span>(mathcal {O}(n^7))</span> time for <i>n</i> points, and a greedy algorithm that computes a 5-spanner in <span>(mathcal {O}(nlog n))</span> time. Expanding these results finally gives us a result for two-dimensional point sets: we prove that for convex point sets the greedy triangulation results in a plane oriented <i>t</i>-spanner with <span>(t=7.2 cdot t_g)</span>, where <span>(t_g)</span> is an upper bound on the dilation of the greedy triangulation.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01342-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729712","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":"Certificates in P and Subquadratic-Time Computation of Radius, Diameter, and all Eccentricities in Graphs","authors":"Feodor Dragan,&nbsp;Guillaume Ducoffe,&nbsp;Michel Habib,&nbsp;Laurent Viennot","doi":"10.1007/s00453-025-01344-6","DOIUrl":"10.1007/s00453-025-01344-6","url":null,"abstract":"<div><p>In the context of fine-grained complexity, we investigate the notion of certificate enabling faster polynomial-time algorithms. We specifically target radius (minimum eccentricity), diameter (maximum eccentricity), and all-eccentricity computations for which quadratic-time lower bounds are known under plausible conjectures. In each case, we introduce a notion of certificate as a specific set of nodes from which appropriate bounds on all eccentricities can be derived in subquadratic time when this set has sublinear size. The existence of small certificates is a barrier against SETH-based lower bounds for these problems. We indeed prove that for graph classes with small certificates, there exist randomized subquadratic-time algorithms for computing the radius, the diameter, and all eccentricities respectively. Moreover, these notions of certificates are tightly related to algorithms probing the graph through one-to-all distance queries and allow to explain the efficiency of practical radius and diameter algorithms from the literature. Our formalization enables a novel primal-dual analysis of a classical approach for diameter computation that leads to algorithms for radius, diameter and all eccentricities with theoretical guarantees with respect to certain graph parameters. This is complemented by experimental results on various types of real-world graphs showing that these parameters appear to be low in practice. Finally, we obtain refined results for several graph classes.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730127","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":"Generalized (k)-Center: Distinguishing Doubling and Highway Dimension","authors":"Andreas Emil Feldmann,&nbsp;Tung Anh Vu","doi":"10.1007/s00453-025-01357-1","DOIUrl":"10.1007/s00453-025-01357-1","url":null,"abstract":"<div><p>We consider generalizations of the <span>(k)</span><span>-Center</span> problem in graphs of low doubling and highway dimension. For the <span>Capacitated </span><span>(k)</span><span>-Supplier with Outliers (CkSwO)</span> problem, we show an efficient parameterized approximation scheme (EPAS) when the parameters are <span>(k)</span>, the number of outliers and the doubling dimension of the graph induced by the supplier set. On the other hand, we show that for the <span>Capacitated </span><span>(k)</span><span>-Center</span> problem, which is a special case of <span>CkSwO</span>, obtaining a parameterized approximation scheme (PAS) is <span>(mathsf {W[1]})</span>-hard when the parameters are <span>(k)</span>, and the highway dimension. This is the first known example of a problem for which it is hard to obtain a PAS for highway dimension, while simultaneously admitting an EPAS for doubling dimension.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730126","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":"Recognition Complexity of Subgraphs of ({textbf {k}})-Connected Planar Cubic Graphs","authors":"Miriam Goetze,&nbsp;Paul Jungeblut,&nbsp;Torsten Ueckerdt","doi":"10.1007/s00453-025-01350-8","DOIUrl":"10.1007/s00453-025-01350-8","url":null,"abstract":"<div><p>We study the recognition complexity of subgraphs of <i>k</i>-connected planar cubic graphs where <span>({k in {0, 1, 2, 3}})</span>. We present polynomial-time algorithms to recognize subgraphs of 1- and 2-connected planar cubic graphs, both in the variable and fixed embedding setting. The main tools involve the <span>Generalized (Anti)factor</span>-problem for the fixed embedding case, and SPQR-trees for the variable embedding case. Secondly, we prove <span>NP</span>-hardness of recognizing subgraphs of 3-connected planar cubic graphs in the variable embedding setting.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01350-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612809","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":"Distributed Model Checking on Graphs of Bounded Treedepth","authors":"Fedor V. Fomin,&nbsp;Pierre Fraigniaud,&nbsp;Pedro Montealegre,&nbsp;Ivan Rapaport,&nbsp;Ioan Todinca","doi":"10.1007/s00453-025-01349-1","DOIUrl":"10.1007/s00453-025-01349-1","url":null,"abstract":"<div><p>We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the <span>CONGEST</span> model. To our knowledge, this marks the first meta-theorem regarding distributed model checking. Various optimization problems on graphs are expressible in MSO. Examples include determining whether a graph <i>G</i> has a clique of size <i>k</i>, whether it admits a coloring with <i>k</i> colors, whether it contains a graph <i>H</i> as a subgraph or minor, or whether terminal vertices in <i>G</i> could be connected via vertex-disjoint paths. Our meta-theorem significantly enhances the work of Bousquet et al. (in: 41st ACM Symposium on Principles of Distributed Computing (PODC), 2022), which was focused on <i>distributed certification</i> of MSO on graphs with bounded treedepth. Moreover, our results can be extended to solving optimization and counting problems expressible in MSO, in graphs of bounded treedepth.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01349-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612766","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":"Combining Crown Structures for Vulnerability Measures","authors":"Katrin Casel,&nbsp;Tobias Friedrich,&nbsp;Aikaterini Niklanovits,&nbsp;Kirill Simonov,&nbsp;Ziena Zeif","doi":"10.1007/s00453-025-01348-2","DOIUrl":"10.1007/s00453-025-01348-2","url":null,"abstract":"<div><p>Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices that need to be removed to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al. [1] and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from <span>(p^3)</span> to <span>(3p^2)</span>, and of wVI from <span>(p^3)</span> to <span>(3(p^2 + p^{1.5} p_ell ))</span>, where <span>(p_ell &lt; p)</span> represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from <span>(mathcal {O}(k^2W + kW^2))</span> to <span>(3mu (k + sqrt{mu }W))</span>, where <span>(mu = max (k,W))</span>. We also give a combinatorial algorithm that provides a 2<i>kW</i> vertex kernel in fixed-parameter tractable time when parameterized by <i>r</i>, where <span>(r le k)</span> is the size of a maximum <span>((W+1))</span>-packing. We further show that the algorithm computing the 2<i>kW</i> vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when <span>(W=1)</span>, which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a 2<i>k</i> vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01348-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145561701","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}