Algorithmica最新文献

{"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}

{"title":"From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem","authors":"Eduard Eiben,&nbsp;Robert Ganian,&nbsp;Iyad Kanj,&nbsp;Sebastian Ordyniak,&nbsp;Stefan Szeider","doi":"10.1007/s00453-025-01354-4","DOIUrl":"10.1007/s00453-025-01354-4","url":null,"abstract":"<div><p>Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently formulated as classical graph problems on induced subgraphs of powers of partially-defined hypercubes. In this paper, we follow up on this recent direction by investigating the Independent Set problem on this graph class, which has been studied in the data science setting under the name Diversity. We obtain a comprehensive picture of the problem’s parameterized complexity and establish its fixed-parameter tractability w.r.t. the solution size plus the power of the hypercube. Given that several such First Order Logic (FO) definable problems have been shown to be fixed-parameter tractable on the considered graph class, one may ask whether fixed-parameter tractability could be extended to capture all FO-definable problems. We answer this question in the negative by showing that FO model checking on induced subgraphs of hypercubes is as difficult as FO model checking on general graphs.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12620328/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145551841","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":"Finding d-Cuts in Graphs of Bounded Diameter, Graphs of Bounded Radius and H-Free Graphs","authors":"Felicia Lucke,&nbsp;Ali Momeni,&nbsp;Daniël Paulusma,&nbsp;Siani Smith","doi":"10.1007/s00453-025-01343-7","DOIUrl":"10.1007/s00453-025-01343-7","url":null,"abstract":"<div><p>The <span>(d)</span><span>-Cut</span> problem is to decide whether a graph has an edge cut such that each vertex has at most <i>d</i> neighbours on the opposite side of the cut. If <span>(d=1)</span>, we obtain the intensively studied <span>Matching Cut</span> problem. The <i>d</i><span>-Cut</span> problem has been studied as well, but a systematic study for special graph classes was lacking. We initiate such a study and consider classes of bounded diameter, bounded radius and <i>H</i>-free graphs. We prove that for all <span>(dge 2)</span>, <span>(d)</span><span>-Cut</span> is polynomial-time solvable for graphs of diameter 2, <span>((P_3+P_4))</span>-free graphs and <span>(P_5)</span>-free graphs. These results extend known results for <span>(d=1)</span>. However, we also prove several <span>NP</span>-hardness results for <span>(d)</span><span>-Cut</span> that contrast known polynomial-time results for <span>(d=1)</span>. Our results lead to full dichotomies for bounded diameter and bounded radius and to almost-complete dichotomies for <i>H</i>-free graphs.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510972","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":"Computing the Minimum Bottleneck Moving Spanning Tree","authors":"Haitao Wang,&nbsp;Yiming Zhao","doi":"10.1007/s00453-025-01358-0","DOIUrl":"10.1007/s00453-025-01358-0","url":null,"abstract":"<div><p>Given a set <i>P</i> of <i>n</i> points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to minimize the bottleneck weight of the spanning tree (i.e., the largest Euclidean length of all edges) during the whole movement. The problem was solved in <span>(O(n^2))</span> time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of <span>(O(n^{4/3} log ^3 n))</span> time.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510673","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":"A Flexible Evolutionary Algorithm with Dynamic Mutation Rate Archive","authors":"Martin S. Krejca,&nbsp;Carsten Witt","doi":"10.1007/s00453-025-01345-5","DOIUrl":"10.1007/s00453-025-01345-5","url":null,"abstract":"<div><p>We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using <b><i>k</i></b>-bit flip mutations. The algorithm adds successful mutation rates to an archive of promising rates that are favored in subsequent steps. Rates expire when their number of unsuccessful trials has exceeded a threshold, while rates currently not present in the archive can enter it in two ways: (i) via user-defined minimum selection probabilities for rates combined with a successful step or (ii) via a stagnation detection mechanism increasing the value for a promising rate after the current bit-flip neighborhood has been explored with high probability. For the minimum selection probabilities, we suggest different options, including heavy-tailed distributions. We conduct rigorous runtime analysis of the flexible evolutionary algorithm on the <span>OneMax</span> and <span>Jump</span> functions, on general unimodal functions, on minimum spanning trees, and on a class of hurdle-like functions with varying hurdle width that benefit particularly from the archive of promising mutation rates. In all cases, the runtime bounds are close to or even outperform the best known results for both stagnation detection and heavy-tailed mutations.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145511005","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":"An FPT Algorithm for Splitting a Necklace Among Two Thieves","authors":"Michaela Borzechowski,&nbsp;Patrick Schnider,&nbsp;Simon Weber","doi":"10.1007/s00453-025-01346-4","DOIUrl":"10.1007/s00453-025-01346-4","url":null,"abstract":"<div><p>It is well-known that the 2-Thief-Necklace-Splitting problem reduces to the discrete Ham Sandwich problem. In fact, this reduction was crucial in the proof of the <span>(textsf{PPA})</span>-completeness of the Ham Sandwich problem [Filos-Ratsikas and Goldberg, STOC’19]. Recently, a variant of the Ham Sandwich problem called <span>(alpha )</span>-Ham Sandwich has been studied, in which the point sets are guaranteed to be well-separated [Steiger and Zhao, DCG’10]. The complexity of this search problem remains unknown, but it is known to lie in the complexity class <span>(textsf{UEOPL})</span> [Chiu, Choudhary and Mulzer, ICALP’20]. We define the analogue of this well-separation condition in the necklace splitting problem — a necklace is <i>n</i>-<i>separable</i>, if every subset <i>A</i> of the <i>n</i> types of jewels can be separated from the types <span>([n]setminus A)</span> by at most <i>n</i> separator points. Since this version of necklace splitting reduces to <span>(alpha )</span>-Ham Sandwich in a solution-preserving way it follows that instances of this version always have unique solutions. We furthermore provide two FPT algorithms: The first FPT algorithm solves 2-Thief-Necklace-Splitting on <span>((n-1+ell ))</span>-separable necklaces with <i>n</i> types of jewels and <i>m</i> total jewels in time <span>(2^{O(ell log ell )}+O(m^2))</span>. In particular, this shows that 2-Thief-Necklace-Splitting is polynomial-time solvable on <i>n</i>-separable necklaces. Thus, attempts to show hardness of <span>(alpha )</span>-Ham Sandwich through reduction from the 2-Thief-Necklace-Splitting problem cannot work. The second FPT algorithm tests <span>((n-1+ell ))</span>-separability of a given necklace with <i>n</i> types of jewels in time <span>(2^{O(ell ^2)}cdot n^4)</span>. In particular, <i>n</i>-separability can thus be tested in polynomial time, even though testing well-separation of point sets is <span>(textsf{coNP})</span>-complete [Bergold et al., SWAT’22]. </p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01346-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145479825","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":"Lettericity of graphs: an FPT algorithm and a bound on the size of obstructions","authors":"Bogdan Alecu,&nbsp;Mamadou Moustapha Kanté,&nbsp;Vadim Lozin,&nbsp;Viktor Zamaraev","doi":"10.1007/s00453-025-01341-9","DOIUrl":"10.1007/s00453-025-01341-9","url":null,"abstract":"<div><p>Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property implies that any hereditary class of graphs of bounded lettericity can be described by finitely many forbidden induced subgraphs. This, in turn, implies, in a non-constructive way, polynomial-time recognition of such classes. However, no constructive algorithms and no specific bounds on the size of forbidden graphs are available up to date. In the present paper, we develop an algorithm that recognizes <i>n</i>-vertex graphs of lettericity at most <i>k</i> in time <span>(f(k) cdot n^3)</span> and show that any minimal graph of lettericity more than <i>k</i> has at most <span>(2^{O(k^2log k)})</span> vertices.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01341-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145479826","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}