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From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem 从数据补全到超立方体问题：独立集问题的参数化分析。

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-17 DOI: 10.1007/s00453-025-01354-4

Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, Stefan Szeider

{"title":"From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem","authors":"Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, Stefan Szeider","doi":"10.1007/s00453-025-01354-4","DOIUrl":"10.1007/s00453-025-01354-4","url":null,"abstract":"<div>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.</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}

引用次数: 0

Finding d-Cuts in Graphs of Bounded Diameter, Graphs of Bounded Radius and H-Free Graphs 在有界直径图、有界半径图和无h图中求d-切

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-15 DOI: 10.1007/s00453-025-01343-7

Felicia Lucke, Ali Momeni, Daniël Paulusma, Siani Smith

引用次数: 0

Computing the Minimum Bottleneck Moving Spanning Tree 计算最小瓶颈移动生成树

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-14 DOI: 10.1007/s00453-025-01358-0

Haitao Wang, Yiming Zhao

引用次数: 0

A Flexible Evolutionary Algorithm with Dynamic Mutation Rate Archive 一种具有动态变异率存档的灵活进化算法

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-13 DOI: 10.1007/s00453-025-01345-5

Martin S. Krejca, Carsten Witt

{"title":"A Flexible Evolutionary Algorithm with Dynamic Mutation Rate Archive","authors":"Martin S. Krejca, Carsten Witt","doi":"10.1007/s00453-025-01345-5","DOIUrl":"10.1007/s00453-025-01345-5","url":null,"abstract":"<div>We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using k-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 OneMax and Jump 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.</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}

引用次数: 0

An FPT Algorithm for Splitting a Necklace Among Two Thieves 两贼分项链的FPT算法

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-10 DOI: 10.1007/s00453-025-01346-4

Michaela Borzechowski, Patrick Schnider, Simon Weber

{"title":"An FPT Algorithm for Splitting a Necklace Among Two Thieves","authors":"Michaela Borzechowski, Patrick Schnider, Simon Weber","doi":"10.1007/s00453-025-01346-4","DOIUrl":"10.1007/s00453-025-01346-4","url":null,"abstract":"<div>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 (textsf{PPA})-completeness of the Ham Sandwich problem [Filos-Ratsikas and Goldberg, STOC’19]. Recently, a variant of the Ham Sandwich problem called (alpha )-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 (textsf{UEOPL}) [Chiu, Choudhary and Mulzer, ICALP’20]. We define the analogue of this well-separation condition in the necklace splitting problem — a necklace is n-separable, if every subset A of the n types of jewels can be separated from the types ([n]setminus A) by at most n separator points. Since this version of necklace splitting reduces to (alpha )-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 ((n-1+ell ))-separable necklaces with n types of jewels and m total jewels in time (2^{O(ell log ell )}+O(m^2)). In particular, this shows that 2-Thief-Necklace-Splitting is polynomial-time solvable on n-separable necklaces. Thus, attempts to show hardness of (alpha )-Ham Sandwich through reduction from the 2-Thief-Necklace-Splitting problem cannot work. The second FPT algorithm tests ((n-1+ell ))-separability of a given necklace with n types of jewels in time (2^{O(ell ^2)}cdot n^4). In particular, n-separability can thus be tested in polynomial time, even though testing well-separation of point sets is (textsf{coNP})-complete [Bergold et al., SWAT’22]. </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}

引用次数: 0

Lettericity of graphs: an FPT algorithm and a bound on the size of obstructions 图的信度：一个FPT算法和障碍物大小的界限

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-10 DOI: 10.1007/s00453-025-01341-9

Bogdan Alecu, Mamadou Moustapha Kanté, Vadim Lozin, Viktor Zamaraev

引用次数: 0

On computing vertex connectivity of 1-planar graphs 1-平面图顶点连通性的计算

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-10 DOI: 10.1007/s00453-025-01355-3

Therese Biedl, Karthik Murali

{"title":"On computing vertex connectivity of 1-planar graphs","authors":"Therese Biedl, Karthik Murali","doi":"10.1007/s00453-025-01355-3","DOIUrl":"10.1007/s00453-025-01355-3","url":null,"abstract":"<div>The vertex connectivity of a graph G is the size of the smallest set of vertices S such that (G setminus S) is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and algorithmic perspectives. Let G be a plane embedded graph, and (Lambda (G)) be an auxiliary graph obtained by inserting a face vertex inside each face and connecting it to all vertices of G incident with the face. If S is a minimal vertex cut of G, then there exists a cycle of length 2|S| whose vertices alternate between vertices of S and face vertices. This structure facilitates the designing of a linear-time algorithm to find minimum vertex cuts of planar graphs. In this paper, we attempt a similar approach for the class of 1-plane graphs—these are graphs with a drawing on the plane where each edge is crossed at most once. We consider different classes of 1-plane graphs based on the subgraphs induced by the endpoints of crossings. For 1-plane graphs where the endpoints of every crossing induce the complete graph (K_4), we show that the structure of minimum vertex cuts is identical to that in plane graphs, as mentioned above. For 1-plane graphs where the endpoints of every crossing induce at least three edges (i.e., one edge apart from the crossing pair of edges), we show that for any minimal vertex cut S, there exists a cycle of diameter O(|S|) in (Lambda (G)) such that all vertices of S are in the neighbourhood of the cycle. This structure enables us to design a linear time algorithm to compute the vertex connectivity of all such 1-plane graphs.</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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145479823","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}

引用次数: 0

Geometric Thickness of Multigraphs is (exists mathbb {R})-Complete 几何厚度的多图是(exists mathbb {R}) -完成

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-11-10 DOI: 10.1007/s00453-025-01351-7

Henry Förster, Philipp Kindermann, Tillmann Miltzow, Irene Parada, Soeren Terziadis, Birgit Vogtenhuber

{"title":"Geometric Thickness of Multigraphs is (exists mathbb {R})-Complete","authors":"Henry Förster, Philipp Kindermann, Tillmann Miltzow, Irene Parada, Soeren Terziadis, Birgit Vogtenhuber","doi":"10.1007/s00453-025-01351-7","DOIUrl":"10.1007/s00453-025-01351-7","url":null,"abstract":"<div>We say that a (multi)graph ( user2{G} = (user2{V},user2{E}) ) has geometric thickness t if there exists a straight-line drawing ( user2{varphi }:user2{V} to mathbb{R}^{{mathbf{2}}} ) and a t-coloring of its edges where no two edges sharing a point in their relative interior have the same color. The Geometric Thickness problem asks whether a given multigraph has geometric thickness at most t. This problem was shown to be NP-hard for ( user2{t} = mathbf{2} ) (Durocher et al. Comput Geom 56:1–18, 2016. https://doi.org/10.1016/j.comgeo.2016.03.003). In this paper, we settle the computational complexity of Geometric Thickness by showing that it is (exists mathbb {R})-complete already for thickness 30. Moreover, our reduction shows that the problem is (exists mathbb {R})-complete for 4392-planar graphs, where a graph is k-planar if it admits a topological drawing with at most k crossings per edge. In the course of our paper we answer previous questions on geometric thickness and on other related problems, in particular that simultaneous graph embeddings of 31 edge-disjoint graphs and pseudo-segment stretchability with chromatic number 30 are (exists mathbb {R})-complete.</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/s00453-025-01351-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145479824","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}

引用次数: 0

A Clique-Based Separator for Intersection Graphs of Geodesic Disks in (mathbb {R}^2) 一种基于团的测地线盘交点图分割方法 (mathbb {R}^2)

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-08-29 DOI: 10.1007/s00453-025-01337-5

Boris Aronov, Mark de Berg, Leonidas Theocharous

{"title":"A Clique-Based Separator for Intersection Graphs of Geodesic Disks in (mathbb {R}^2)","authors":"Boris Aronov, Mark de Berg, Leonidas Theocharous","doi":"10.1007/s00453-025-01337-5","DOIUrl":"10.1007/s00453-025-01337-5","url":null,"abstract":"<div>Let d be a (well-behaved) shortest-path metric defined on a path-connected subset of (mathbb {R}^2) and let (mathcal {D}={D_1,ldots,D_n}) be a set of geodesic disks with respect to the metric d. We prove that (mathcal {G}^{times }(mathcal {D})), the intersection graph of the disks in (mathcal {D}), has a clique-based separator consisting of (O(n^{3/4+varepsilon })) cliques. This significantly extends the class of objects whose intersection graphs have small clique-based separators. Our clique-based separator yields an algorithm for q-Coloring that runs in time (2^{O(n^{3/4+varepsilon })}), assuming the boundaries of the disks (D_i) can be computed in polynomial time. We also use our clique-based separator to obtain a simple, efficient, and almost exact distance oracle for intersection graphs of geodesic disks. Our distance oracle uses (O(n^{7/4+varepsilon })) storage and can report the hop distance between any two nodes in (mathcal {G}^{times }(mathcal {D})) in (O(n^{3/4+varepsilon })) time, up to an additive error of one. So far, distance oracles with an additive error of one that use subquadratic storage and sublinear query time were not known for such general graph classes.</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 12","pages":"1997 - 2017"},"PeriodicalIF":0.7,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01337-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227881","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}

引用次数: 0

Reconfiguration of Multisets with Applications to Bin Packing 多集的重新配置及其在装箱中的应用

IF 0.7 4区计算机科学

Algorithmica Pub Date : 2025-08-21 DOI: 10.1007/s00453-025-01324-w

Jeffrey Kam, Shahin Kamali, Avery Miller, Naomi Nishimura

{"title":"Reconfiguration of Multisets with Applications to Bin Packing","authors":"Jeffrey Kam, Shahin Kamali, Avery Miller, Naomi Nishimura","doi":"10.1007/s00453-025-01324-w","DOIUrl":"10.1007/s00453-025-01324-w","url":null,"abstract":"<div>We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of rearrangement could be improving efficiency or increasing locality. To cover problems arising in a wide range of application areas, we define the general Repacking problem as the rearrangement of multisets of multisets. We present hardness results for the general case and algorithms for various restricted classes of instances. By limiting the total size of items in each multiset, our results can be viewed as an offline approach to Bin Packing, in which each bin is represented as a multiset. In addition to providing the first results on reconfiguration of multisets, our contributions open up several research avenues: the interplay between reconfiguration and online algorithms and parallel algorithms; the use of the tools of linear programming in reconfiguration; and, in the longer term, a focus on extra resources in reconfiguration. A preliminary version of this paper appeared in the proceedings of the 18th International Conference and Workshops on Algorithms and Computation (WALCOM 2024).</div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 12","pages":"1933 - 1996"},"PeriodicalIF":0.7,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227882","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}

引用次数: 0