Algorithmica最新文献

{"title":"Approximation Algorithms for Directed Weighted Spanners","authors":"Elena Grigorescu,&nbsp;Nithish Kumar,&nbsp;Young-San Lin","doi":"10.1007/s00453-026-01384-6","DOIUrl":"10.1007/s00453-026-01384-6","url":null,"abstract":"<div><p>In the <i>pairwise weighted spanner</i> problem, we are given a directed graph with <i>n</i> vertices and <i>k</i> terminal vertex pairs. Each edge is assigned both a <i>cost</i> and a <i>length</i>. The goal is to find a minimum-cost subgraph in which the terminal distance constraints are satisfied. A more restricted variant of this problem was shown to be <span>(O(2^{{log ^{1-varepsilon } n}}))</span>-hard to approximate under a standard complexity assumption, by Elkin and Peleg (Theory of Computing Systems, 2007). This general formulation captures many well-studied network connectivity problems, including spanners, distance preservers, and Steiner forests. For the weighted spanner problem where the edges have positive <i>integral</i> lengths with magnitudes <i>polynomial</i> in <i>n</i>, we show an <span>(tilde{O}(n^{4/5 + varepsilon }))</span>-approximation algorithm. When the edges have unit costs and lengths, the best previous algorithm gives an <span>(tilde{O}(n^{3/5 + varepsilon }))</span>-approximation, due to Chlamtáč, Dinitz, Kortsarz, and Laekhanukit (Transactions on Algorithms, 2020). We also consider the <i>online</i> setting, where the vertex pairs arrive one at a time, and edges must be added irrevocably to satisfy the distance constraints. We show an <span>(tilde{O}(k^{1/2 + varepsilon }))</span>-competitive algorithm. The state-of-the-art results are an <span>(tilde{O}(n^{4/5}))</span>-competitive algorithm when edges have unit costs and arbitrary positive lengths, and a <span>(min {tilde{O}(k^{1/2 + varepsilon }), tilde{O}(n^{2/3 + varepsilon })})</span>-competitive algorithm when edges have unit costs and lengths, due to Grigorescu, Lin, and Quanrud (APPROX, 2021). To the best of our knowledge, our results are the first approximation (online) polynomial-time algorithms with sublinear approximation (competitive) ratios for the weighted spanner problems.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01384-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737666","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":"A General Technique for Searching in Implicit Sets via Function Inversion","authors":"Boris Aronov,&nbsp;Jean Cardinal,&nbsp;Justin Dallant,&nbsp;John Iacono","doi":"10.1007/s00453-026-01385-5","DOIUrl":"10.1007/s00453-026-01385-5","url":null,"abstract":"<div><p>In recent years, the Fiat-Naor function inversion scheme has been used to disprove conjectures in fine-grained complexity theory and design state of the art data structures for a number of combinatorial problems. We pursue this line of research by considering its application to data structures for searching in implicit sets, defined as the image of a function. Given a function <i>f</i> from the set [<i>N</i>] to a <i>d</i>-dimensional integer grid, we consider data structures that allow efficient orthogonal range searching queries in the image of <i>f</i>, without explicitly storing it. We show that if <i>f</i> is of the form <span>([N]rightarrow [2^{w}]^d)</span> for some <span>(w=textrm{polylog} (N))</span> and is computable in constant time, then, for any <span>(0&lt;alpha &lt;1)</span>, we can obtain a data structure using <span>(tilde{O}(N^{1-alpha / 3}))</span> space such that, for a given <i>d</i>-dimensional axis-aligned box <i>B</i>, we can search for some <span>(xin [N])</span> such that <span>(f(x) in B)</span> in time <span>(tilde{O}(N^{alpha }))</span>. (Here the <span>(tilde{O}(.))</span> notation omits polylogarithmic factors.) Using similar techniques, we further obtain</p><ul>\u0000 <li>\u0000 <p>data structures for range counting and reporting, predecessor, selection, ranking queries, and combinations thereof, on the set <i>f</i>([<i>N</i>]),</p>\u0000 </li>\u0000 <li>\u0000 <p>data structures for preimage size and preimage selection queries for a given value of <i>f</i>, and</p>\u0000 </li>\u0000 <li>\u0000 <p>data structures for selection and ranking queries on geometric quantities computed from tuples of points in <i>d</i>-space.</p>\u0000 </li>\u0000 </ul><p> These results unify and generalize previously known results on 3SUM-indexing and string searching, and are widely applicable as a black box to a variety of problems. In particular, we give a data structure for a generalized version of gapped string indexing, and show how to preprocess a set of points on an integer grid in order to efficiently compute (in sublinear time), for points contained in a given axis-aligned box, their Theil-Sen estimator, the <i>k</i>th largest area triangle, or the induced hyperplane that is the <i>k</i>th furthest from the origin.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737772","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 Fast Algorithm for Computing Zigzag Representatives","authors":"Tamal K. Dey,&nbsp;Tao Hou,&nbsp;Dmitriy Morozov","doi":"10.1007/s00453-026-01386-4","DOIUrl":"10.1007/s00453-026-01386-4","url":null,"abstract":"<div><p>Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting <i>representatives</i> may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with <i>m</i> insertions and deletions can be computed in <span>(O(m^omega ))</span> time, where <span>(omega &lt; 2.373)</span> is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in <span>(O(m^3))</span> time, which can be improved to <span>(O(m^omega ))</span>. However, no known algorithm for zigzag filtrations computes the representatives with the <span>(O(m^3))</span> time bound. We present an <span>(O(m^2n))</span> time algorithm for this problem, where <span>(nle m)</span> is the size of the largest complex in the filtration.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01386-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631829","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":"Correction: 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/s00453-026-01379-3","DOIUrl":"10.1007/s00453-026-01379-3","url":null,"abstract":"","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642635","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":"Approximation Algorithms for Clustering with Minimum Sum of Radii, Diameters, and Squared Radii","authors":"Zachary Friggstad,&nbsp;Mahya Jamshidian","doi":"10.1007/s00453-026-01382-8","DOIUrl":"10.1007/s00453-026-01382-8","url":null,"abstract":"<div><p>We present an improved approximation algorithm for three related clustering problems. In the Minimum Sum of Radii clustering problem (MSR), we are to select <i>k</i> balls in a metric space to cover all points while minimizing the sum of their radii. In the Minimum Sum of Diameters clustering problem (MSD), we are to pick <i>k</i> clusters to cover all the points such that sum of diameters of all the clusters is minimized. Finally, in the Minimum Sum of Squared Radii problem (MSSR), the goal is to choose <i>k</i> balls, similar to MSR but the goal is to minimize the sum of squares of radii of the balls. We present a 3.389-approximation for MSR and a 6.546-approximation for MSD, improving over respective 3.504 and 7.008 developed by Charikar and Panigrahy (2001). In particular, our guarantee for MSD is better than twice our guarantee for MSR. Note that since our result, Buchem et al. proved a <span>(3+epsilon )</span>-approximation for MSR. In the case of MSSR, the best known approximation guarantee is <span>(4cdot (540)^{2})</span> based on the work of Bhowmick, Inamdar, and Varadarajan in their general analysis of the <i>t</i>-Metric Multicover Problem. Furthermore, our analysis yields an 11.078-approximation algorithm for the Minimum Sum of Squared Radii problem</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607403","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":"Sweeping Arrangements of Non-Piercing Regions in the Plane","authors":"Suryendu Dalal,&nbsp;Rahul Gangopadhyay,&nbsp;Rajiv Raman,&nbsp;Saurabh Ray","doi":"10.1007/s00453-026-01380-w","DOIUrl":"10.1007/s00453-026-01380-w","url":null,"abstract":"<div><p>Let <span>(Gamma )</span> be an arrangement of Jordan curves in the plane, i.e., simple closed curves in the plane. For any curve <span>(gamma in Gamma )</span>, we denote the bounded region enclosed by <span>(gamma )</span> as <span>(tilde{gamma })</span>. We say that <span>(Gamma )</span> is non-piercing if for any two curves <span>(alpha , beta in Gamma )</span>, both <span>(tilde{alpha } ,setminus , tilde{beta })</span> and <span>(tilde{beta },setminus ,tilde{beta })</span> is connected. A non-piercing arrangement of curves generalizes a set of 2-intersecting curves in which each pair of curves intersect in at most two points. Snoeyink and Hershberger (“Sweeping Arrangements of Curves”, SoCG ’89) proved that if we are given an arrangement <span>(Gamma )</span> of 2-intersecting curves and a <i>sweep</i> curve <span>(gamma in {Gamma })</span>, then the arrangement can be <i>swept</i> by <span>(gamma )</span> while always maintaining the 2-intersecting property of the curves in <span>(Gamma )</span>. We generalize the result of Snoeyink and Hershberger to the setting of non-piercing arrangements. Given an arrangement <span>(Gamma )</span> of non-piercing curves, a sweep curve <span>(gamma in Gamma )</span>, and a point <i>P</i> in <span>(tilde{gamma })</span>, we show that we can continuously shrink <span>(gamma )</span> to <i>P</i> so that throughout the process, the arrangement remains non-piercing (except at a finite set of points in time where <span>(gamma )</span> crosses other curves), and <i>P</i> lies in <span>(tilde{gamma })</span>. We show that our arguments can be modified if <i>P</i> lies outside <span>(tilde{gamma })</span>, and we want to sweep <span>(gamma )</span> <i>outwards</i> so that <i>P</i> lies outside <span>(tilde{gamma })</span>, and the arrangement remains non-piercing. We give several applications of our results to combinatorial and algorithmic questions including to the <i>multi-hitting set</i> problem involving points and non-piercing regions.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561095","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 SLO Hierarchy of Pseudo-Boolean Functions and Runtime of Evolutionary Algorithms","authors":"Duc-Cuong Dang,&nbsp;Per Kristian Lehre","doi":"10.1007/s00453-025-01359-z","DOIUrl":"10.1007/s00453-025-01359-z","url":null,"abstract":"<div><p>While some common fitness landscape characteristics are critical when determining the runtime of evolutionary algorithms (EAs), the relationship between fitness landscape structure and the runtime of EAs is poorly understood. Recently, Dang, Eremeev, and Lehre introduced a classification of pseudo-Boolean problems showing that “sparsity” of local optima and the “density” of fitness valleys can be crucial characteristics when determining the runtime of EAs Dang et al. (in Proceedings of the Genetic and Evolutionary Computation Conference. Association for Computing Machinery, New York, NY, USA, GECCO’21, pp 1133–1141, https://doi.org/10.1145/3449639.3459398, 2021c). However, their approach could only classify some classes of pseudo-Boolean functions and thus defined an incomplete hierarchy. We generalise the previous work to a complete hierarchy for all pseudo-Boolean functions, denoted <span>Slo</span><span>(^alpha _{varepsilon ,r})</span>. The hierarchy is consistent with existing results for the runtime of EAs. The easiest problems are in <span>Slo</span><span>(^{alpha }_{varepsilon })</span> for <span>(alpha =1)</span> and <span>(varepsilon =0)</span>. As we increase <span>(varepsilon )</span> and decrease <span>(alpha )</span>, the function class contains more interesting functions, including instances of hard combinatorial optimisation problems and problems perturbed by static noise. For <span>(alpha =O(1/n))</span> and <span>(varepsilon =1,)</span> the problem class contains every problem, including problems closed under permutation (No Free Lunch). Problem classes where local optima sparsity exceed fitness valley density are shown to have exponential black-box complexity. We also study how random perturbations of a function can change its classification. E.g., randomly perturbing search points in <span>OneMax</span> with constant probability leads to a problem class that can still be optimised efficiently with appropriately tuned non-elitist EAs.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13013112/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147522531","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":"Shortest Two Disjoint Paths in Conservative Graphs","authors":"Ildikó Schlotter","doi":"10.1007/s00453-026-01375-7","DOIUrl":"10.1007/s00453-026-01375-7","url":null,"abstract":"<div><p>We consider the following problem that we call the <span>Shortest Two Disjoint Paths</span> problem: given an undirected graph <span>(G=(V,E))</span> with edge weight function <span>({w:Erightarrow mathbb {R}})</span>, two terminals <i>s</i> and <i>t</i> in <i>G</i>, find two internally vertex-disjoint paths between <i>s</i> and <i>t</i> with minimum total weight. As shown recently by Schlotter and Sebő (2022), this problem becomes <span>(textsf{NP})</span>-hard if edges can have negative weights, even if the weight function is conservative, i.e., there are no cycles in <i>G</i> with negative total weight. We propose a polynomial-time algorithm that solves the <span>Shortest Two Disjoint Paths</span> problem for conservative weights in the case when the negative-weight edges form a constant number of trees in <i>G</i>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01375-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561240","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":"Max-Utility Matchings with Popularity via Critical Vertices","authors":"Telikepalli Kavitha","doi":"10.1007/s00453-025-01347-3","DOIUrl":"10.1007/s00453-025-01347-3","url":null,"abstract":"<div><p>Let <i>G</i> be a bipartite graph where every vertex has a strict preference order over its neighbors. The preferences of a vertex over its neighbors extend naturally to preferences over matchings. A matching <i>N</i> is more <i>popular</i> than matching <i>M</i> if the vertices that prefer <i>N</i> to <i>M</i> outnumber those that prefer <i>M</i> to <i>N</i>. A matching <i>M</i> is popular if there is no matching more popular than <i>M</i>. Every stable matching is popular, thus popular matchings always exist in <i>G</i> and can be efficiently computed. We consider the following problem: edges in <i>G</i> have utilities and it is only max-utility matchings that are relevant. Our goal is to find a <i>popular max-utility matching</i>, i.e., a max-utility matching <i>M</i> such that there is no max-utility matching more popular than <i>M</i>. We show there always exists a popular max-utility matching; furthermore, such a matching can be efficiently computed. The popular <i>critical</i> matching algorithm is the key subroutine in our algorithm. Given a set of prioritized or critical vertices in <i>G</i>, we are interested in only those matchings that match as many critical vertices as possible. We call such matchings “critical” and seek a <i>popular critical matching</i>, i.e., a critical matching <i>M</i> such that there is no critical matching more popular than <i>M</i>. We show popular critical matchings always exist in <i>G</i> and a min-size/max-size such matching can be efficiently computed. We focus on max-size critical matchings and show a compact extended formulation for the <i>popular max-critical</i> matching polytope, i.e., the polytope of max-size critical matchings that are popular within the set of all max-size critical matchings. Thus we can efficiently solve linear optimization problems over the set of popular max-size critical matchings.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01347-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560418","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":"Testing Isomorphism of Chordal Graphs of Bounded Leafage is Fixed-Parameter Tractable","authors":"Vikraman Arvind,&nbsp;Roman Nedela,&nbsp;Ilia Ponomarenko,&nbsp;Peter Zeman","doi":"10.1007/s00453-026-01374-8","DOIUrl":"10.1007/s00453-026-01374-8","url":null,"abstract":"<div><p>The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general graph isomorphism problem. Every chordal graph can be represented as the intersection graph of some subtrees of a representing tree, and the leafage of a chordal graph is defined to be the minimum number of leaves in a representing tree for it. We prove that chordal graph isomorphism is fixed parameter tractable with leafage as parameter. In the process, we introduce the problem of isomorphism testing for higher-order hypergraphs and show that finding the automorphism group of an order-<span>({k})</span> hypergraph of size <i>s</i> with vertex color classes of size at most <i>b</i> can be done in time <span>((b!,s)^{O(k)})</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560088","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}