Algorithmica最新文献

{"title":"Constrained Truthful Obnoxious Two-Facility Location with Optional Preferences","authors":"Panagiotis Kanellopoulos,&nbsp;Alexandros A. Voudouris","doi":"10.1007/s00453-026-01391-7","DOIUrl":"10.1007/s00453-026-01391-7","url":null,"abstract":"<div><p>We consider a truthful facility location problem with agents that have private positions on the line of real numbers and known optional preferences over two obnoxious facilities that must be placed at locations chosen from a given set of candidate ones. Each agent wants to maximize the sum of distances from the facilities that affect her, and our goal is to design mechanisms that decide where to place the facilities so as to maximize the total happiness of the agents as well as provide the right incentives to them to truthfully report their positions. We consider separately the setting in which all agents are affected by both facilities (i.e., they have non-optional preferences) and the general optional setting. We show tight bounds on the approximation ratio of deterministic strategyproof mechanisms for both settings, and almost tight bounds for randomized mechanisms.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01391-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829245","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":"Fast and Simple Sorting Using Partial Information","authors":"Bernhard Haeupler,&nbsp;Richard Hladík,&nbsp;John Iacono,&nbsp;Václav Rozhoň,&nbsp;Robert E. Tarjan,&nbsp;Jakub Tětek","doi":"10.1007/s00453-026-01387-3","DOIUrl":"10.1007/s00453-026-01387-3","url":null,"abstract":"<div><p>We consider the problem of sorting <i>n</i> items, given the outcomes of <i>m</i> pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in <span>(textrm{O}(m+log T))</span> time and does <span>(textrm{O}(log T))</span> comparisons, where <i>T</i> is the number of total orders consistent with the pre-existing comparisons. Our running time and comparison bounds are best possible up to constant factors, thus resolving a problem that has been studied intensely since 1976 (Fredman, Theoretical Computer Science). The best previous algorithm with a bound of <span>(textrm{O}(log T))</span> on the number of comparisons has a time bound of <span>(textrm{O}(n^{2.5}))</span> and is more complicated. Our algorithm combines three classic algorithms: topological sort, heapsort with the right kind of heap, and efficient search in a sorted list. It outputs the items in sorted order one by one. It can be modified to stop early, thereby solving the important and more general top-<i>k</i> sorting problem: Given <i>k</i> and the outcomes of some pre-existing comparisons, output the smallest <i>k</i> items in sorted order. The modified algorithm solves the top-<i>k</i> sorting problem in minimum time and comparisons, to within constant factors.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829714","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":"Zip-zip Trees: Making Zip Trees More Balanced, Biased, Compact, or Persistent","authors":"Ofek Gila,&nbsp;Michael T. Goodrich,&nbsp;Robert E. Tarjan","doi":"10.1007/s00453-025-01364-2","DOIUrl":"10.1007/s00453-025-01364-2","url":null,"abstract":"<div><p>We define simple variants of zip trees, called <i>zip-zip trees</i>, which provide several advantages over zip trees, including overcoming a bias that favors smaller keys over larger ones. We analyze zip-zip trees theoretically and empirically, showing, e.g., that the expected depth of a node in an <i>n</i>-node zip-zip tree is at most <span>(1.3863log n-1+o(1))</span>, which matches the expected depth of treaps and binary search trees built by uniformly random insertions. Unlike these other data structures, however, zip-zip trees achieve their bounds using only <span>(O(log log n))</span> bits of metadata per node, w.h.p., as compared to the <span>(Theta (log n))</span> bits per node required by treaps. In addition, we describe a “just-in-time” zip-zip tree variant, which needs just an expected <i>O</i>(1) number of bits of metadata per node. Moreover, we can define zip-zip trees to be strongly history independent, whereas treaps are generally only weakly history independent. We also introduce <i>biased zip-zip trees</i>, which have an explicit bias based on key weights, so the expected depth of a key, <i>k</i>, with weight, <span>(w_k)</span>, is <span>(O(log (W/w_k)))</span>, where <i>W</i> is the weight of all keys in the weighted zip-zip tree. Finally, we show that one can easily make zip-zip trees partially persistent with only <i>O</i>(<i>n</i>) space overhead w.h.p.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-025-01364-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738086","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":"Parameterized Complexities of Dominating and Independent Set Reconfiguration","authors":"Hans L. Bodlaender,&nbsp;Carla Groenland,&nbsp;Céline M. F. Swennenhuis","doi":"10.1007/s00453-026-01381-9","DOIUrl":"10.1007/s00453-026-01381-9","url":null,"abstract":"<div><p>We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves, XNL-complete when a maximum length <span>(ell )</span> for the sequence is given in binary in the input, and XNLP-complete when <span>(ell )</span> is given in unary. The problems were known to be <span>(textrm{W}[1])</span>- and <span>(textrm{W}[2])</span>-hard respectively when <span>(ell )</span> is also a parameter. We complete the picture by showing membership in those classes. Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13083404/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147724523","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":"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}