Algorithmica最新文献

{"title":"Faster Combinatorial k-Clique Algorithms","authors":"Amir Abboud,&nbsp;Nick Fischer,&nbsp;Yarin Shechter","doi":"10.1007/s00453-026-01390-8","DOIUrl":"10.1007/s00453-026-01390-8","url":null,"abstract":"<div><p>Detecting if a graph contains a <i>k</i>-Clique is one of the most fundamental problems in computer science. The asymptotically fastest algorithm runs in time <span>(O(n^{omega k/3}))</span>, where <span>(omega )</span> is the exponent of Boolean matrix multiplication. To date, this is the only technique capable of beating the trivial <span>(O(n^k))</span> bound by a polynomial factor. Due to this technique’s various limitations, much effort has gone into designing “combinatorial” algorithms that improve over exhaustive search via other techniques. The first contribution of this work is a faster combinatorial algorithm for <i>k</i>-Clique, improving Vassilevska’s bound of <span>(O(n^{k}/log ^{k-1}{n}))</span> by two log factors. Technically, our main result is a new reduction from <i>k</i>-Clique to Triangle detection that exploits the same divide-and-conquer at the core of recent combinatorial algorithms by Chan (SODA’15) and Yu (ICALP’15). Our second contribution is exploiting combinatorial techniques to improve the state-of-the-art (even of non-combinatorial algorithms) for generalizations of the <i>k</i>-Clique problem. Specifically we introduce the first non-trivial clique listing algorithms: A general algorithm for detecting cliques in hypergraphs that also improves the state of the art for detection, and an additional algorithm for the specific case of triangle listing with improved bounds.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01390-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009404","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":"Fully Characterizing Lossy Catalytic Computation","authors":"Marten Folkertsma,&nbsp;Ian Mertz,&nbsp;Florian Speelman,&nbsp;Quinten Tupker","doi":"10.1007/s00453-026-01376-6","DOIUrl":"10.1007/s00453-026-01376-6","url":null,"abstract":"<div><p>A <i>catalytic machine</i> is a model of computation where a traditional space-bounded machine is augmented with an additional, significantly larger, “catalytic” tape, which, while being available as a work tape, has the caveat of being initialized with an arbitrary string, which must be preserved at the end of the computation. Despite this restriction, catalytic machines have been shown to have surprising additional power; a logspace machine with a polynomial length catalytic tape, known as <i>catalytic logspace</i> (<span>({textsf {CL}} )</span>), can compute problems which are believed to be impossible for <span>(textsf {L} )</span>. A fundamental question of the model is whether the catalytic condition, of leaving the catalytic tape in its exact original configuration, is robust to minor deviations. This study was initialized by Gupta et al. (2024), who defined <i>lossy catalytic logspace</i> (<span>({textsf {LCL}} [e])</span>) as a variant of <span>({textsf {CL}} )</span> where we allow up to <i>e</i> errors when resetting the catalytic tape. They showed that <span>({textsf {LCL}} [e] = {textsf {CL}} )</span> for any <span>(e = O(1))</span>, which remains the frontier of our understanding. In this work we completely characterize lossy catalytic space (<span>({textsf {LCSPACE}} [s,c,e])</span>) in terms of ordinary catalytic space (<span>({textsf {CSPACE}} [s,c])</span>). We show that </p><div><div><span>$$begin{aligned} {textsf {LCSPACE}} [s,c,e] = {textsf {CSPACE}} [Theta (s + e log c), Theta (c)] end{aligned}$$</span></div></div><p>In other words, allowing <i>e</i> errors on a catalytic tape of length <i>c</i> is equivalent, up to a constant stretch, to an equivalent errorless catalytic machine with an additional <span>(e log c)</span> bits of ordinary working memory. As a consequence, we show that for any <i>e</i>, <span>({textsf {LCL}} [e] = {textsf {CL}} )</span> implies <span>({textsf {SPACE}} [e log n] subseteq {textsf {ZPP}} )</span>, thus giving a barrier to any improvement beyond <span>({textsf {LCL}} [O(1)] = {textsf {CL}} )</span>. We also extend all our results to every variant of catalytic space.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01376-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009024","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":"Computing Pivot-Minors","authors":"Konrad K. Dabrowski,&nbsp;François Dross,&nbsp;Jisu Jeong,&nbsp;Mamadou Moustapha Kanté,&nbsp;O-joung Kwon,&nbsp;Sang-il Oum,&nbsp;Daniël Paulusma","doi":"10.1007/s00453-026-01393-5","DOIUrl":"10.1007/s00453-026-01393-5","url":null,"abstract":"<div><p>A graph <i>G</i> contains a graph <i>H</i> as a pivot-minor if <i>H</i> can be obtained from <i>G</i> by applying a sequence of vertex deletions and edge pivots. Pivot-minors play an important role in the study of rank-width. Pivot-minors have mainly been studied from a structural perspective. In this paper we perform the first systematic computational complexity study of pivot-minors. We first prove that the <span>Pivot-Minor</span> problem, which asks if a given graph <i>G</i> contains a pivot-minor isomorphic to a given graph <i>H</i>, is <span>NP</span>-complete. If <i>H</i> is not part of the input, we denote the problem by <i>H</i>-<span>Pivot-Minor</span>. We give a certifying polynomial-time algorithm for <i>H</i><span>-Pivot-Minor</span> when</p><ul>\u0000 <li>\u0000 <p><i>H</i> is an induced subgraph of <span>(P_3+tP_1)</span> for some integer <span>(tge 0)</span>,</p>\u0000 </li>\u0000 <li>\u0000 <p><span>(H=K_{1,t})</span> for some integer <span>(tge 1)</span>, or</p>\u0000 </li>\u0000 <li>\u0000 <p><span>(|V(H)|le 4)</span> except when <span>(H in {K_4,C_3+P_1})</span>.</p>\u0000 </li>\u0000 </ul><p> Let <span>(mathcal{F}_H)</span> be the set of induced-subgraph-minimal graphs that contain a pivot-minor isomorphic to <i>H</i>. To prove the above statement, we either show that there is an integer <span>(c_H)</span> such that all graphs in <span>(mathcal{F}_H)</span> have at most <span>(c_H)</span> vertices, or we determine <span>(mathcal{F}_H)</span> precisely, for each of the above cases.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009023","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":"Ex-post Stability under Two-Sided Matching: Complexity and Characterization","authors":"Haris Aziz,&nbsp;Péter Biró,&nbsp;Gergely Csáji,&nbsp;Ali Pourmiri","doi":"10.1007/s00453-026-01388-2","DOIUrl":"10.1007/s00453-026-01388-2","url":null,"abstract":"<div><p>We study the problem of determining whether a given random matching can be implemented as a lottery over weakly stable deterministic matchings – a property known as ex-post stability. This concept arises in randomized allocation mechanisms such as school choice, where stability in each realized outcome is essential for fairness. Despite its importance in practice, the computational complexity of verifying ex-post stability has remained unresolved. We settle this question by showing that testing ex-post stability is NP-complete, even under highly restricted conditions – specifically, when both sides have dichotomous preferences or one of the sides has strict preferences. On the positive side, we present an integer programming formulation that finds a decomposition of a random matching with maximum weight on stable matchings. We also consider stronger versions of ex-post stability (in particular robust ex-post stability and ex-post strong stability) and prove that they can be tested in polynomial time.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01388-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938613","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":"Sparse Suffix and LCP Array: Simple, Direct, Small, and Fast","authors":"Lorraine A. K. Ayad,&nbsp;Grigorios Loukides,&nbsp;Solon P. Pissis,&nbsp;Hilde Verbeek","doi":"10.1007/s00453-026-01383-7","DOIUrl":"10.1007/s00453-026-01383-7","url":null,"abstract":"<div><p>Sparse suffix sorting is the problem of sorting <span>(b=o(n))</span> suffixes of a string of length <i>n</i>. Efficient sparse suffix sorting algorithms have existed for more than a decade. Despite the multitude of works and their justified claims for applications in text indexing, the existing algorithms have not been employed by practitioners. Arguably this is because there are no simple, direct, <i>and</i> efficient algorithms for sparse suffix array construction. We provide two new algorithms for constructing the sparse suffix and LCP arrays that are simultaneously simple, direct, small, and fast. In particular, our algorithms are: <i>simple</i> in the sense that they can be implemented using only basic data structures; <i>direct</i> in the sense that the output arrays are not a byproduct of constructing the sparse suffix tree or an LCE data structure; <i>fast</i> in the sense that they run in <span>(mathcal {O}(nlog b))</span> time, in the worst case, or in <span>(mathcal {O}(n))</span> time, when the total number of suffixes with an LCP value greater than <span>(2^{lfloor log frac{n}{b} rfloor + 1}-1)</span> is in <span>(mathcal {O}(b/log b))</span>, matching the time of optimal yet much more complicated algorithms [Gawrychowski and Kociumaka, SODA 2017; Birenzwige et al., SODA 2020]; and <i>small</i> in the sense that they can be implemented using <i>only</i> <span>(8b+o(b))</span> machine words. Our algorithms are non-trivial space-efficient adaptations of the Monte Carlo algorithm by I et al. for constructing the sparse suffix tree in <span>(mathcal {O}(nlog b))</span> time [STACS 2014]. We provide extensive experiments to justify our claims on simplicity and on efficiency. A preliminary version of this paper appeared in the proceedings of LATIN 2024.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-026-01383-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938355","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":"Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment","authors":"Tomer Ezra,&nbsp;Stefano Leonardi,&nbsp;Michał Pawłowski,&nbsp;Matteo Russo,&nbsp;Seeun William Umboh","doi":"10.1007/s00453-026-01389-1","DOIUrl":"10.1007/s00453-026-01389-1","url":null,"abstract":"<div><p>The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [44] developed a non-clairvoyant framework that provided an <span>(O(sqrt{n log n}))</span> upper bound for a wide class of generalized JRP, where <i>n</i> is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed <i>disjoint</i>. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight <span>(O(sqrt{n}))</span>-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is <span>(Omega (sqrt{n log n}))</span>-competitive for both of these problems.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"88 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937794","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":"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}