{"title":"Reforming an Envy-Free Matching","authors":"Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki","doi":"10.1007/s00453-025-01294-z","DOIUrl":"10.1007/s00453-025-01294-z","url":null,"abstract":"<div><p>We consider the problem of reforming an envy-free matching when each agent has a strict preference over items and is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain. We also give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 4","pages":"594 - 620"},"PeriodicalIF":0.9,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668425","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}
AlgorithmicaPub Date : 2025-01-11DOI: 10.1007/s00453-024-01292-7
Omrit Filtser, Erik Krohn, Bengt J. Nilsson, Christian Rieck, Christiane Schmidt
{"title":"Guarding Polyominoes Under k-Hop Visibility","authors":"Omrit Filtser, Erik Krohn, Bengt J. Nilsson, Christian Rieck, Christiane Schmidt","doi":"10.1007/s00453-024-01292-7","DOIUrl":"10.1007/s00453-024-01292-7","url":null,"abstract":"<div><p>We study the <span>Art Gallery Problem</span> under <i>k</i>-hop visibility in polyominoes. In this visibility model, two unit squares of a polyomino can see each other if and only if the shortest path between the respective vertices in the dual graph of the polyomino has length at most <i>k</i>. In this paper, we show that the VC dimension of this problem is 3 in simple polyominoes, and 4 in polyominoes with holes. Furthermore, we provide a reduction from <span>Planar Monotone 3Sat</span>, thereby showing that the problem is <span>NP</span>-complete even in thin polyominoes (i.e., polyominoes that do not a contain a <span>(2times 2)</span> block of cells). Complementarily, we present a linear-time 4-approximation algorithm for simple 2-thin polyominoes (which do not contain a <span>(3times 3)</span> block of cells) for all <span>(kin {mathbb {N}})</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 4","pages":"572 - 593"},"PeriodicalIF":0.9,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01292-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668301","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}
AlgorithmicaPub Date : 2025-01-08DOI: 10.1007/s00453-024-01290-9
Samuel Baguley, Tobias Friedrich, Aneta Neumann, Frank Neumann, Marcus Pappik, Ziena Zeif
{"title":"Fixed Parameter Multi-Objective Evolutionary Algorithms for the W-Separator Problem","authors":"Samuel Baguley, Tobias Friedrich, Aneta Neumann, Frank Neumann, Marcus Pappik, Ziena Zeif","doi":"10.1007/s00453-024-01290-9","DOIUrl":"10.1007/s00453-024-01290-9","url":null,"abstract":"<div><p>Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of evolutionary multi-objective algorithms for the <i>W</i>-separator problem, which is a natural generalization of the vertex cover problem. The goal is to remove the minimum number of vertices such that each connected component in the resulting graph has at most <i>W</i> vertices. We provide different multi-objective formulations involving two or three objectives that provably lead to fixed-parameter evolutionary algorithms with respect to the value of an optimal solution <i>OPT</i> and <i>W</i>. Of particular interest are kernelizations and the reducible structures used for them. We show that in expectation the algorithms make incremental progress in finding such structures and beyond. The current best known kernelization of the <i>W</i>-separator uses linear programming methods and requires non-trivial post-processing steps to extract the reducible structures. We provide additional structural features to show that evolutionary algorithms with appropriate objectives are also capable of extracting them. Our results show that evolutionary algorithms with different objectives guide the search and admit fixed parameterized runtimes to solve or approximate (even arbitrarily close) the <i>W</i>-separator problem.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 4","pages":"537 - 571"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01290-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668295","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}
AlgorithmicaPub Date : 2025-01-05DOI: 10.1007/s00453-024-01289-2
Matthew Johnson, Barnaby Martin, Jelle J. Oostveen, Sukanya Pandey, Daniël Paulusma, Siani Smith, Erik Jan van Leeuwen
{"title":"Complexity Framework for Forbidden Subgraphs I: The Framework","authors":"Matthew Johnson, Barnaby Martin, Jelle J. Oostveen, Sukanya Pandey, Daniël Paulusma, Siani Smith, Erik Jan van Leeuwen","doi":"10.1007/s00453-024-01289-2","DOIUrl":"10.1007/s00453-024-01289-2","url":null,"abstract":"<div><p>For a set of graphs <span>({mathcal {H}})</span>, a graph <i>G</i> is <span>({mathcal {H}})</span>-subgraph-free if <i>G</i> does not contain any graph from <span>({{{mathcal {H}}}})</span> as a subgraph. We propose general and easy-to-state conditions on graph problems that explain a large set of results for <span>({mathcal {H}})</span>-subgraph-free graphs. Namely, a graph problem must be efficiently solvable on graphs of bounded treewidth, computationally hard on subcubic graphs, and computational hardness must be preserved under edge subdivision of subcubic graphs. Our meta-classification says that if a graph problem <span>(Pi )</span> satisfies all three conditions, then for every finite set <span>({{{mathcal {H}}}})</span>, it is “efficiently solvable” on <span>({{{mathcal {H}}}})</span>-subgraph-free graphs if <span>({mathcal {H}})</span> contains a disjoint union of one or more paths and subdivided claws, and <span>(Pi )</span> is “computationally hard” otherwise. We apply our <i>meta-classification</i> on many well-known partitioning, covering and packing problems, network design problems and width parameter problems to obtain a dichotomy between polynomial-time solvability and <span>NP</span>-completeness. For distance-metric problems, we obtain a dichotomy between almost-linear-time solvability and having no subquadratic-time algorithm (conditioned on some hardness hypotheses). Apart from capturing a large number of explicitly and implicitly known results in the literature, we also prove a number of new results. Moreover, we perform an extensive comparison between the subgraph framework and the existing frameworks for the minor and topological minor relations, and pose several new open problems and research directions.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 3","pages":"429 - 464"},"PeriodicalIF":0.9,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01289-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446414","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}
AlgorithmicaPub Date : 2025-01-03DOI: 10.1007/s00453-024-01291-8
Kamal Eyubov, Marcelo Fonseca Faraj, Christian Schulz
{"title":"FREIGHT: Fast Streaming Hypergraph Partitioning","authors":"Kamal Eyubov, Marcelo Fonseca Faraj, Christian Schulz","doi":"10.1007/s00453-024-01291-8","DOIUrl":"10.1007/s00453-024-01291-8","url":null,"abstract":"<div><p>Partitioning the vertices of a (hyper)graph into <i>k</i> roughly balanced blocks such that few (hyper)edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge (hyper)graphs using low computational resources are streaming algorithms. In this work, we propose FREIGHT: a Fast stREamInG Hypergraph parTitioning algorithm which is an adaptation of the widely-known graph-based algorithm Fennel. By using an efficient data structure, we make the overall running of FREIGHT linearly dependent on the pin-count of the hypergraph and the memory consumption linearly dependent on the numbers of nets and blocks. The results of our extensive experimentation showcase the promising performance of FREIGHT as a highly efficient and effective solution for streaming hypergraph partitioning. Our algorithm demonstrates competitive running time with the Hashing algorithm, with a geometric mean runtime within a factor of four compared to the Hashing algorithm. Significantly, our findings highlight the superiority of FREIGHT over all existing (buffered) streaming algorithms and even the in-memory algorithm HYPE, with respect to both cut-net and connectivity measures. This indicates that our proposed algorithm is a promising hypergraph partitioning tool to tackle the challenge posed by large-scale and dynamic data processing.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 3","pages":"405 - 428"},"PeriodicalIF":0.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01291-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446391","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}
AlgorithmicaPub Date : 2024-12-23DOI: 10.1007/s00453-024-01283-8
Thomas Bläsius, Max Göttlicher
{"title":"An Efficient Algorithm for Power Dominating Set","authors":"Thomas Bläsius, Max Göttlicher","doi":"10.1007/s00453-024-01283-8","DOIUrl":"10.1007/s00453-024-01283-8","url":null,"abstract":"<div><p>The problem <span>Power Dominating Set</span> (<span>PDS</span>) is motivated by the placement of phasor measurement units to monitor electrical networks. It asks for a minimum set of vertices in a graph that observes all remaining vertices by exhaustively applying two observation rules. Our contribution is twofold. First, we determine the parameterized complexity of <span>PDS</span> by proving it is <i>W</i>[<i>P</i>]-complete when parameterized with respect to the solution size. We note that it was only known to be <i>W</i>[2]-hard before. Our second and main contribution is a new algorithm for <span>PDS</span> that efficiently solves practical instances. Our algorithm consists of two complementary parts. The first is a set of reduction rules for <span>PDS</span> that can also be used in conjunction with previously existing algorithms. The second is an algorithm for solving the remaining kernel based on the implicit hitting set approach. Our evaluation on a set of power grid instances from the literature shows that our solver outperforms previous state-of-the-art solvers for <span>PDS</span> by more than one order of magnitude on average. Furthermore, our algorithm can solve previously unsolved instances of continental scale within a few minutes.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 3","pages":"344 - 376"},"PeriodicalIF":0.9,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01283-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446557","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}
AlgorithmicaPub Date : 2024-12-23DOI: 10.1007/s00453-024-01288-3
Pedro Montealegre, Diego Ramírez-Romero, Ivan Rapaport
{"title":"Shared Versus Private Randomness in Distributed Interactive Proofs","authors":"Pedro Montealegre, Diego Ramírez-Romero, Ivan Rapaport","doi":"10.1007/s00453-024-01288-3","DOIUrl":"10.1007/s00453-024-01288-3","url":null,"abstract":"<div><p>In distributed interactive proofs, the nodes of a graph G interact with a powerful but untrustable prover who tries to convince them, in a small number of rounds and through short messages, that G satisfies some property. This series of rounds is followed by a phase of distributed verification, which may be either deterministic or randomized, where nodes exchange messages with their neighbors. The nature of this last verification round defines the two types of interactive protocols. We say that the protocol is of Arthur–Merlin type if the verification round is deterministic. We say that the protocol is of Merlin–Arthur type if, in the verification round, the nodes are allowed to use a fresh set of random bits. In the original model introduced by Kol, Oshman, and Saxena [PODC 2018], the randomness was private in the sense that each node had only access to an individual source of random coins. Crescenzi, Fraigniaud, and Paz [DISC 2019] initiated the study of the impact of shared randomness (the situation where the coin tosses are visible to all nodes) in the distributed interactive model. In this work, we continue that research line by showing that the impact of the two forms of randomness is very different depending on whether we are considering Arthur–Merlin protocols or Merlin–Arthur protocols. While private randomness gives more power to the first type of protocols, shared randomness provides more power to the second. We also show that there exists at most an exponential gap between the certificate size in distributed interactive proofs with respect to distributed verification protocols without any randomness.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 3","pages":"377 - 404"},"PeriodicalIF":0.9,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446558","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}
AlgorithmicaPub Date : 2024-12-11DOI: 10.1007/s00453-024-01286-5
Jurek Czyzowicz, Leszek Gąsieniec, Ryan Killick, Evangelos Kranakis
{"title":"Symmetry Breaking in the Plane","authors":"Jurek Czyzowicz, Leszek Gąsieniec, Ryan Killick, Evangelos Kranakis","doi":"10.1007/s00453-024-01286-5","DOIUrl":"10.1007/s00453-024-01286-5","url":null,"abstract":"<div><p>We study a fundamental question related to the feasibility of deterministic symmetry breaking in the infinite Euclidean plane for two robots that have minimal or no knowledge of the respective capabilities and “measuring instruments” of themselves and each other. Assume that two anonymous mobile robots are placed at different locations at unknown distance <i>d</i> from each other on the infinite Euclidean plane. Each robot knows neither the location of itself nor of the other robot. The robots cannot communicate wirelessly, but have a certain nonzero visibility radius <i>r</i> (with range <i>r</i> unknown to the robots). By rendezvous we mean that they are brought at distance at most <i>r</i> of each other by executing symmetric (identical) mobility algorithms. The robots are moving with unknown and constant but not necessarily identical speeds, their clocks and pedometers may be asymmetric, and their chirality inconsistent. We demonstrate that rendezvous for two robots is feasible under the studied model iff the robots have either: different speeds; or different clocks; or different orientations but equal chiralities. When the rendezvous is feasible, we provide a universal algorithm which always solves rendezvous despite the fact that the robots have no knowledge of which among their respective parameters may be different.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 3","pages":"321 - 343"},"PeriodicalIF":0.9,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01286-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446411","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}
AlgorithmicaPub Date : 2024-12-10DOI: 10.1007/s00453-024-01287-4
Telikepalli Kavitha
{"title":"Popular Roommates in Simply Exponential Time","authors":"Telikepalli Kavitha","doi":"10.1007/s00453-024-01287-4","DOIUrl":"10.1007/s00453-024-01287-4","url":null,"abstract":"<div><p>We consider the popular matching problem in a <i>roommates</i> instance <i>G</i> on <i>n</i> vertices, i.e., <i>G</i> is a graph where each vertex has a strict preference order over its neighbors. A matching <i>M</i> is <i>popular</i> if there is no matching <i>N</i> such that the vertices that prefer <i>N</i> to <i>M</i> outnumber those that prefer <i>M</i> to <i>N</i>. It is known that it is NP-hard to decide if <i>G</i> admits a popular matching or not. There is no better algorithm known for this problem than the brute force algorithm that enumerates all matchings and tests each for popularity—this could take <i>n</i>! time. Here we show an <span>(O^*(k^n))</span> time algorithm for this problem, where <span>(k < 7.32)</span>. We use the recent breakthrough result on the maximum number of stable matchings possible in a roommates instance to analyze our algorithm for the popular matching problem. We identify a natural (also, hard) subclass of popular matchings called <i>truly popular</i> matchings that are “popular fractional” and show an <span>(O^*(2^n))</span> time algorithm for the truly popular matching problem in <i>G</i>. We also identify a subclass of max-size popular matchings called <i>super-dominant</i> matchings and show a linear time algorithm for the super-dominant roommates problem.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 2","pages":"292 - 320"},"PeriodicalIF":0.9,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01287-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396525","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}
AlgorithmicaPub Date : 2024-12-09DOI: 10.1007/s00453-024-01285-6
Elahe Ghasemi, Vincent Jugé, Ghazal Khalighinejad, Helia Yazdanyar
{"title":"Galloping in Fast-Growth Natural Merge Sorts","authors":"Elahe Ghasemi, Vincent Jugé, Ghazal Khalighinejad, Helia Yazdanyar","doi":"10.1007/s00453-024-01285-6","DOIUrl":"10.1007/s00453-024-01285-6","url":null,"abstract":"<div><p>We study the impact of merging routines in merge-based sorting algorithms. More precisely, we focus on the <i>galloping</i> routine that TimSort uses to merge monotonic sub-arrays, hereafter called <i>runs</i>, and on the impact on the number of element comparisons performed if one uses this routine instead of a naïve merging routine. This routine was introduced in order to make TimSort more efficient on arrays with few distinct values. Alas, we prove that, although it makes TimSort sort array with two values in linear time, it does not prevent TimSort from requiring up to <span>(Theta (n log (n)))</span> element comparisons to sort arrays of length <i>n</i> with three distinct values. However, we also prove that slightly modifying TimSort ’s galloping routine results in requiring only <span>(mathcal {O}(n + n log (sigma )))</span> element comparisons in the worst case, when sorting arrays of length <i>n</i> with <span>(sigma )</span> distinct values. We do so by focusing on the notion of <i>dual runs</i>, which was introduced in the 1990s, and on the associated <i>dual run-length entropy</i>. This notion is both related to the number of distinct values and to the number of runs in an array, which came with its own <i>run-length entropy</i> that was used to explain TimSort ’s otherwise “supernatural” efficiency. We also introduce new notions of <i>fast-</i> and <i>middle-growth</i> for natural merge sorts (i.e., algorithms based on merging runs), which are found in several sorting algorithms similar to TimSort. We prove that algorithms with the fast- or middle-growth property, provided that they use our variant of TimSort ’s galloping routine for merging runs, are as efficient as possible at sorting arrays with low run-induced or dual-run-induced complexities.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 2","pages":"242 - 291"},"PeriodicalIF":0.9,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396524","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}
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