Algorithmica最新文献

{"title":"Testing Connectedness of Images","authors":"Piotr Berman,&nbsp;Meiram Murzabulatov,&nbsp;Sofya Raskhodnikova,&nbsp;Dragos-Florian Ristache","doi":"10.1007/s00453-024-01248-x","DOIUrl":"10.1007/s00453-024-01248-x","url":null,"abstract":"<div><p>We investigate algorithms for testing whether an image is connected. Given a proximity parameter <span>({epsilon }in (0,1))</span> and query access to a black-and-white image represented by an <span>(ntimes n)</span> matrix of Boolean pixel values, a (1-sided error) connectedness tester accepts if the image is connected and rejects with probability at least 2/3 if the image is <span>({epsilon })</span>-far from connected. We show that connectedness can be tested nonadaptively with <span>(OBig (frac{1}{{epsilon }^2}Big ))</span> queries and adaptively with <span>(OBig (frac{1}{{epsilon }^{3/2}} sqrt{log frac{1}{{epsilon }}}Big ))</span> queries. The best connectedness tester to date, by Berman, Raskhodnikova, and Yaroslavtsev (STOC 2014) had query complexity <span>(OBig (frac{1}{{epsilon }^2}log frac{1}{{epsilon }}Big ))</span> and was adaptive. We also prove that every nonadaptive, 1-sided error tester for connectedness must make <span>(Omega Big (frac{1}{{epsilon }}log frac{1}{{epsilon }}Big ))</span> queries.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3496 - 3517"},"PeriodicalIF":0.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197061","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":"Romeo and Juliet Meeting in Forest Like Regions","authors":"Neeldhara Misra,&nbsp;Manas Mulpuri,&nbsp;Prafullkumar Tale,&nbsp;Gaurav Viramgami","doi":"10.1007/s00453-024-01264-x","DOIUrl":"10.1007/s00453-024-01264-x","url":null,"abstract":"<div><p>The game of rendezvous with adversaries is a game on a graph played by two players: <i>Facilitator</i> and <i>Divider</i>. Facilitator has two agents and Divider has a team of <span>(k ge 1)</span> agents. While the initial positions of Facilitator’s agents are fixed, Divider gets to select the initial positions of his agents. Then, they take turns to move their agents to adjacent vertices (or stay put) with Facilitator’s goal to bring both her agents at same vertex and Divider’s goal to prevent it. The computational question of interest is to determine if Facilitator has a winning strategy against Divider with <i>k</i> agents. Fomin, Golovach, and Thilikos [WG, 2021] introduced this game and proved that it is <span>PSPACE</span>-<span>hard</span> and <span>co</span>-<span>W</span>[2]-<span>hard</span> parameterized by the number of agents. This hardness naturally motivates the structural parameterization of the problem. The authors proved that it admits an <span>FPT</span> algorithm when parameterized by the modular width and the number of allowed rounds. However, they left open the complexity of the problem from the perspective of other structural parameters. In particular, they explicitly asked whether the problem admits an <span>FPT</span> or <span>XP</span>-algorithm with respect to the treewidth of the input graph. We answer this question in the negative and show that <span>Rendezvous</span> is <span>co</span>-<span>NP</span>-<span>hard</span> even for graphs of constant treewidth. Further, we show that the problem is <span>co</span>-<span>W</span>[1]-<span>hard</span> when parameterized by the feedback vertex set number and the number of agents, and is unlikely to admit a polynomial kernel when parameterized by the vertex cover number and the number of agents. Complementing these hardness results, we show that the <span>Rendezvous</span> is <span>FPT</span> when parameterized by both the vertex cover number and the solution size. Finally, for graphs of treewidth at most two and girds, we show that the problem can be solved in polynomial time.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3465 - 3495"},"PeriodicalIF":0.9,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197065","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":"Connected k-Center and k-Diameter Clustering","authors":"Lukas Drexler,&nbsp;Jan Eube,&nbsp;Kelin Luo,&nbsp;Dorian Reineccius,&nbsp;Heiko Röglin,&nbsp;Melanie Schmidt,&nbsp;Julian Wargalla","doi":"10.1007/s00453-024-01266-9","DOIUrl":"10.1007/s00453-024-01266-9","url":null,"abstract":"<div><p>Motivated by an application from geodesy, we study the <i>connected k-center problem</i> and the <i>connected k-diameter problem</i>. The former problem has been introduced by Ge et al. (ACM Trans Knowl Discov Data 2(2):1–35, 2008. https://doi.org/10.1145/1376815.1376816) to model clustering of data sets with both attribute and relationship data. These problems arise from the classical <i>k</i>-center and <i>k</i>-diameter problems by adding a side constraint. For the side constraint, we are given an undirected <i>connectivity graph</i> <i>G</i> on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in <i>G</i>. Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints. Our main result is an <span>(O(log ^2k))</span>-approximation algorithm for the disjoint connected <i>k</i>-center and <i>k</i>-diameter problem. For Euclidean spaces of constant dimension and for metrics with constant doubling dimension, the approximation factor improves to <i>O</i>(1). Our algorithm works by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering. We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3425 - 3464"},"PeriodicalIF":0.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01266-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197063","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":"Algorithmic Meta-Theorems for Combinatorial Reconfiguration Revisited","authors":"Tatsuya Gima,&nbsp;Takehiro Ito,&nbsp;Yasuaki Kobayashi,&nbsp;Yota Otachi","doi":"10.1007/s00453-024-01261-0","DOIUrl":"10.1007/s00453-024-01261-0","url":null,"abstract":"<div><p>Given a graph and two vertex sets satisfying a certain feasibility condition, a reconfiguration problem asks whether we can reach one vertex set from the other by repeating prescribed modification steps while maintaining feasibility. In this setting, as reported by Mouawad et al. (IPEC, Springer, Berlin, 2014) presented an algorithmic meta-theorem for reconfiguration problems that says if the feasibility can be expressed in monadic second-order logic (MSO), then the problem is fixed-parameter tractable parameterized by <span>(text {treewidth} + ell )</span>, where <span>(ell )</span> is the number of steps allowed to reach the target set. On the other hand, it is shown by Wrochna (J Comput Syst Sci 93:1–10, 2018). https://doi.org/10.1016/j.jcss.2017.11.003) that if <span>(ell )</span> is not part of the parameter, then the problem is PSPACE-complete even on graphs of constant bandwidth. In this paper, we present the first algorithmic meta-theorems for the case where <span>(ell )</span> is not part of the parameter, using some structural graph parameters incomparable with bandwidth. We show that if the feasibility is defined in MSO, then the reconfiguration problem under the so-called token jumping rule is fixed-parameter tractable parameterized by neighborhood diversity. We also show that the problem is fixed-parameter tractable parameterized by <span>(text {treedepth} + k)</span>, where <i>k</i> is the size of sets being transformed. We finally complement the positive result for treedepth by showing that the problem is PSPACE-complete on forests of depth 3.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3395 - 3424"},"PeriodicalIF":0.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197064","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 Framework for Adversarial Streaming Via Differential Privacy and Difference Estimators","authors":"Idan Attias,&nbsp;Edith Cohen,&nbsp;Moshe Shechner,&nbsp;Uri Stemmer","doi":"10.1007/s00453-024-01259-8","DOIUrl":"10.1007/s00453-024-01259-8","url":null,"abstract":"<div><p>Classical streaming algorithms operate under the (not always reasonable) assumption that the input stream is fixed in advance. Recently, there is a growing interest in designing <i>robust streaming algorithms</i> that provide provable guarantees even when the input stream is chosen adaptively as the execution progresses. We propose a new framework for robust streaming that combines techniques from two recently suggested frameworks by Hassidim et al. (NeurIPS 2020) and by Woodruff and Zhou (FOCS 2021). These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks into a single hybrid framework that obtains the “best of both worlds”, thereby solving a question left open by Woodruff and Zhou.\u0000</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 11","pages":"3339 - 3394"},"PeriodicalIF":0.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01259-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197066","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":"Reconfiguring Shortest Paths in Graphs","authors":"Kshitij Gajjar,&nbsp;Agastya Vibhuti Jha,&nbsp;Manish Kumar,&nbsp;Abhiruk Lahiri","doi":"10.1007/s00453-024-01263-y","DOIUrl":"10.1007/s00453-024-01263-y","url":null,"abstract":"<div><p>Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely: (a) repaving road networks, (b) rerouting data packets in a synchronous multiprocessing setting, (c) the shipping container stowage problem, and (d) the train marshalling problem. When modelled as graph problems, (a) is the most general case while (b), (c), (d) are restrictions to different graph classes. We show that (a) does not admit polynomial-time algorithms (assuming <span>({{,mathrm{texttt {P}},}}ne {{,mathrm{texttt {NP}},}})</span>), even for relaxed variants of the problem (assuming <span>({{,mathrm{texttt {P}},}}ne {{,mathrm{texttt {PSPACE}},}})</span>). For (b), (c), (d), we present polynomial-time algorithms to solve the respective problems. We also generalize the problem to when at most <i>k</i> (for a fixed integer <span>(kge 2)</span>) contiguous vertices on a shortest path can be changed at a time.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 10","pages":"3309 - 3338"},"PeriodicalIF":0.9,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01263-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197067","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 Complexity of Reconfiguration of Atoms","authors":"Alexandre Cooper,&nbsp;Stephanie Maaz,&nbsp;Amer E. Mouawad,&nbsp;Naomi Nishimura","doi":"10.1007/s00453-024-01262-z","DOIUrl":"10.1007/s00453-024-01262-z","url":null,"abstract":"<div><p>Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate the atoms so that they form a dense and regular arrangement, such as all locations in a grid, atoms are rearranged using moving optical tweezers. Time is of the essence, as the longer that the process takes and the more that atoms are moved, the higher the chance that atoms will be lost in the process. Viewed as a problem on graphs, we wish to solve the problem of reconfiguring one arrangement of tokens (representing atoms) to another using as few moves as possible. Because the problem is <span>NP</span>-complete on general graphs as well as on grids, we focus on the parameterized complexity for various parameters, considering both undirected and directed graphs, and tokens with and without labels. For unlabelled tokens, the problem is fixed-parameter tractable when parameterized by the number of tokens, the number of moves, or the number of moves plus the number of vertices without tokens in either the source or target configuration, but intractable when parameterized by the difference between the number of moves and the number of differences in the placement of tokens in the source and target configurations. When labels are added to tokens, however, most of the tractability results are replaced by hardness results.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 10","pages":"3284 - 3308"},"PeriodicalIF":0.9,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197068","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":"Runtime Analysis of Quality Diversity Algorithms","authors":"Jakob Bossek,&nbsp;Dirk Sudholt","doi":"10.1007/s00453-024-01254-z","DOIUrl":"10.1007/s00453-024-01254-z","url":null,"abstract":"<div><p>Quality diversity (QD) is a branch of evolutionary computation that gained increasing interest in recent years. The Map-Elites QD approach defines a feature space, i.e., a partition of the search space, and stores the best solution for each cell of this space. We study a simple QD algorithm in the context of pseudo-Boolean optimisation on the “number of ones” feature space, where the <i>i</i>th cell stores the best solution amongst those with a number of ones in <span>([(i-1)k, ik-1])</span>. Here <i>k</i> is a granularity parameter <span>(1 le k le n+1)</span>. We give a tight bound on the expected time until all cells are covered for arbitrary fitness functions and for all <i>k</i> and analyse the expected optimisation time of QD on <span>OneMax</span> and other problems whose structure aligns favourably with the feature space. On combinatorial problems we show that QD finds a <span>({(1-1/e)})</span>-approximation when maximising any monotone sub-modular function with a single uniform cardinality constraint efficiently. Defining the feature space as the number of connected components of an edge-weighted graph, we show that QD finds a minimum spanning forest in expected polynomial time. We further consider QD’s performance on classes of transformed functions in which the feature space is not well aligned with the problem. The asymptotic performance is unaffected by transformations on easy functions like <span>OneMax</span>. Applying a worst-case transformation to a deceptive problem increases the expected optimisation time from <span>(O(n^2 log n))</span> to an exponential time. However, QD is still faster than a (1+1) EA by an exponential factor.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 10","pages":"3252 - 3283"},"PeriodicalIF":0.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01254-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197069","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":"On the Parameterized Complexity of Bend-Minimum Orthogonal Planarity","authors":"Emilio Di Giacomo,&nbsp;Walter Didimo,&nbsp;Giuseppe Liotta,&nbsp;Fabrizio Montecchiani,&nbsp;Giacomo Ortali","doi":"10.1007/s00453-024-01260-1","DOIUrl":"10.1007/s00453-024-01260-1","url":null,"abstract":"<div><p>Computing planar orthogonal drawings with the minimum number of bends is one of the most studied topics in Graph Drawing. The problem is known to be NP-hard, even when we want to test the existence of a rectilinear planar drawing, i.e., an orthogonal drawing without bends (Garg and Tamassia in SIAM J Comput 31(2):601–625, 2001). From the parameterized complexity perspective, the problem is fixed-parameter tractable when parameterized by the sum of three parameters: the number <i>b</i> of bends, the number <i>k</i> of vertices of degree at most two, and the treewidth <span>(textsf{tw})</span> of the input graph (Di Giacomo et al. in J Comput Syst Sci 125:129–148, 2022). We improve this last result by showing that the problem remains fixed-parameter tractable when parameterized only by <span>(b+k)</span>. As a consequence, rectilinear planarity testing lies in FPT parameterized by the number of vertices of degree at most two. We also prove that our choice of parameters is minimal, as deciding if an orthogonal drawing with at most <i>b</i> bends exists is already NP-hard when <i>k</i> is zero (i.e., the problem is para-NP-hard parameterized in <i>k</i>); hence, there is neither an FPT nor an XP algorithm parameterized only by the parameter <i>k</i> (unless P = NP). In addition, we prove that the problem is W[1]-hard parameterized by <span>(k+textsf{tw})</span>, complementing a recent result (Jansen et al. in Upward and orthogonal planarity are W[1]-hard parameterized by treewidth. CoRR, abs/2309.01264, 2023; in: Bekos MA, Chimani M (eds) Graph Drawing and Network Visualization, vol 14466, Springer, Cham, pp 203–217, 2023) that shows W[1]-hardness for the parameterization <span>(b+textsf{tw})</span>. As a consequence, we are able to trace a clear parameterized tractability landscape for the bend-minimum orthogonal planarity problem with respect to the three parameters <i>b</i>, <i>k</i>, and <span>(textsf{tw})</span>.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 10","pages":"3231 - 3251"},"PeriodicalIF":0.9,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01260-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948974","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":"The Complexity of Finding and Enumerating Optimal Subgraphs to Represent Spatial Correlation","authors":"Jessica Enright,&nbsp;Duncan Lee,&nbsp;Kitty Meeks,&nbsp;William Pettersson,&nbsp;John Sylvester","doi":"10.1007/s00453-024-01256-x","DOIUrl":"10.1007/s00453-024-01256-x","url":null,"abstract":"<div><p>Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee et al. (Stat Comput 31(4):51, 2021. https://doi.org/10.1007/s11222-021-10025-7) recently demonstrated that improved inference for areal unit count data can be achieved by carrying out modifications to a graph representing spatial correlations; specifically, they delete edges of the planar graph derived from border-sharing between geographic regions in order to maximise a specific objective function. In this paper, we address the computational complexity of the associated graph optimisation problem. We demonstrate that this optimisation problem is NP-hard; we further show intractability for two simpler variants of the problem. We follow these results with two parameterised algorithms that exactly solve the problem. The first is parameterised by both treewidth and maximum degree, while the second is parameterised by the maximum number of edges that can be removed and is also restricted to settings where the input graph has maximum degree three. Both of these algorithms solve not only the decision problem, but also enumerate all solutions with polynomial time precalculation, delay, and postcalculation time in respective restricted settings. For this problem, efficient enumeration allows the uncertainty in the spatial correlation to be utilised in the modelling. The first enumeration algorithm utilises dynamic programming on a tree decomposition of the input graph, and has polynomial time precalculation and linear delay if both the treewidth and maximum degree are bounded. The second algorithm is restricted to problem instances with maximum degree three, as may arise from triangulations of planar surfaces, but can output all solutions with FPT precalculation time and linear delay when the maximum number of edges that can be removed is taken as the parameter.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 10","pages":"3186 - 3230"},"PeriodicalIF":0.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01256-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882957","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}