Information Processing Letters最新文献

{"title":"Top-down complementation of automata on finite trees","authors":"Laurent Doyen","doi":"10.1016/j.ipl.2024.106499","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106499","url":null,"abstract":"<div><p>We present a new complementation construction for nondeterministic automata on finite trees. The traditional complementation involves determinization of the corresponding bottom-up automaton (recall that top-down deterministic automata are less powerful than nondeterministic automata, whereas bottom-up deterministic automata are equally powerful).</p><p>The construction works directly in a top-down fashion, therefore without determinization. The main advantages of this construction are: (<em>i</em>) in the special case of finite words it boils down to the standard subset construction (which is not the case of the traditional bottom-up complementation construction), and <span><math><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></math></span> it illustrates the core argument of the complementation lemma for infinite trees, central in the proof of Rabin's tree theorem, in a simpler setting where issues related to acceptance conditions over infinite words and determinacy of infinite games are not present.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106499"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000292/pdfft?md5=c514386574ffd52c0851a3a48a6c2db9&pid=1-s2.0-S0020019024000292-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825394","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":"Optimal randomized algorithms of weakly-balanced multi-branching AND-OR trees","authors":"Fuki Ito","doi":"10.1016/j.ipl.2024.106512","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106512","url":null,"abstract":"<div><p>This article treats AND-OR tree computation in terms of query complexity. We are interested in the cases where assignments (inputs) or algorithms are randomized. For the former case, it is known that there is a unique randomized assignment achieving the distributional complexity of balanced trees. On the other hand, the dual problem has the opposite result; the optimal randomized algorithms for balanced trees are not unique. We extend the latter study on randomized algorithms to weakly-balanced trees, and see that the uniqueness still fails.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106512"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140924529","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":"Hamiltonian cycles of balanced hypercube with disjoint faulty edges","authors":"Ting Lan,&nbsp;Huazhong Lü","doi":"10.1016/j.ipl.2024.106518","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106518","url":null,"abstract":"<div><p>The balanced hypercube <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, a variant of the hypercube, is a novel interconnection network topology for massive parallel systems. It is showed in [Theor. Comput. Sci. 947 (2023) 113708] that for any edge subset <em>F</em> of <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> there exists a fault-free Hamiltonian cycle in <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>F</mi></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> with <span><math><mrow><mo>|</mo><mi>F</mi><mo>|</mo></mrow><mo>≤</mo><mn>5</mn><mi>n</mi><mo>−</mo><mn>7</mn></math></span> if the degree of every vertex in <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>F</mi></math></span> is at least two and there exist no <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-cycles in <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>F</mi></math></span>. In this paper, we consider the existence of Hamiltonian cycles of <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> when <em>F</em> is a matching (a set of disjoint edges), and show that each edge <span><math><mi>e</mi><mo>∉</mo><mi>F</mi></math></span> lies on a fault-free Hamiltonian cycle of <span><math><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>F</mi></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>. The number of faulty edges in <em>F</em> can be up to <span><math><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, which is exponential to the dimension <em>n</em>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106518"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483423","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":"Weighted fair division of indivisible items: A review","authors":"Warut Suksompong","doi":"10.1016/j.ipl.2024.106519","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106519","url":null,"abstract":"<div><p>Fair division is a longstanding problem in economics and has recently received substantial interest in computer science. Several applications of fair division involve agents with unequal entitlements represented by weights. We review work on weighted fair division of indivisible items, discuss the range of weighted fairness notions that have been proposed, and highlight a number of open questions.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106519"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000498/pdfft?md5=542bbcb05fc9701066d615985a892ca7&pid=1-s2.0-S0020019024000498-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483424","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":"Improved lower bound for differentially private facility location","authors":"Pasin Manurangsi","doi":"10.1016/j.ipl.2024.106502","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106502","url":null,"abstract":"<div><p>We consider the differentially private (DP) facility location problem in the so called <em>super-set output</em> setting proposed by Gupta et al. <span>[13]</span>. The current best known expected approximation ratio for an <em>ϵ</em>-DP algorithm is <span><math><mi>O</mi><mrow><mo>(</mo><mfrac><mrow><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow><mrow><msqrt><mrow><mi>ϵ</mi></mrow></msqrt></mrow></mfrac><mo>)</mo></mrow></math></span> due to Cohen-Addad et al. <span>[3]</span> where <em>n</em> denote the size of the metric space, meanwhile the best known lower bound is <span><math><mi>Ω</mi><mo>(</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mi>ϵ</mi></mrow></msqrt><mo>)</mo></math></span> <span>[8]</span>.</p><p>In this short note, we give a lower bound of <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>˜</mo></mrow></mover><mrow><mo>(</mo><mi>min</mi><mo>⁡</mo><mrow><mo>{</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>,</mo><msqrt><mrow><mfrac><mrow><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow><mrow><mi>ϵ</mi></mrow></mfrac></mrow></msqrt><mo>}</mo></mrow><mo>)</mo></mrow></math></span> on the expected approximation ratio of any <em>ϵ</em>-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106502"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880174","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":"Regular D-length: A tool for improved prefix-stable forward Ramsey factorisations","authors":"Théodore Lopez,&nbsp;Benjamin Monmege,&nbsp;Jean-Marc Talbot","doi":"10.1016/j.ipl.2024.106497","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106497","url":null,"abstract":"<div><p>Recently, Jecker has introduced and studied the regular <span><math><mi>D</mi></math></span>-length of a monoid, as the length of its longest chain of regular <span><math><mi>D</mi></math></span>-classes. We use this parameter in order to improve the construction, originally proposed by Colcombet, of a deterministic automaton that allows to map a word to one of its forward Ramsey splits: these are a relaxation of factorisation forests that enjoy prefix stability, thus allowing a compositional construction. For certain monoids that have a small regular <span><math><mi>D</mi></math></span>-length, our construction produces an exponentially more succinct deterministic automaton. Finally, we apply it to obtain better complexity result for the problem of fast infix evaluation.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106497"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140647631","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":"Spanners under the Hausdorff and Fréchet distances","authors":"Tsuri Farhana,&nbsp;Matthew J. Katz","doi":"10.1016/j.ipl.2024.106513","DOIUrl":"10.1016/j.ipl.2024.106513","url":null,"abstract":"<div><p>We initiate the study of spanners under the Hausdorff and Fréchet distances. Let <em>S</em> be a set of points in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> and <em>ε</em> a non-negative real number. A subgraph <em>H</em> of the Euclidean graph over <em>S</em> is an <em>ε-Hausdorff-spanner</em> (resp., an <em>ε-Fréchet-spanner</em>) of <em>S</em>, if for any two points <span><math><mi>u</mi><mo>,</mo><mi>v</mi><mo>∈</mo><mi>S</mi></math></span> there exists a path <span><math><mi>P</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> in <em>H</em> between <em>u</em> and <em>v</em>, such that the Hausdorff distance (resp., the Fréchet distance) between <span><math><mi>P</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> and <span><math><mover><mrow><mi>u</mi><mi>v</mi></mrow><mo>‾</mo></mover></math></span> is at most <em>ε</em>. We show that any <em>t</em>-spanner of a planar point-set <em>S</em> is a <span><math><mfrac><mrow><msqrt><mrow><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>-Hausdorff-spanner and a <span><math><mi>min</mi><mo>⁡</mo><mo>{</mo><mfrac><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><msqrt><mrow><mn>5</mn><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>2</mn><mi>t</mi><mo>−</mo><mn>3</mn></mrow></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac><mo>}</mo></math></span>-Fréchet spanner. We also prove that for any <span><math><mi>t</mi><mo>&gt;</mo><mn>1</mn></math></span>, there exist a set of points <em>S</em> and an <span><math><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-Hausdorff-spanner of <em>S</em> and an <span><math><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-Fréchet-spanner of <em>S</em>, where <span><math><msub><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are constants, such that neither of them is a <em>t</em>-spanner.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106513"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141046033","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":"Improving compressed matrix multiplication using control variate method","authors":"Bhisham Dev Verma ,&nbsp;Punit Pankaj Dubey ,&nbsp;Rameshwar Pratap ,&nbsp;Manoj Thakur","doi":"10.1016/j.ipl.2024.106517","DOIUrl":"10.1016/j.ipl.2024.106517","url":null,"abstract":"<div><p>The seminal work by Pagh <span>[1]</span> proposed a matrix multiplication algorithm for real-valued squared matrices called Compressed Matrix Multiplication (CMM) having a sparse matrix output product. The algorithm is based on a popular sketching technique called Count-Sketch <span>[2]</span> and Fast Fourier Transform (FFT). For input square matrices <strong>A</strong> and <strong>B</strong> of order <em>n</em> and the product matrix <strong>AB</strong> with Frobenius norm <span><math><mo>|</mo><mo>|</mo><mrow><mi>AB</mi></mrow><mo>|</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>F</mi></mrow></msub></math></span>, the algorithm offers an unbiased estimate for each entry, <em>i.e.</em>, <span><math><msub><mrow><mo>(</mo><mrow><mi>AB</mi></mrow><mo>)</mo></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> of the product matrix <strong>AB</strong> with a variance bounded by <span><math><mo>|</mo><mo>|</mo><mrow><mi>AB</mi></mrow><mo>|</mo><msubsup><mrow><mo>|</mo></mrow><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>/</mo><mi>b</mi></math></span>, where <em>b</em> is the compressed bucket size. Thus, the variance will eventually become high for a small bucket size. In this work, we address the high variance problem of CMM with the help of a simple and practical technique based on classical variance reduction methods in statistics. Our techniques rely on the Control Variate (CV) method. We suggest rigorous theoretical analysis for variance reduction and complement it via supporting empirical evidence.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106517"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141402112","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":"Defying gravity and gadget numerosity: The complexity of the Hanano Puzzle and beyond","authors":"Michael C. Chavrimootoo","doi":"10.1016/j.ipl.2024.106520","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106520","url":null,"abstract":"<div><p>Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of reversible games with pushing blocks). Direct use of this property introduces an explosion in the number of gadgets needed to show PSPACE-hardness, but we show how to bring that number from 32 down to only three in the general case, and down to two in our specific case! We propose it as a step towards a broader and more general framework for studying games with irreversible gravity, and use this connection to guide an indirect polynomial-time many-one reduction from the NCL problem to the Hanano Puzzle—which is NP-hard—to prove it is PSPACE-complete.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106520"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141605828","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":"Dispersion problem on a convex polygon","authors":"Pawan K. Mishra ,&nbsp;S.V. Rao ,&nbsp;Gautam K. Das","doi":"10.1016/j.ipl.2024.106498","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106498","url":null,"abstract":"<div><p>Given a set <span><math><mi>P</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></math></span> of <em>n</em> points in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a positive integer <em>k</em> <span><math><mo>(</mo><mo>≤</mo><mi>n</mi><mo>)</mo></math></span>, we wish to find a subset <em>S</em> of <em>P</em> of size <em>k</em> such that the cost of a subset <em>S</em>, <span><math><mi>c</mi><mi>o</mi><mi>s</mi><mi>t</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>=</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>d</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo><mo>|</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mi>S</mi><mo>}</mo></math></span>, is maximized, where <span><math><mi>d</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> is the Euclidean distance between two points <em>p</em> and <em>q</em>. The problem is called the <em>max-min k-dispersion problem</em>. In this article, we consider the max-min <em>k</em>-dispersion problem, where a given set <em>P</em> of <em>n</em> points are vertices of a convex polygon. We refer to this variant of the problem as the <em>convex k-dispersion</em> problem.</p><p>We propose an 1.733-factor approximation algorithm for the convex <em>k</em>-dispersion problem. In addition, we study the convex <em>k</em>-dispersion problem for <span><math><mi>k</mi><mo>=</mo><mn>4</mn></math></span>. We propose an iterative algorithm that returns an optimal solution of size 4 in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> time.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106498"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140843117","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}