Information Processing Letters最新文献

{"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":"2024-07-01","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":"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":"2024-06-26","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":"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":"2024-06-20","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":"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":"2024-06-12","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":"Leveraging parameterized Chernoff bounds for simplified algorithm analyses","authors":"Michael Dillencourt ,&nbsp;Michael T. Goodrich ,&nbsp;Michael Mitzenmacher","doi":"10.1016/j.ipl.2024.106516","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106516","url":null,"abstract":"<div><p>In this paper, we derive parameterized Chernoff bounds and show their applications for simplifying the analysis of some well-known probabilistic algorithms and data structures. The parameterized Chernoff bounds we provide give probability bounds that are powers of two, with a clean formulation of the relation between the constant in the exponent and the relative distance from the mean. In addition, we provide new simplified analyses with these bounds for hash tables, randomized routing, and a simplified, non-recursive adaptation of the Floyd-Rivest selection algorithm.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106516"},"PeriodicalIF":0.5,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000462/pdfft?md5=67dfff867dbb54118accce695281b16f&pid=1-s2.0-S0020019024000462-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141323310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on the k-restriction problem","authors":"Jing-You Lin,&nbsp;Shi-Chun Tsai","doi":"10.1016/j.ipl.2024.106515","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106515","url":null,"abstract":"<div><p>Consider a set of demands, each taking length-<em>k</em> strings as input. The <em>k</em>-restriction problem is to construct a small set of length-<em>m</em> strings, such that given any <em>k</em> positions and any demand, there exists a string in the set satisfying the demand at these positions. The <em>k</em>-restriction problem relates to many problems, such as <em>k</em>-independent sets, covering arrays, and many other combinatorial applications. By considering the VC-dimension of demands, we prove bounds independent of the number of demands with the Lovász Local Lemma. As a result, we can prove better bounds for demands with finite VC-dimension.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106515"},"PeriodicalIF":0.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141250243","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":"Reduced meet over labelling-based semantics in abstract argumentation","authors":"Lixing Tan ,&nbsp;Zhaohui Zhu ,&nbsp;Jinjin Zhang","doi":"10.1016/j.ipl.2024.106514","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106514","url":null,"abstract":"<div><p>The labelling-based approach of <em>abstract argumentation frameworks</em> (AAFs) is beneficial for various applications requiring different levels of decisiveness. For labelling-based semantics, this paper provides an operator so-called reduced meet modulo an ultrafilter, which is inspired by its counterpart over extensions. All criteria involved in the definitions of fundamental labelling-based semantics in AAFs are shown to be closed under this operator. Based on this fact, this paper develops a simple and uniform way for exploring common properties of labelling-based semantics in AAFs, including the compactness of extensibility, the Dcpo and Lindenbaum properties, etc.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106514"},"PeriodicalIF":0.5,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141250242","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":"2024-05-16","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":"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":"2024-05-10","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":"Lower and upper bounds on graph communicabilities","authors":"Amir Hossein Ghodrati ,&nbsp;Mohammad Ali Hosseinzadeh","doi":"10.1016/j.ipl.2024.106501","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106501","url":null,"abstract":"<div><p>In this paper, some lower and upper bounds for the subgraph centrality and communicability of a graph are proved. The expected value of the normalized total communicability of a random <span><math><mi>G</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></span> graph is also considered and asymptotically determined. Moreover, some computational results are presented to compare the bounds obtained in this paper with some other bounds in the literature.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106501"},"PeriodicalIF":0.5,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140905396","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}