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Ranking and unranking bordered and unbordered words 排序和取消排序有边框和无边框的单词
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-10-12 DOI: 10.1016/j.ipl.2023.106452
Daniel Gabric
{"title":"Ranking and unranking bordered and unbordered words","authors":"Daniel Gabric","doi":"10.1016/j.ipl.2023.106452","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106452","url":null,"abstract":"<div><p>A <em>border</em> of a word <em>w</em> is a word that is both a non-empty proper prefix and suffix of <em>w</em>. If <em>w</em> has a border, then it is said to be <em>bordered</em>; otherwise, it is said to be <em>unbordered</em>. The main results of this paper are the first algorithms to rank and unrank length-<em>n</em> bordered and unbordered words over a <em>k</em>-letter alphabet. We show that, under the unit-cost RAM model, ranking bordered and unbordered words can be done in <span><math><mi>O</mi><mo>(</mo><mi>k</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> time using <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> space, and unranking them can be done in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>k</mi><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></math></span> time using <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> space.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106452"},"PeriodicalIF":0.5,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192085","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}
引用次数: 0
Vertex-connectivity for node failure identification in Boolean Network Tomography 布尔网络层析成像中用于节点故障识别的顶点连通性
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-10-10 DOI: 10.1016/j.ipl.2023.106450
Nicola Galesi , Fariba Ranjbar , Michele Zito
{"title":"Vertex-connectivity for node failure identification in Boolean Network Tomography","authors":"Nicola Galesi ,&nbsp;Fariba Ranjbar ,&nbsp;Michele Zito","doi":"10.1016/j.ipl.2023.106450","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106450","url":null,"abstract":"<div><p>We study the node failure identification problem in undirected graphs by means of Boolean Network Tomography. We argue that vertex-connectivity plays a central role. We prove bounds on the maximum number of simultaneous node failures that can be identified in arbitrary networks. We argue that (augmented) grids are a class of networks with large failure identifiability, and provide very tight results in this context.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106450"},"PeriodicalIF":0.5,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192157","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}
引用次数: 0
Checking in polynomial time whether or not a regular tree language is deterministic top-down 在多项式时间中检查正则树语言是否是自上而下的确定性语言
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-29 DOI: 10.1016/j.ipl.2023.106449
Sebastian Maneth , Helmut Seidl
{"title":"Checking in polynomial time whether or not a regular tree language is deterministic top-down","authors":"Sebastian Maneth ,&nbsp;Helmut Seidl","doi":"10.1016/j.ipl.2023.106449","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106449","url":null,"abstract":"<div><p><span>It is well known that for a given bottom-up tree automaton it can be decided whether or not an equivalent deterministic top-down tree automaton exists. Recently it was claimed that such a decision can be carried out in </span>polynomial time<span> (Leupold and Maneth, FCT'2021); but their procedure and corresponding property is wrong. Here we address this mistake and present a correct property which allows to determine in polynomial time whether or not a given tree language can be recognized by a deterministic top-down tree automaton. Furthermore, our new property is stated for arbitrary deterministic bottom-up tree automata, and not only for minimal such automata (as before).</span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106449"},"PeriodicalIF":0.5,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192082","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}
引用次数: 0
Inapproximability of counting independent sets in linear hypergraphs 线性超图中独立集计数的不逼近性
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-29 DOI: 10.1016/j.ipl.2023.106448
Guoliang Qiu , Jiaheng Wang
{"title":"Inapproximability of counting independent sets in linear hypergraphs","authors":"Guoliang Qiu ,&nbsp;Jiaheng Wang","doi":"10.1016/j.ipl.2023.106448","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106448","url":null,"abstract":"<div><p>It is shown in this note that approximating the number of independent sets in a <em>k</em>-uniform linear hypergraph with maximum degree at most Δ is <strong>NP</strong>-hard if <span><math><mi>Δ</mi><mo>≥</mo><mn>5</mn><mo>⋅</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mn>1</mn></math></span>. This confirms that for the relevant sampling and approximate counting problems, the regimes on the maximum degree where the state-of-the-art algorithms work are tight, up to some small factors. These algorithms include: the approximate sampler and randomised approximation scheme by Hermon et al. (2019) <span>[5]</span>, the perfect sampler by Qiu et al. (2022) <span>[6]</span>, and the deterministic approximation scheme by Feng et al. (2023) <span>[7]</span>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106448"},"PeriodicalIF":0.5,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192083","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}
引用次数: 0
The facility location problem with maximum distance constraint 具有最大距离约束的设施选址问题
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-20 DOI: 10.1016/j.ipl.2023.106447
Xiaowei Li, Xiwen Lu
{"title":"The facility location problem with maximum distance constraint","authors":"Xiaowei Li,&nbsp;Xiwen Lu","doi":"10.1016/j.ipl.2023.106447","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106447","url":null,"abstract":"<div><p>Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of <em>L</em>. The goal is to minimise the sum of the opening costs of the facilities. We show that this problem is NP-hard and analyse its lower bound. As no <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-approximation algorithm with <span><math><mi>α</mi><mo>&lt;</mo><mn>3</mn></math></span> exists, we provide a (3,1)-approximation algorithm that violates the maximum distance constraint. Based on this algorithm, we propose a 3-approximation algorithm for the <em>k</em>-supplier problem. The difference between this algorithm and the previous one in <span>[12]</span> is that the proposed algorithm avoids the construction of many bottleneck graphs, making the proposed algorithm less demanding in terms of memory and more suitable for large-scale problems.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106447"},"PeriodicalIF":0.5,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192081","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}
引用次数: 0
Relating planar graph drawings to planar satisfiability problems 平面图与平面可满足性问题的关联
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-18 DOI: 10.1016/j.ipl.2023.106446
Md. Manzurul Hasan , Debajyoti Mondal , Md. Saidur Rahman
{"title":"Relating planar graph drawings to planar satisfiability problems","authors":"Md. Manzurul Hasan ,&nbsp;Debajyoti Mondal ,&nbsp;Md. Saidur Rahman","doi":"10.1016/j.ipl.2023.106446","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106446","url":null,"abstract":"<div><p>A SAT graph <span><math><mi>G</mi><mo>(</mo><mi>Φ</mi><mo>)</mo></math></span><span> of a satisfiability instance Φ consists of a vertex for each clause and a vertex for each variable, where there exists an edge between a clause vertex and a variable vertex if and only if the variable or its negation appears in that clause. Many satisfiability problems<span>, which are NP-hard, become polynomial-time solvable when the SAT graph is restricted to satisfy some graph properties. A rich body of research attempts to narrow down the boundary between the NP-hardness and polynomial-time solvability of various satisfiability problems. In this paper, we examine planar satisfiability problems and leverage planar graph drawing algorithms to improve our understanding of these problems. A rich body of graph drawing algorithms exists to check whether a planar graph admits a drawing that satisfies certain drawing aesthetics. We show how the existing graph drawing knowledge could be used to establish sufficient conditions for a SAT instance to always be satisfiable and give algorithms to efficiently find a satisfying truth assignment. In some cases, our algorithm can find a truth assignment by setting a small number of variables to true, which relates to the satisfiability variants that seek to minimize the number of ones.</span></span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106446"},"PeriodicalIF":0.5,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192079","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}
引用次数: 0
A new class of generalized almost perfect nonlinear monomial functions 一类新的广义几乎完全非线性单项函数
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-15 DOI: 10.1016/j.ipl.2023.106445
Lijing Zheng , Haibin Kan , Jie Peng , Yanjun Li , Yanbin Zheng
{"title":"A new class of generalized almost perfect nonlinear monomial functions","authors":"Lijing Zheng ,&nbsp;Haibin Kan ,&nbsp;Jie Peng ,&nbsp;Yanjun Li ,&nbsp;Yanbin Zheng","doi":"10.1016/j.ipl.2023.106445","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106445","url":null,"abstract":"<div><p>In this short note, we present a new class of GAPN power functions of the type <span><math><msup><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn><mi>i</mi></mrow></msup><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup></math></span> over finite fields <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math></span> with <em>p</em> odd and <span><math><mrow><mi>gcd</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>i</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span> (up to EA-equivalence).</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106445"},"PeriodicalIF":0.5,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192080","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}
引用次数: 0
The computational complexity of some explainable clustering problems 一些可解释聚类问题的计算复杂性
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-04 DOI: 10.1016/j.ipl.2023.106437
Eduardo Sany Laber
{"title":"The computational complexity of some explainable clustering problems","authors":"Eduardo Sany Laber","doi":"10.1016/j.ipl.2023.106437","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106437","url":null,"abstract":"<div><p>Let <span><math><mi>X</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> be a set of points and <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> be an integer. Dasgupta et al. <span>[1]</span> considered the problem of building a partition of <span><math><mi>X</mi></math></span> into <em>k</em><span> groups, induced by an axis-aligned decision tree with </span><em>k</em><span> leaves. The motivation is obtaining partitions that are simple to explain. We study the computational complexity of this problem for </span><em>k</em>-means, <em>k</em>-medians and the <em>k</em><span>-center cost-functions. We prove that the optimization problems induced by these cost-functions are hard to approximate.</span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106437"},"PeriodicalIF":0.5,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192162","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}
引用次数: 0
On semi-transitive orientability of split graphs 关于分裂图的半传递可定向性
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-01 DOI: 10.1016/j.ipl.2023.106435
Sergey Kitaev , Artem Pyatkin
{"title":"On semi-transitive orientability of split graphs","authors":"Sergey Kitaev ,&nbsp;Artem Pyatkin","doi":"10.1016/j.ipl.2023.106435","DOIUrl":"https://doi.org/10.1016/j.ipl.2023.106435","url":null,"abstract":"<div><p>A directed graph is semi-transitive if and only if it is acyclic and for any directed path <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>→</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>→</mo><mo>⋯</mo><mo>→</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span>, <span><math><mi>t</mi><mo>≥</mo><mn>2</mn></math></span>, either there is no edge from <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> to <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> or all edges <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>→</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> exist for <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>&lt;</mo><mi>j</mi><mo>≤</mo><mi>t</mi></math></span>. An undirected graph is semi-transitive if it admits a semi-transitive orientation. Recognizing semi-transitive orientability of a graph is an NP-complete problem.</p><p>A split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Semi-transitive orientability of split graphs was recently studied in a series of papers in the literature. The main result in this paper is proving that recognition of semi-transitive orientability of split graphs can be done in a polynomial time.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106435"},"PeriodicalIF":0.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50192161","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}
引用次数: 0
Exploring the optimality of byte-wise permutations of a piccolo-type block cipher 探索短笛型分组密码按字节排列的最优性
IF 0.5 4区 计算机科学
Information Processing Letters Pub Date : 2023-09-01 DOI: 10.1016/j.ipl.2023.106436
Shion Utsumi, Motoki Nakahashi, Kosei Sakamoto, Takanori Isobe
{"title":"Exploring the optimality of byte-wise permutations of a piccolo-type block cipher","authors":"Shion Utsumi,&nbsp;Motoki Nakahashi,&nbsp;Kosei Sakamoto,&nbsp;Takanori Isobe","doi":"10.1016/j.ipl.2023.106436","DOIUrl":"10.1016/j.ipl.2023.106436","url":null,"abstract":"<div><p>Piccolo is a lightweight block cipher based on a 16-bit word 4-line generalized Feistel structure. Piccolo adopts byte-wise round permutation (RP) instead of the typical word-based RP to improve diffusion. In this paper, we explore the optimality of byte-based RP from the viewpoint of security. We evaluate the security of differential, linear, impossible differential, and integral attacks for all byte-wise RPs using mixed integer linear programming (MILP). We show that the RP of Piccolo is optimal in terms of the number of rounds required to guarantee security against such attacks. In addition, we introduce new two classes of RPs that require 7 rounds for security against impossible differential attacks, which is one round less than required by Piccolo. These new classes require 7/9 and 8/8 rounds to guarantee security against differential/linear attacks, respectively, which is more rounds than required by Piccolo.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106436"},"PeriodicalIF":0.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46880389","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}
引用次数: 0
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