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Instability results for cosine-dissimilarity-based nearest neighbor search on high dimensional Gaussian data 基于余弦不相似度的高维高斯数据近邻搜索的不稳定性结果
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-03-01 Epub Date: 2024-11-22 DOI: 10.1016/j.ipl.2024.106542
Chris R. Giannella
{"title":"Instability results for cosine-dissimilarity-based nearest neighbor search on high dimensional Gaussian data","authors":"Chris R. Giannella","doi":"10.1016/j.ipl.2024.106542","DOIUrl":"10.1016/j.ipl.2024.106542","url":null,"abstract":"<div><div>Because many dissimilarity functions behave differently in low versus high-dimensional spaces, the behavior of high-dimensional nearest neighbor search has been studied extensively. One line of research involves the characterization of nearest neighbor queries as unstable if their query points have nearly identical dissimilarity with most points in the dataset. This research has shown that, for various data distributions and dissimilarity functions, the probability of query instability approaches one. Previous work in <em>Information Processing Letters</em> by C. Giannella in 2021 explicated this phenomenon for centered Gaussian data and Euclidean distance. This paper addresses the problem of characterizing query instability behavior over centered Gaussian data and a fundamentally different dissimilarity function, cosine dissimilarity. Conditions are provided on the covariance matrices and dataset size function guaranteeing that the probability of query instability goes to one. Furthermore, conditions are provided under which the instability probability is bounded away from one.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"189 ","pages":"Article 106542"},"PeriodicalIF":0.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698622","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 simple division-free algorithm for computing Pfaffians 一个简单的无除法计算算法
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-03-01 Epub Date: 2024-12-09 DOI: 10.1016/j.ipl.2024.106550
Adam J. Przeździecki
{"title":"A simple division-free algorithm for computing Pfaffians","authors":"Adam J. Przeździecki","doi":"10.1016/j.ipl.2024.106550","DOIUrl":"10.1016/j.ipl.2024.106550","url":null,"abstract":"<div><div>We present a very simple algorithm for computing Pfaffians which uses no division operations. Essentially, it amounts to iterating matrix multiplication and truncation.</div><div>Its complexity, for a <span><math><mn>2</mn><mi>n</mi><mo>×</mo><mn>2</mn><mi>n</mi></math></span> matrix, is <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>M</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>)</mo></math></span>, where <span><math><mi>M</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> is the cost of matrix multiplication. In case of a sparse matrix, <span><math><mi>M</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> is the cost of the dense-sparse matrix multiplication.</div><div>The algorithm is an adaptation of the Bird algorithm for determinants. We show how to extract, with practically no additional work, the characteristic polynomial and the Pfaffian characteristic polynomial from these algorithms.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"189 ","pages":"Article 106550"},"PeriodicalIF":0.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099045","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
Improved hardness of approximation for Geometric Bin Packing 改进了几何料仓包装的近似硬度
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-03-01 Epub Date: 2024-12-17 DOI: 10.1016/j.ipl.2024.106552
Arka Ray , Sai Sandeep
{"title":"Improved hardness of approximation for Geometric Bin Packing","authors":"Arka Ray ,&nbsp;Sai Sandeep","doi":"10.1016/j.ipl.2024.106552","DOIUrl":"10.1016/j.ipl.2024.106552","url":null,"abstract":"<div><div>The Geometric Bin Packing (GBP) problem is a generalization of Bin Packing where the input is a set of <em>d</em>-dimensional rectangles, and the goal is to pack them into <em>d</em>-dimensional unit cubes efficiently. It is NP-hard to obtain a PTAS for the problem, even when <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>. For general <em>d</em>, the best-known approximation algorithm has an approximation guarantee that is exponential in <em>d</em>. In contrast, the best hardness of approximation is still a small constant inapproximability from the case when <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>. In this paper, we show that the problem cannot be approximated within a <span><math><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>ϵ</mi></mrow></msup></math></span> factor unless <span><math><mtext>NP</mtext><mo>=</mo><mtext>P</mtext></math></span>.</div><div>Recently, <em>d</em>-dimensional Vector Bin Packing, a problem closely related to the GBP, was shown to be hard to approximate within a <span><math><mi>Ω</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>d</mi><mo>)</mo></math></span> factor when <em>d</em> is a fixed constant, using a notion of Packing Dimension of set families. In this paper, we introduce a geometric analog of it, the Geometric Packing Dimension of set families. While we fall short of obtaining similar inapproximability results for the Geometric Bin Packing problem when <em>d</em> is fixed, we prove a couple of key properties of the Geometric Packing Dimension which highlight fundamental differences between Geometric Bin Packing and Vector Bin Packing.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"189 ","pages":"Article 106552"},"PeriodicalIF":0.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099046","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
An improved uniform convergence bound with fat-shattering dimension 具有碎脂维度的改进均匀收敛约束
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-10-31 DOI: 10.1016/j.ipl.2024.106539
Roberto Colomboni , Emmanuel Esposito , Andrea Paudice
{"title":"An improved uniform convergence bound with fat-shattering dimension","authors":"Roberto Colomboni ,&nbsp;Emmanuel Esposito ,&nbsp;Andrea Paudice","doi":"10.1016/j.ipl.2024.106539","DOIUrl":"10.1016/j.ipl.2024.106539","url":null,"abstract":"<div><div>The fat-shattering dimension characterizes the uniform convergence property of real-valued function classes. The state-of-the-art upper bounds in <span><span>[6]</span></span> feature a multiplicative squared logarithmic factor on the sample complexity, leaving an open gap with the existing lower bound. By relying on a refined packing number bound given in <span><span>[20]</span></span>, we provide an improved uniform convergence bound that closes this gap.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106539"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653224","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
4/3 rectangle tiling lower bound 4/3 矩形平铺下限
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-08-08 DOI: 10.1016/j.ipl.2024.106523
Grzegorz Głuch, Krzysztof Loryś
{"title":"4/3 rectangle tiling lower bound","authors":"Grzegorz Głuch,&nbsp;Krzysztof Loryś","doi":"10.1016/j.ipl.2024.106523","DOIUrl":"10.1016/j.ipl.2024.106523","url":null,"abstract":"<div><p>The problem that we consider is the following: given an <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> array <em>A</em> of positive numbers and a natural number <em>p</em>, find a tiling using at most <em>p</em> rectangles (which means that each array element must be covered by some rectangle and no two rectangles must overlap) that minimizes the maximum weight of any rectangle (the weight of a rectangle is the sum of elements which are covered by it). We prove that it is NP-hard to approximate this problem to within a factor of <strong>1</strong><span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> (the previous best result was <span><math><mn>1</mn><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math></span>).</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106523"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940421","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
Tighter bound for generalized multiple discrete logarithm problem via MDS matrix method 通过 MDS 矩阵法实现广义多重离散对数问题的更严格约束
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-10-16 DOI: 10.1016/j.ipl.2024.106535
Haoxuan Wu , Jincheng Zhuang
{"title":"Tighter bound for generalized multiple discrete logarithm problem via MDS matrix method","authors":"Haoxuan Wu ,&nbsp;Jincheng Zhuang","doi":"10.1016/j.ipl.2024.106535","DOIUrl":"10.1016/j.ipl.2024.106535","url":null,"abstract":"<div><div>Discrete logarithm problem (DLP) is one of the fundamental hard problems used in cryptography. For <span><math><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi></math></span>, solving the <em>k</em>-out-of-<em>n</em> DLP instances is an important problem emerging in certain scenarios in public-key cryptography. Ying and Kunihiro (ACNS 2017) pioneered in studying <em>k</em>-out-of-<em>n</em> instance solutions of DLP, which is a generalized version of multiple DLP. By reducing the multiple DLP to the generalized version, they established lower bounds on the computational complexity of <em>k</em>-out-of-<em>n</em> DLP for different parameter values of <em>k</em>.</div><div>In this paper, we further reduce the reduction complexity presented in Ying and Kunihiro's work and increase the range of <em>k</em> and <em>n</em> for the tight lower bound of <em>k</em>-out-of-<em>n</em> DLP in the generic group model, which has applications in related cryptographic schemes. To achieve the goal, the key technique is to utilize a variant of fast multipoint evaluation. We divide the discussion into two cases. In the special case when <em>n</em> divides <span><math><mi>p</mi><mo>−</mo><mn>1</mn></math></span>, by leveraging Number Theory Transform (NTT) technique, we expand <em>k</em> and <em>n</em> to a larger range. In the general case, by using a variant of fast multipoint evaluation, we increase <em>k</em> and <em>n</em> to a moderately larger range.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106535"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441884","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}
引用次数: 0
Counter abstraction for regular open teams 常规开放团队的反抽象
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-09-16 DOI: 10.1016/j.ipl.2024.106533
Shabana A.T., Alphy George, S. Sheerazuddin
{"title":"Counter abstraction for regular open teams","authors":"Shabana A.T.,&nbsp;Alphy George,&nbsp;S. Sheerazuddin","doi":"10.1016/j.ipl.2024.106533","DOIUrl":"10.1016/j.ipl.2024.106533","url":null,"abstract":"<div><p>We study <em>open swarms</em> and <em>teams</em> of multi-agent systems where agents may join or leave the system at runtime. Kouvaros et al. <span><span>[1]</span></span> defined the verification problem for such systems and showed it to be undecidable, in general. Also, they have found one decidable class of open multi-agent systems and provided a partial decision procedure for another. In the same vein we present a subclass of open teams called <em>regular open teams</em> for which reachability is decidable. This is shown by employing a counter abstraction technique wherein the regular open team is abstracted into a finite state multi-counter system.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106533"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240002","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
Robust probabilistic temporal logics 稳健的概率时态逻辑
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-08-08 DOI: 10.1016/j.ipl.2024.106522
Martin Zimmermann
{"title":"Robust probabilistic temporal logics","authors":"Martin Zimmermann","doi":"10.1016/j.ipl.2024.106522","DOIUrl":"10.1016/j.ipl.2024.106522","url":null,"abstract":"<div><p>We robustify PCTL and PCTL<sup>⁎</sup>, the most important specification languages for probabilistic systems, and show that robustness does not increase the complexity of their model-checking problems.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106522"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000528/pdfft?md5=a8b85e941455bedd212a2027c3c635b8&pid=1-s2.0-S0020019024000528-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940422","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}
引用次数: 0
A 22k-approximation algorithm for minimum power k edge disjoint st-paths 最小功率 k 边相邻 st 路径的 22k 近似算法
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-08-14 DOI: 10.1016/j.ipl.2024.106532
Zeev Nutov
{"title":"A 22k-approximation algorithm for minimum power k edge disjoint st-paths","authors":"Zeev Nutov","doi":"10.1016/j.ipl.2024.106532","DOIUrl":"10.1016/j.ipl.2024.106532","url":null,"abstract":"<div><p>In minimum power network design problems we are given an undirected graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> with edge costs <span><math><mo>{</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>:</mo><mi>e</mi><mo>∈</mo><mi>E</mi><mo>}</mo></math></span>. The goal is to find an edge set <span><math><mi>F</mi><mo>⊆</mo><mi>E</mi></math></span> that satisfies a prescribed property of minimum power <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>F</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>v</mi><mo>∈</mo><mi>V</mi></mrow></msub><mi>max</mi><mo>⁡</mo><mo>{</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>:</mo><mi>e</mi><mo>∈</mo><mi>F</mi><mtext> is incident to </mtext><mi>v</mi><mo>}</mo></math></span>. In the <span>Min-Power</span> <em>k</em> <span>Edge Disjoint</span> <em>st</em><span>-Paths</span> problem <em>F</em> should contain <em>k</em> edge disjoint <em>st</em>-paths. The problem admits a <em>k</em>-approximation algorithm, and it was an open question to achieve an approximation ratio sublinear in <em>k</em> for simple graphs, even for unit costs. We give a <span><math><mn>2</mn><msqrt><mrow><mn>2</mn><mi>k</mi></mrow></msqrt></math></span>-approximation algorithm for general costs.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106532"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012369","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
Reducing the space used by the sieve of Eratosthenes when factoring 减少埃拉托塞尼斯筛子在进行因式分解时使用的空间
IF 0.7 4区 计算机科学
Information Processing Letters Pub Date : 2025-02-01 Epub Date: 2024-10-24 DOI: 10.1016/j.ipl.2024.106537
Samuel Hartman, Jonathan P. Sorenson
{"title":"Reducing the space used by the sieve of Eratosthenes when factoring","authors":"Samuel Hartman,&nbsp;Jonathan P. Sorenson","doi":"10.1016/j.ipl.2024.106537","DOIUrl":"10.1016/j.ipl.2024.106537","url":null,"abstract":"<div><div>We present a version of the sieve of Eratosthenes that can factor all integers ≤<em>x</em> in <span><math><mi>O</mi><mo>(</mo><mi>x</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>x</mi><mo>)</mo></math></span> arithmetic operations using at most <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>x</mi></mrow></msqrt><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>x</mi><mo>)</mo></math></span> bits of space. Among algorithms that take the optimal <span><math><mi>O</mi><mo>(</mo><mi>x</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>x</mi><mo>)</mo></math></span> time, this new space bound is an improvement of a factor proportional to <span><math><mi>log</mi><mo>⁡</mo><mi>x</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>x</mi></math></span> over the implied previous bound of <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>x</mi></mrow></msqrt><mi>log</mi><mo>⁡</mo><mi>x</mi><mo>)</mo></math></span>. We also show our algorithm performs well in practice.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106537"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552395","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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