Pub Date : 2024-11-28DOI: 10.1016/j.tcs.2024.115005
Shoshana Marcus , Dina Sokol , Sarah Zelikovitz
A side-sharing tandem is a rectangular array that is composed of two adjacent non-overlapping occurrences of the same rectangular block. Furthering our understanding of side-sharing tandems can facilitate the development of more efficient 2d pattern matching techniques and may lead to improvements in multi-dimensional compression schemes. Existing algorithms for finding side-sharing tandems are far from optimal on 2d arrays that contain relatively few side-sharing tandems. In this paper, we introduce the idea of a run of side-sharing tandems, as a maximally extended chain of 2d tandems. We demonstrate tight upper bounds on the number of runs of side-sharing tandems that can occur in a rectangular array. We develop an algorithm that locates all τ runs of side-sharing tandems in an input array in time. We also introduce several versions of approximate side-sharing tandems with k mismatches along with efficient algorithms for locating them in a rectangular array.
{"title":"Exact and inexact search for 2d side-sharing tandems","authors":"Shoshana Marcus , Dina Sokol , Sarah Zelikovitz","doi":"10.1016/j.tcs.2024.115005","DOIUrl":"10.1016/j.tcs.2024.115005","url":null,"abstract":"<div><div>A side-sharing tandem is a rectangular array that is composed of two adjacent non-overlapping occurrences of the same rectangular block. Furthering our understanding of side-sharing tandems can facilitate the development of more efficient 2d pattern matching techniques and may lead to improvements in multi-dimensional compression schemes. Existing algorithms for finding side-sharing tandems are far from optimal on 2d arrays that contain relatively few side-sharing tandems. In this paper, we introduce the idea of a run of side-sharing tandems, as a maximally extended chain of 2d tandems. We demonstrate tight upper bounds on the number of runs of side-sharing tandems that can occur in a rectangular array. We develop an algorithm that locates all <em>τ</em> runs of side-sharing tandems in an <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> input array in <span><math><mi>O</mi><mo>(</mo><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>τ</mi><mo>)</mo><mi>log</mi><mo></mo><mi>n</mi><mo>/</mo><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> time. We also introduce several versions of approximate side-sharing tandems with <em>k</em> mismatches along with efficient algorithms for locating them in a rectangular array.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 115005"},"PeriodicalIF":0.9,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178840","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}
Pub Date : 2024-11-28DOI: 10.1016/j.tcs.2024.115004
Elena Biagi , Davide Cenzato , Zsuzsanna Lipták , Giuseppe Romana
The Bijective Burrows-Wheeler Transform (BBWT) is a variant of the famous BWT [Burrows and Wheeler, 1994]. The BBWT was introduced by Gil and Scott in 2012, and is based on the extended BWT of Mantaci et al. [TCS 2007] and on the Lyndon factorization of the input string. In the original paper, the compression achieved with the BBWT was shown to be competitive with that of the BWT, and it has been gaining interest in recent years. In this work, we present the first study of the number of runs of the BBWT, which is a measure of its compression power. We exhibit an infinite family of strings on which of the string and of its reverse differ by a multiplicative factor of , where n is the length of the string. We also give several theoretical results on the BBWT, including a characterization of binary strings for which the BBWT has two runs. Finally, we present experimental results and statistics on and , as well as on the number of Lyndon factors in the Lyndon factorization of s and .
{"title":"On the number of equal-letter runs of the bijective Burrows-Wheeler transform","authors":"Elena Biagi , Davide Cenzato , Zsuzsanna Lipták , Giuseppe Romana","doi":"10.1016/j.tcs.2024.115004","DOIUrl":"10.1016/j.tcs.2024.115004","url":null,"abstract":"<div><div>The Bijective Burrows-Wheeler Transform (BBWT) is a variant of the famous BWT [Burrows and Wheeler, 1994]. The BBWT was introduced by Gil and Scott in 2012, and is based on the extended BWT of Mantaci et al. [TCS 2007] and on the Lyndon factorization of the input string. In the original paper, the compression achieved with the BBWT was shown to be competitive with that of the BWT, and it has been gaining interest in recent years. In this work, we present the first study of the number <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>B</mi></mrow></msub></math></span> of runs of the BBWT, which is a measure of its compression power. We exhibit an infinite family of strings on which <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>B</mi></mrow></msub></math></span> of the string and of its reverse differ by a multiplicative factor of <span><math><mi>Θ</mi><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>, where <em>n</em> is the length of the string. We also give several theoretical results on the BBWT, including a characterization of binary strings for which the BBWT has two runs. Finally, we present experimental results and statistics on <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>(</mo><mi>s</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>(</mo><msup><mrow><mi>s</mi></mrow><mrow><mtext>rev</mtext></mrow></msup><mo>)</mo></math></span>, as well as on the number of Lyndon factors in the Lyndon factorization of <em>s</em> and <span><math><msup><mrow><mi>s</mi></mrow><mrow><mtext>rev</mtext></mrow></msup></math></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1027 ","pages":"Article 115004"},"PeriodicalIF":0.9,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138842","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}
Pub Date : 2024-11-28DOI: 10.1016/j.tcs.2024.115003
Maria Constantin , Alexandru Popa
Biological computation is the field that studies the computations performed by the biological systems and includes the development of algorithms or other computational techniques inspired by nature. The genome rearrangements that occur during genome evolution are an important example of a natural computation process which inspired multiple problems that can be solved using combinatorial models. A popular problem inspired by genome evolution is computing the genetic distance between two organisms by identifying the minimum number of genome rearrangements needed to obtain one genome from the other. Given two chromosomes, represented as strings over the DNA alphabet {A, C, G, T}, the translocation operation is defined as a prefix interchange between these chromosomes. Thus, two new chromosomes are obtained after a translocation. When the chromosomes are interchanging equal length prefixes, the translocation operation is called uniform. A translocation sequence is a series of translocation operations applied to an initial genome, represented as a set of strings (initial set), resulting in a new genome, also represented as a set of strings (target set). Given a translocation sequence, if the strings exchanging prefixes are part of the initial set or have additional copies created by preceding translocations than those utilised, then the translocation sequence is referred to as contiguous. The translocation distance between two given genomes is defined as the minimum number of translocation operations necessary to obtain one genome from the other. We introduce a new polynomial time exact algorithm to compute the uniform contiguous translocation distance for a target genome of size two. Then, we present a polynomial time 2-approximation algorithm for the non-uniform contiguous translocation distance considering a target genome of size one.
{"title":"Exact and approximation algorithms for the contiguous translocation distance problem","authors":"Maria Constantin , Alexandru Popa","doi":"10.1016/j.tcs.2024.115003","DOIUrl":"10.1016/j.tcs.2024.115003","url":null,"abstract":"<div><div>Biological computation is the field that studies the computations performed by the biological systems and includes the development of algorithms or other computational techniques inspired by nature. The genome rearrangements that occur during genome evolution are an important example of a natural computation process which inspired multiple problems that can be solved using combinatorial models. A popular problem inspired by genome evolution is computing the genetic distance between two organisms by identifying the minimum number of genome rearrangements needed to obtain one genome from the other. Given two chromosomes, represented as strings over the DNA alphabet {A, C, G, T}, the translocation operation is defined as a prefix interchange between these chromosomes. Thus, two new chromosomes are obtained after a translocation. When the chromosomes are interchanging equal length prefixes, the translocation operation is called uniform. A translocation sequence is a series of translocation operations applied to an initial genome, represented as a set of strings (initial set), resulting in a new genome, also represented as a set of strings (target set). Given a translocation sequence, if the strings exchanging prefixes are part of the initial set or have additional copies created by preceding translocations than those utilised, then the translocation sequence is referred to as contiguous. The translocation distance between two given genomes is defined as the minimum number of translocation operations necessary to obtain one genome from the other. We introduce a new polynomial time exact algorithm to compute the uniform contiguous translocation distance for a target genome of size two. Then, we present a polynomial time 2-approximation algorithm for the non-uniform contiguous translocation distance considering a target genome of size one.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 115003"},"PeriodicalIF":0.9,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178841","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}
Pub Date : 2024-11-26DOI: 10.1016/j.tcs.2024.114988
Naonori Kakimura , Tomohiro Nakayoshi
In this paper, we study the Min-cost Perfect k-way Matching with Delays (k-MPMD), recently introduced by Melnyk et al. In the problem, m requests arrive one-by-one over time in a metric space. At any time, we can irrevocably make a group of k requests who arrived so far, that incurs the distance cost among the k requests in addition to the sum of the waiting cost for the k requests. The goal is to partition all the requests into groups of k requests, minimizing the total cost. The problem is a generalization of the min-cost perfect matching with delays (corresponding to 2-MPMD). It is known that no online algorithm for k-MPMD can achieve a bounded competitive ratio in general, where the competitive ratio is the worst-case ratio between its performance and the offline optimal value. On the other hand, k-MPMD is known to admit a randomized online algorithm with competitive ratio for a certain class of k-point metrics called the H-metric, where n is the size of the metric space. In this paper, we propose a deterministic online algorithm with a competitive ratio of for the k-MPMD in H-metric space. Furthermore, we show that the competitive ratio can be improved to if the metric is given as a diameter on a line.
{"title":"Deterministic primal-dual algorithms for online k-way matching with delays","authors":"Naonori Kakimura , Tomohiro Nakayoshi","doi":"10.1016/j.tcs.2024.114988","DOIUrl":"10.1016/j.tcs.2024.114988","url":null,"abstract":"<div><div>In this paper, we study the Min-cost Perfect <em>k</em>-way Matching with Delays (<em>k</em>-MPMD), recently introduced by Melnyk et al. In the problem, <em>m</em> requests arrive one-by-one over time in a metric space. At any time, we can irrevocably make a group of <em>k</em> requests who arrived so far, that incurs the distance cost among the <em>k</em> requests in addition to the sum of the waiting cost for the <em>k</em> requests. The goal is to partition all the requests into groups of <em>k</em> requests, minimizing the total cost. The problem is a generalization of the min-cost perfect matching with delays (corresponding to 2-MPMD). It is known that no online algorithm for <em>k</em>-MPMD can achieve a bounded competitive ratio in general, where the competitive ratio is the worst-case ratio between its performance and the offline optimal value. On the other hand, <em>k</em>-MPMD is known to admit a randomized online algorithm with competitive ratio <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>5</mn></mrow></msup><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> for a certain class of <em>k</em>-point metrics called the <em>H</em>-metric, where <em>n</em> is the size of the metric space. In this paper, we propose a deterministic online algorithm with a competitive ratio of <span><math><mi>O</mi><mo>(</mo><mi>m</mi><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> for the <em>k</em>-MPMD in <em>H</em>-metric space. Furthermore, we show that the competitive ratio can be improved to <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> if the metric is given as a diameter on a line.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 114988"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179772","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}
Pub Date : 2024-11-26DOI: 10.1016/j.tcs.2024.114986
Hongjie Guo , Jianzhong Li , Hong Gao
Multi-criteria decision-making typically requires selecting a concise, representative set from large databases. Regret minimization set (RMS) queries have emerged as a solution to circumvent the necessity of a utility function in top-k queries and to address the expansive result sets produced by skyline queries. However, traditional RMS formulations only ensure one result under any utility function and do not account for the diversity and freshness of results. This study introduces the concept of strong regret minimization set (SRMS), ensuring the utility value accuracy of selected k data points under any utility function while incorporating result diversity and freshness. We explore two new computational challenges: the Minimum Size problem, focusing on reducing the result set size with bounded utility error, and the Max-sum Diversity and Freshness problem, aiming to optimize the diversity and freshness of the selected set. Both problems are proved to be NP-hard, and we develop approximation algorithms for them. Experimental results on both real-world and synthetic data show high efficiency and scalability of proposed algorithms.
多标准决策通常需要从大型数据库中选择具有代表性的简明集合。遗憾最小化集（RMS）查询作为一种解决方案应运而生，它规避了 top-k 查询中效用函数的必要性，并解决了天际线查询产生的庞大结果集问题。然而，传统的 RMS 公式只能确保在任何效用函数下都有一个结果，而且不考虑结果的多样性和新鲜度。本研究引入了强遗憾最小化集（SRMS）的概念，在任意效用函数下确保所选 k 个数据点的效用值准确性，同时考虑结果的多样性和新鲜度。我们探索了两个新的计算挑战：最小尺寸问题（侧重于在效用误差受限的情况下缩小结果集尺寸）和最大总和多样性和新鲜度问题（旨在优化所选结果集的多样性和新鲜度）。这两个问题都被证明是 NP 难问题，我们为它们开发了近似算法。在真实世界和合成数据上的实验结果表明，所提出的算法具有很高的效率和可扩展性。
{"title":"Towards strong regret minimization sets: Balancing freshness and diversity in data selection","authors":"Hongjie Guo , Jianzhong Li , Hong Gao","doi":"10.1016/j.tcs.2024.114986","DOIUrl":"10.1016/j.tcs.2024.114986","url":null,"abstract":"<div><div>Multi-criteria decision-making typically requires selecting a concise, representative set from large databases. Regret minimization set (RMS) queries have emerged as a solution to circumvent the necessity of a utility function in top-<em>k</em> queries and to address the expansive result sets produced by skyline queries. However, traditional RMS formulations only ensure one result under any utility function and do not account for the diversity and freshness of results. This study introduces the concept of strong regret minimization set (SRMS), ensuring the utility value accuracy of selected <em>k</em> data points under any utility function while incorporating result diversity and freshness. We explore two new computational challenges: the Minimum Size problem, focusing on reducing the result set size with bounded utility error, and the Max-sum Diversity and Freshness problem, aiming to optimize the diversity and freshness of the selected set. Both problems are proved to be NP-hard, and we develop approximation algorithms for them. Experimental results on both real-world and synthetic data show high efficiency and scalability of proposed algorithms.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 114986"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720861","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}
Pub Date : 2024-11-26DOI: 10.1016/j.tcs.2024.114987
Shuzhen Chen , Yuan Yuan , Youming Tao , Tianzhu Wang , Zhipeng Cai , Dongxiao Yu
Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning environments, due to obstacles such as high computation and communication costs of the Hessian matrix, sub-model diversity, staleness of training, and data heterogeneity. To overcome these obstacles, this paper presents a novel and efficient algorithm named Distributed Adaptive Newton Learning (DANL), which solves the drawbacks of Newton's method by using a simple Hessian initialization and adaptive allocation of training regions. The algorithm exhibits remarkable convergence properties, which are rigorously examined under standard assumptions in stochastic optimization. The theoretical analysis proves that DANL attains a linear convergence rate while efficiently adapting to available resources and keeping high efficiency. Furthermore, DANL shows notable independence from the condition number of the problem and removes the necessity for complex parameter tuning. Experiments demonstrate that DANL achieves linear convergence with efficient communication and strong performance across different datasets.
{"title":"Adaptive pruning-based Newton's method for distributed learning","authors":"Shuzhen Chen , Yuan Yuan , Youming Tao , Tianzhu Wang , Zhipeng Cai , Dongxiao Yu","doi":"10.1016/j.tcs.2024.114987","DOIUrl":"10.1016/j.tcs.2024.114987","url":null,"abstract":"<div><div>Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning environments, due to obstacles such as high computation and communication costs of the Hessian matrix, sub-model diversity, staleness of training, and data heterogeneity. To overcome these obstacles, this paper presents a novel and efficient algorithm named Distributed Adaptive Newton Learning (<span>DANL</span>), which solves the drawbacks of Newton's method by using a simple Hessian initialization and adaptive allocation of training regions. The algorithm exhibits remarkable convergence properties, which are rigorously examined under standard assumptions in stochastic optimization. The theoretical analysis proves that <span>DANL</span> attains a linear convergence rate while efficiently adapting to available resources and keeping high efficiency. Furthermore, <span>DANL</span> shows notable independence from the condition number of the problem and removes the necessity for complex parameter tuning. Experiments demonstrate that <span>DANL</span> achieves linear convergence with efficient communication and strong performance across different datasets.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 114987"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178789","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}
Pub Date : 2024-11-26DOI: 10.1016/j.tcs.2024.115006
Yanbo Chen , Yunlei Zhao
Sign-then-encrypt is a classical composition method of public-key encryption (PKE) and signatures. It is also viewed as a generic construction of signcryption scheme, a primitive that provides confidentiality and authenticity simultaneously. In this work, we study how to sign-then-encrypt with CPA-to-CCA security enhancement and shorter ciphertext.
Our first step is to combine sign-then-encrypt with the Fujisaki-Okamoto (FO) transformation. The FO transformation is a useful technique to construct CCA-secure PKE from CPA-secure schemes in the random oracle model (ROM). Some extra randomness should be encrypted in the FO transformation. We show that when combined with sign-then-encrypt, we can realize “free” FO transformation by replacing the encrypted randomness in the FO transformation with a high-entropy signature. Then we give another construction based on a variant of the FO transformation, requiring a CPA-secure key encapsulation mechanism (KEM) instead of PKE.
Our second step is to further compress the ciphertext, focusing on signatures from the Fiat-Shamir transformation. We use the challenge part of the signature as the random coins used in the KEM, for which we call our general construction “Encrypt-with-Challenge”. Requiring some joint properties between the signature scheme and the KEM, the symmetric key or the key encapsulation can replace the challenge in the signature. We thus further remove the encrypted challenge from the ciphertext.
Finally, we give instantiations of Encrypt-with-Challenge. Our ElGamal-based construction has comparable ciphertext size with existing signcryption schemes and is the first to achieve CCA security from standard CDH assumption.
{"title":"Sign-then-encrypt with security enhancement and compressed ciphertext","authors":"Yanbo Chen , Yunlei Zhao","doi":"10.1016/j.tcs.2024.115006","DOIUrl":"10.1016/j.tcs.2024.115006","url":null,"abstract":"<div><div>Sign-then-encrypt is a classical composition method of public-key encryption (PKE) and signatures. It is also viewed as a generic construction of signcryption scheme, a primitive that provides confidentiality and authenticity simultaneously. In this work, we study how to sign-then-encrypt with CPA-to-CCA security enhancement and shorter ciphertext.</div><div>Our first step is to combine sign-then-encrypt with the Fujisaki-Okamoto (FO) transformation. The FO transformation is a useful technique to construct CCA-secure PKE from CPA-secure schemes in the random oracle model (ROM). Some extra randomness should be encrypted in the FO transformation. We show that when combined with sign-then-encrypt, we can realize “free” FO transformation by replacing the encrypted randomness in the FO transformation with a high-entropy signature. Then we give another construction based on a variant of the FO transformation, requiring a CPA-secure key encapsulation mechanism (KEM) instead of PKE.</div><div>Our second step is to further compress the ciphertext, focusing on signatures from the Fiat-Shamir transformation. We use the challenge part of the signature as the random coins used in the KEM, for which we call our general construction “Encrypt-with-Challenge”. Requiring some joint properties between the signature scheme and the KEM, the symmetric key or the key encapsulation can replace the challenge in the signature. We thus further remove the encrypted challenge from the ciphertext.</div><div>Finally, we give instantiations of Encrypt-with-Challenge. Our ElGamal-based construction has comparable ciphertext size with existing signcryption schemes and is the first to achieve CCA security from standard CDH assumption.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1027 ","pages":"Article 115006"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138845","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}
Pub Date : 2024-11-22DOI: 10.1016/j.tcs.2024.114985
Julien Bensmail , Hervé Hocquard , Clara Marcille
In connection with the so-called 1-2-3 Conjecture, we introduce and study a new variant of proper labellings, obtained when aiming at designing, for an oriented graph, an oriented colouring through the sums of labels incident to its vertices. Formally, for an oriented graph and a k-labelling of its arcs, for every vertex , one can compute the sum of labels assigned by ℓ to its incident arcs. We call ℓ an oriented labelling if the sum function σ indeed forms an oriented colouring of . That is, for any two arcs and of , if , then we must have . We denote by the smallest k such that oriented k-labellings of exist (if any).
We study this new parameter in general and in particular contexts. In particular, we observe that there is no constant bound on in general, contrarily to the undirected case. Still, we establish connections between this parameter and others, such as the oriented chromatic number, from which we deduce other types of bounds, some of which we improve upon for some classes of oriented graphs. We also investigate other aspects of this parameter, such as the complexity of determining for a given oriented graph , or the possible relationships between and the underlying graph G of .
关于所谓的 1-2-3 猜想，我们介绍并研究了适当标记的一种新变体，其目的是通过其顶点的标记之和为定向图设计定向着色。形式上，对于一个定向图及其弧的 k 标签，对于每个顶点 ，我们可以计算 ℓ 分配给其入射弧的标签之和σ(v)。如果和函数 σ 确实构成了 ℓ 的定向着色，我们称 ℓ 为定向标签。 也就是说，对于 ℓ 的任意两条弧，如果 σ(a)=σ(d), 那么我们必须有 σ(b)≠σ(c).我们用最小的 k 表示，这样就存在定向 k 标签（如果有的话）。我们将研究这个新参数的一般情况和特殊情况。特别是，我们观察到，与不定向情况相反，一般情况下没有常数约束。尽管如此，我们还是在这个参数和其他参数（如有向色度数）之间建立了联系，并由此推导出其他类型的约束，其中一些约束在某些有向图类中得到了改进。我们还研究了这一参数的其他方面，例如确定给定定向图 ，或其底层图 G 之间可能存在的关系的复杂性。
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The problem of determining whether a graph G contains another graph H as a minor, referred to as the minor containment problem, is a fundamental problem in the field of graph algorithms. While the problem is -complete in general, it can be tractable on some restricted graph classes. This study focuses on the case where both G and H are trees, known as the tree minor containment problem. Even in this case, the problem is known to be -complete. In contrast, polynomial-time algorithms are known for the case when both trees are caterpillars or when the maximum degree of H is a constant. Our research aims to clarify the boundary of tractability and intractability for the tree minor containment problem. Specifically, we provide complexity dichotomies for the problem based on three structural parameters: diameter, pathwidth, and path eccentricity.
确定一个图 G 是否包含另一个图 H 作为次要图的问题，称为次要图包含问题，是图算法领域的一个基本问题。虽然这个问题在一般情况下是 NP-完全的，但在某些受限的图类中是可以解决的。本研究侧重于 G 和 H 都是树的情况，即所谓的树次要包含问题。即使在这种情况下，该问题也是已知的 NP-完全问题。相比之下，已知的多项式时间算法适用于两棵树都是毛毛虫或 H 的最大度是常数的情况。我们的研究旨在澄清树小包含问题的可处理性和不可处理性的界限。具体来说，我们根据三个结构参数：直径、路径宽度和路径偏心率，为该问题提供了复杂性二分法。
{"title":"Dichotomies for tree minor containment with structural parameters","authors":"Tatsuya Gima , Soh Kumabe , Kazuhiro Kurita , Yuto Okada , Yota Otachi","doi":"10.1016/j.tcs.2024.114984","DOIUrl":"10.1016/j.tcs.2024.114984","url":null,"abstract":"<div><div>The problem of determining whether a graph <em>G</em> contains another graph <em>H</em> as a minor, referred to as the <em>minor containment problem</em>, is a fundamental problem in the field of graph algorithms. While the problem is <span><math><mi>NP</mi></math></span>-complete in general, it can be tractable on some restricted graph classes. This study focuses on the case where both <em>G</em> and <em>H</em> are trees, known as the <em>tree minor containment problem</em>. Even in this case, the problem is known to be <span><math><mi>NP</mi></math></span>-complete. In contrast, polynomial-time algorithms are known for the case when both trees are caterpillars or when the maximum degree of <em>H</em> is a constant. Our research aims to clarify the boundary of tractability and intractability for the tree minor containment problem. Specifically, we provide complexity dichotomies for the problem based on three structural parameters: diameter, pathwidth, and path eccentricity.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 114984"},"PeriodicalIF":0.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720862","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}
Pub Date : 2024-11-22DOI: 10.1016/j.tcs.2024.114983
David F. Anderson , Badal Joshi
Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting values of other chemical species. In this paper, we design chemical systems that carry out the elementary arithmetic computations of: identification, inversion, mth roots (for ), addition, multiplication, absolute difference, rectified subtraction over non-negative real numbers, and partial real inversion over real numbers. We prove that these “elementary modules” have a speed of computation that is independent of the inputs to the computation. Moreover, we prove that finite sequences of such elementary modules, running in parallel, can carry out composite arithmetic over real numbers, also at a rate that is independent of inputs. Furthermore, we show that the speed of a composite computation is precisely the speed of the slowest elementary step. Specifically, the scale of the composite computation, i.e. the number of elementary steps involved in the composite, does not affect the overall asymptotic speed – a feature of the parallel computing nature of our algorithm. Our proofs require the careful mathematical analysis of certain non-autonomous systems, and we believe this analysis will be useful in different areas of applied mathematics, dynamical systems, and the theory of computation. We close with a discussion on future research directions, including numerous important open theoretical questions pertaining to the field of computation with reaction networks.
最近的技术进步使我们能够将化学物质作用系统视为模拟计算机。在这种情况下，计算的输入被编码为某些化学物质的初始值，而输出则是其他化学物质的极限值。在本文中，我们设计的化学系统可进行以下基本算术计算：识别、反演、第 m 次根（m≥2 时）、加法、乘法、绝对差、非负实数的整除减法和实数的部分实数反演。我们证明，这些 "基本模块 "的计算速度与计算的输入无关。此外，我们还证明，并行运行的此类基本模块的有限序列可以对实数进行复合运算，而且运算速度与输入无关。此外，我们还证明，复合计算的速度正是最慢基本步骤的速度。具体来说，复合计算的规模，即复合计算所涉及的基本步骤的数量，不会影响整体渐近速度--这是我们算法并行计算特性的一个特征。我们的证明需要对某些非自治系统进行仔细的数学分析，我们相信这种分析将有助于应用数学、动力系统和计算理论等不同领域的研究。最后，我们讨论了未来的研究方向，包括与反应网络计算领域相关的许多重要的开放性理论问题。
{"title":"Chemical mass-action systems as analog computers: Implementing arithmetic computations at specified speed","authors":"David F. Anderson , Badal Joshi","doi":"10.1016/j.tcs.2024.114983","DOIUrl":"10.1016/j.tcs.2024.114983","url":null,"abstract":"<div><div>Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting values of other chemical species. In this paper, we design chemical systems that carry out the elementary arithmetic computations of: identification, inversion, <em>m</em>th roots (for <span><math><mi>m</mi><mo>≥</mo><mn>2</mn></math></span>), addition, multiplication, absolute difference, rectified subtraction over non-negative real numbers, and partial real inversion over real numbers. We prove that these “elementary modules” have a speed of computation that is independent of the inputs to the computation. Moreover, we prove that finite sequences of such elementary modules, running in parallel, can carry out composite arithmetic over real numbers, also at a rate that is independent of inputs. Furthermore, we show that the speed of a composite computation is precisely the speed of the slowest elementary step. Specifically, the scale of the composite computation, i.e. the number of elementary steps involved in the composite, does not affect the overall asymptotic speed – a feature of the parallel computing nature of our algorithm. Our proofs require the careful mathematical analysis of certain non-autonomous systems, and we believe this analysis will be useful in different areas of applied mathematics, dynamical systems, and the theory of computation. We close with a discussion on future research directions, including numerous important open theoretical questions pertaining to the field of computation with reaction networks.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1025 ","pages":"Article 114983"},"PeriodicalIF":0.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719766","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}
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