Theoretical Computer Science最新文献

{"title":"EFX allocations for indivisible chores: Matching-based approach","authors":"Yusuke Kobayashi ,&nbsp;Ryoga Mahara ,&nbsp;Souta Sakamoto","doi":"10.1016/j.tcs.2024.115010","DOIUrl":"10.1016/j.tcs.2024.115010","url":null,"abstract":"<div><div>One of the most important topics in discrete fair division is whether an EFX allocation exists for any instance. Although the existence of EFX allocations is a standing open problem for both goods and chores, the understanding of the existence of EFX allocations for chores is less established compared to goods. We study the existence of EFX allocation for chores under the assumption that all agents' cost functions are additive. Specifically, we design polynomial time algorithms for computing EFX allocations for the following three cases: (i) the number of chores is at most twice the number of agents, (ii) the cost functions of all agents except for one induce the same ordering, and (iii) the number of agents is three and each agent has a personalized bi-valued cost function.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 115010"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178791","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":"Complexity issues concerning the quadruple Roman domination problem in graphs","authors":"Venkata Subba Reddy Palagiri ,&nbsp;Guru Pratap Sharma ,&nbsp;Ismael G. Yero","doi":"10.1016/j.tcs.2024.115013","DOIUrl":"10.1016/j.tcs.2024.115013","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Given a graph &lt;em&gt;G&lt;/em&gt; with vertex set &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, a mapping &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is called a quadruple Roman dominating function (4RDF) for &lt;em&gt;G&lt;/em&gt; if it holds the following. Every vertex &lt;em&gt;x&lt;/em&gt; such that &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; satisfies that &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;and&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; stands for the open and closed neighborhood of &lt;em&gt;x&lt;/em&gt;, respectively. The smallest possible weight &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; among all possible 4RDFs &lt;em&gt;h&lt;/em&gt; for &lt;em&gt;G&lt;/em&gt; is the quadruple Roman domination number of &lt;em&gt;G&lt;/em&gt;, denoted by &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;This work is focused on complexity aspects for the problem of computing the value of this parameter for several graph classes. Specifically, it is shown that the decision problem concerning &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is NP-complete when restricted to star convex bipartite, comb convex bipartite, split and planar graphs. In contrast, it is also proved that such problem can be efficiently solved for threshold graphs where an exact solution is demonstrated, while for graphs having an efficient dominating set, tight upper and lower bounds in terms of the classical domination number are given. In addition, some approximation results to the problem are given. That is, we show that the problem cannot be approximated within &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for any &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; unless &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;.","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 115013"},"PeriodicalIF":0.9,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178839","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":"Egalitarian roommate allocations: Complexity and stability","authors":"Vincenzo Bonifaci ,&nbsp;Helena Rivera Dallorto","doi":"10.1016/j.tcs.2024.115009","DOIUrl":"10.1016/j.tcs.2024.115009","url":null,"abstract":"<div><div>We study two roommate assignment problems, called Ordinal Roommate Allocation and Cardinal Roommate Allocation, where students have preferences over roommates, rooms have varying capacities, and the goal is to maximize the minimum payoff of the students (under two distinct notions of payoff). Both problems are <span><math><mi>NP</mi></math></span>-hard when room sizes are unrestricted. In contrast, the Ordinal Roommate Allocation problem becomes tractable when the maximum room capacity is fixed, while the Cardinal Roommate Allocation problem remains <span><math><mi>NP</mi></math></span>-hard even with bounded room capacity and number of preferences. We then analyze the problems through the lens of stability, considering envy-freeness and a weaker notion we call swap-resistance. Not all instances guarantee an envy-free outcome, and it is shown to be <span><math><mi>NP</mi></math></span>-hard to determine which ones do. However, swap-resistance is always achievable using an efficient algorithm. We discuss connections and distinctions between our work and existing research about utilitarian matchings and stable roommate problems.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1026 ","pages":"Article 115009"},"PeriodicalIF":0.9,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178790","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":"Exact and inexact search for 2d side-sharing tandems","authors":"Shoshana Marcus ,&nbsp;Dina Sokol ,&nbsp;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}

{"title":"On the number of equal-letter runs of the bijective Burrows-Wheeler transform","authors":"Elena Biagi ,&nbsp;Davide Cenzato ,&nbsp;Zsuzsanna Lipták ,&nbsp;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}

{"title":"Exact and approximation algorithms for the contiguous translocation distance problem","authors":"Maria Constantin ,&nbsp;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}

{"title":"Deterministic primal-dual algorithms for online k-way matching with delays","authors":"Naonori Kakimura ,&nbsp;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}

{"title":"Towards strong regret minimization sets: Balancing freshness and diversity in data selection","authors":"Hongjie Guo ,&nbsp;Jianzhong Li ,&nbsp;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}

{"title":"Adaptive pruning-based Newton's method for distributed learning","authors":"Shuzhen Chen ,&nbsp;Yuan Yuan ,&nbsp;Youming Tao ,&nbsp;Tianzhu Wang ,&nbsp;Zhipeng Cai ,&nbsp;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}

{"title":"Sign-then-encrypt with security enhancement and compressed ciphertext","authors":"Yanbo Chen ,&nbsp;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}