Theoretical Computer Science最新文献_第7页

Stand-up indulgent gathering on lines 站立式放纵聚会

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-22 DOI: 10.1016/j.tcs.2024.114796

引用次数: 0

An accelerated deterministic algorithm for maximizing monotone submodular minus modular function with cardinality constraint 一种加速确定性算法，用于最大化具有卡方约束的单调亚模态减模态函数

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-22 DOI: 10.1016/j.tcs.2024.114798

{"title":"An accelerated deterministic algorithm for maximizing monotone submodular minus modular function with cardinality constraint","authors":"","doi":"10.1016/j.tcs.2024.114798","DOIUrl":"10.1016/j.tcs.2024.114798","url":null,"abstract":"<div>Submodular optimization not only covers some classical combinatorial optimization problems, but also has a wide range of applications in fields such as machine learning and artificial intelligence. For submodular maximization problems with constraints, some work has been done including the design of approximation algorithms, the measurement of approximation algorithms in terms of quality and efficiency, etc. In this paper, we consider the problem of maximizing a non-negative monotone submodular function minus a non-negative modular function with the cardinality constraint. This model has been applied to many scenarios, such as team formation problem, influence maximization problem, recommender systems problem, etc. We propose a threshold algorithm that achieve a <math><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>−</mo><mi>O</mi><mo>(</mo><mi>ε</mi><mo>)</mo><mo>,</mo><mn>2</mn><mo>)</mo></math>-bicriteria approximation ratio and query complexity <math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math>. Our algorithm makes a small sacrifice in the approximation ratio but improves the best query complexity result of existing deterministic algorithms from <math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> to <math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> in the worst case.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142050030","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 the connectedness of arithmetic hyperplanes 论算术超平面的连通性

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-22 DOI: 10.1016/j.tcs.2024.114797

{"title":"On the connectedness of arithmetic hyperplanes","authors":"","doi":"10.1016/j.tcs.2024.114797","DOIUrl":"10.1016/j.tcs.2024.114797","url":null,"abstract":"<div>Discrete geometry is a geometry specific to computers that studies <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math> structures. It appears naturally in image analysis or 3D printing. Our goal is to find efficient algorithms to characterise these geometric structures and their properties.We are interested in a fundamental structure of discrete geometry, the arithmetic hyperplanes, and more particularly in their connectedness. Many works have studied a connectedness defined from the neighbourhood by faces and have allowed to observe a percolation phenomenon. These studies have also allowed to decide the connectedness of a plane in an efficient way. We propose an extension of these results in the case of connectivity defined from general neighbourhoods.Beyond the new concepts that this extension requires, the main contribution of the paper lies in the use of analysis to solve this arithmetic problem and in the design of an algorithm that decides the general connectedness problem. The study of the thickness of connectedness as a function reveals discontinuities at each rational point. However, a much more regular underlying structure appears in the irrational case. Thus, the consideration of irrational vectors allows a simpler approach to the connectedness of arithmetic hyperplanes.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142087845","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

Process-commutative distributed objects: From cryptocurrencies to Byzantine-Fault-Tolerant CRDTs 进程互变分布式对象：从加密货币到拜占庭容错 CRDT

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-20 DOI: 10.1016/j.tcs.2024.114794

引用次数: 0

Transformations of probability distributions 概率分布的变换

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-20 DOI: 10.1016/j.tcs.2024.114786

{"title":"Transformations of probability distributions","authors":"","doi":"10.1016/j.tcs.2024.114786","DOIUrl":"10.1016/j.tcs.2024.114786","url":null,"abstract":"<div>Almost all of computer science is concerned with transformations of information in the form of strings. We initiate the study of a neglected transformation type, namely transformations between probability distributions. We begin by examining the deceivingly simple-looking case of Bernoulli distributions and procedures to transform them.A p-coin is a coin that, whenever tossed, lands heads up with probability p and tails up with probability <math><mn>1</mn><mo>−</mo><mi>p</mi></math>. A neat trick due to von Neumann allows us to simulate a 1/2-coin with any p-coin for an arbitrary unknown <math><mi>p</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>. We show how to apply this trick to simulate a q-coin for an arbitrary computable <math><mi>q</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>. In contrast, it is impossible to simulate a q-coin with a noncomputable q.More generally, we are interested in what transformations between probability distributions are feasible. Is it possible to simulate a <math><mi>p</mi><mo>/</mo><mn>2</mn></math>-coin with a p-coin for unknown p? How about 2p or <math><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></math>? We attempt to characterize the feasible transformations. For example, we show how to transform a p-coin into an <math><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo></math>-coin where any finite number of pairs <math><mo>(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>)</mo></math> of non-zero, non-one probabilities is prescribed, and that it is impossible to do the same for an infinite number of pairs. We also examine which probability distributions are feasible to approximate to arbitrary precision, showing that this is impossible for discontinuous ones but feasible for most but not all remaining ones.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136055","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

γ-clustering problems: Classical and parametrized complexity γ 聚类问题：经典复杂性和参数复杂性

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-20 DOI: 10.1016/j.tcs.2024.114784

引用次数: 0

Binary distinguishability operation 二进制区分操作

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-20 DOI: 10.1016/j.tcs.2024.114782

引用次数: 0

Dichotomies for Maximum Matching Cut: H-freeness, bounded diameter, bounded radius 最大匹配切割的二分法：无 H 值、有界直径、有界半径

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-20 DOI: 10.1016/j.tcs.2024.114795

{"title":"Dichotomies for Maximum Matching Cut: H-freeness, bounded diameter, bounded radius","authors":"","doi":"10.1016/j.tcs.2024.114795","DOIUrl":"10.1016/j.tcs.2024.114795","url":null,"abstract":"<div>The (Perfect) Matching Cut problem is to decide if a graph G has a (perfect) matching cut, i.e., a (perfect) matching that is also an edge cut of G. Both Matching Cut and Perfect Matching Cut are known to be NP-complete. A perfect matching cut is also a matching cut with maximum number of edges. To increase our understanding of the relationship between the two problems, we perform a complexity study for the Maximum Matching Cut problem, which is to determine a largest matching cut in a graph. Our results yield full dichotomies of Maximum Matching Cut for graphs of bounded diameter, bounded radius and H-free graphs. A disconnected perfect matching of a graph G is a perfect matching that contains a matching cut of G. We also show how our new techniques can be used for finding a disconnected perfect matching with a largest matching cut for special graph classes. In this way we can prove that the decision problem Disconnected Perfect Matching is polynomial-time solvable for <math><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>+</mo><mi>s</mi><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math>-free graphs for every <math><mi>s</mi><mo>≥</mo><mn>0</mn></math>, extending a known result for <math><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub></math>-free graphs (Bouquet and Picouleau, 2020).</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004122/pdfft?md5=080f5be8832cd8e314696c9f4da5ed04&pid=1-s2.0-S0304397524004122-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142075947","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

Multiagent learning for competitive opinion optimization 竞争性意见优化的多代理学习

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-19 DOI: 10.1016/j.tcs.2024.114787

引用次数: 0

The parameterized complexity of welfare guarantees in Schelling segregation 谢林隔离中福利保障的参数化复杂性

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-08-16 DOI: 10.1016/j.tcs.2024.114783

{"title":"The parameterized complexity of welfare guarantees in Schelling segregation","authors":"","doi":"10.1016/j.tcs.2024.114783","DOIUrl":"10.1016/j.tcs.2024.114783","url":null,"abstract":"<div>Schelling's model considers k types of agents each of whom needs to select a vertex on an undirected graph and prefers neighboring agents of the same type. We are motivated by a recent line of work that studies solutions which are optimal with respect to notions related to the welfare of the agents. We explore the parameterized complexity of computing such solutions. We focus on the well-studied notions of social welfare (WO) and Pareto optimality (PO), alongside the recently proposed notions of group-welfare optimality (GWO) and utility-vector optimality (UVO), both of which lie between WO and PO. Firstly, we focus on the fundamental case where <math><mi>k</mi><mo>=</mo><mn>2</mn></math> with r red agents and b blue agents. We show that all solution-notions we consider are intractable even when <math><mi>b</mi><mo>=</mo><mn>1</mn></math> and that they do not admit any FPT algorithm when parameterized by r and b, unless <math><mtext>FPT</mtext><mo>=</mo><mtext>W</mtext><mo>[</mo><mn>1</mn><mo>]</mo></math>. In addition, we show that WO and GWO remain intractable even on cubic graphs. We complement these negative results with an FPT algorithm parameterized by <math><mi>r</mi><mo>,</mo><mi>b</mi></math> and the maximum degree of the graph. For the general case with <math><mi>k</mi><mo>≥</mo><mn>2</mn></math> types of agents, we prove that for any of the notions we consider the problem remains hard when parameterized by k for a large family of graphs that includes trees. We accompany these negative results with an XP algorithm parameterized by k and the treewidth of the graph.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004006/pdfft?md5=7297943aa04e1b17616df20ad757dfa3&pid=1-s2.0-S0304397524004006-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142086965","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