Information Processing Letters最新文献_第9页

Red Blue Set Cover problem on axis-parallel hyperplanes and other objects 轴平行超平面和其他物体上的红蓝套覆盖问题

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-29 DOI: 10.1016/j.ipl.2024.106485

V.P. Abidha , Pradeesha Ashok

{"title":"Red Blue Set Cover problem on axis-parallel hyperplanes and other objects","authors":"V.P. Abidha , Pradeesha Ashok","doi":"10.1016/j.ipl.2024.106485","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106485","url":null,"abstract":"<div>Given a universe <math><mi>U</mi><mo>=</mo><mi>R</mi><mo>∪</mo><mi>B</mi></math> of a finite set of red elements R, and a finite set of blue elements B and a family <math><mi>F</mi></math> of subsets of <math><mi>U</mi></math>, the Red Blue Set Cover problem is to find a subset <math><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup></math> of <math><mi>F</mi></math> that covers all blue elements of B and minimum number of red elements from R.We prove that the Red Blue Set Cover problem is NP-hard even when R and B respectively are sets of red and blue points in <math><msup><mrow><mi>IR</mi></mrow><mrow><mn>2</mn></mrow></msup></math> and the sets in <math><mi>F</mi></math> are defined by axis−parallel lines i.e., every set is a maximal set of points with the same x or y coordinate.We then study the parameterized complexity of a generalization of this problem, where <math><mi>U</mi></math> is a set of points in <math><msup><mrow><mi>IR</mi></mrow><mrow><mi>d</mi></mrow></msup></math> and <math><mi>F</mi></math> is a collection of set of axis−parallel hyperplanes in <math><msup><mrow><mi>IR</mi></mrow><mrow><mi>d</mi></mrow></msup></math> under different parameterizations, where d is a constant. For every parameter, we show that the problem is fixed-parameter tractable and also show the existence of a polynomial kernel. We further consider the Red Blue Set Cover problem for some special types of rectangles in <math><msup><mrow><mi>IR</mi></mrow><mrow><mn>2</mn></mrow></msup></math>.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106485"},"PeriodicalIF":0.5,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140042109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The group factorization problem in finite groups of Lie type 有限列群的群因式分解问题

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-28 DOI: 10.1016/j.ipl.2024.106484

Haibo Hong, Shi Bai, Fenghao Liu

引用次数: 0

Regular resolution effectively simulates resolution 常规分辨率有效模拟分辨率

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-28 DOI: 10.1016/j.ipl.2024.106489

Sam Buss , Emre Yolcu

引用次数: 0

Learning-augmented maximum flow 学习增强最大流量

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-28 DOI: 10.1016/j.ipl.2024.106487

Adam Polak , Maksym Zub

{"title":"Learning-augmented maximum flow","authors":"Adam Polak , Maksym Zub","doi":"10.1016/j.ipl.2024.106487","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106487","url":null,"abstract":"<div>We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since these were unknown at the time of learning). We present an algorithm that, given an m-edge flow network and a predicted flow, computes a maximum flow in <math><mi>O</mi><mo>(</mo><mi>m</mi><mi>η</mi><mo>)</mo></math> time, where η is the <math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> error of the prediction, i.e., the sum over the edges of the absolute difference between the predicted and optimal flow values. Moreover, we prove that, given an oracle access to a distribution over flow networks, it is possible to efficiently PAC-learn a prediction minimizing the expected <math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> error over that distribution. Our results fit into the recent line of research on learning-augmented algorithms, which aims to improve over worst-case bounds of classical algorithms by using predictions, e.g., machine-learned from previous similar instances. So far, the main focus in this area was on improving competitive ratios for online problems. Following Dinitz et al. (2021) [6], our results are among the firsts to improve the running time of an offline problem.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106487"},"PeriodicalIF":0.5,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140030945","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

Prenex universal first-order safety properties Prenex 通用一阶安全特性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-28 DOI: 10.1016/j.ipl.2024.106488

Besik Dundua , Ioane Kapanadze , Helmut Seidl

引用次数: 0

Tight inapproximability of Nash equilibria in public goods games 公共物品博弈中纳什均衡的严密不可逼近性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-27 DOI: 10.1016/j.ipl.2024.106486

Jérémi Do Dinh , Alexandros Hollender

引用次数: 0

Recognizing LBFS trees of bipartite graphs 识别二方图的 LBFS 树

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-09 DOI: 10.1016/j.ipl.2024.106483

Robert Scheffler

{"title":"Recognizing LBFS trees of bipartite graphs","authors":"Robert Scheffler","doi":"10.1016/j.ipl.2024.106483","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106483","url":null,"abstract":"<div>The graph searches Breadth First Search (BFS) and Depth First Search (DFS) and the spanning trees constructed by them are some of the most basic concepts in algorithmic graph theory. BFS trees are first-in trees, i.e., every vertex is connected to its first visited neighbor. DFS trees are last-in trees, i.e., every vertex is connected to the last visited neighbor before it. The problem whether a given spanning tree can be the first-in tree or last-in tree of a graph search ordering was introduced in the 1980s and has been studied for several graph searches and graph classes. Here, we consider the problem of deciding whether a given spanning tree of a bipartite graph can be a first-in tree or a last-in tree of the Lexicographic Breadth First Search (LBFS), a special variant of BFS that is commonly used in graph algorithms. We show that the recognition of both first-in trees and last-in trees of LBFS is <math><mi>NP</mi></math>-hard even if the start vertex of the search ordering is fixed and the height of the tree is four. We prove that the bound on the height is tight (unless <math><mi>P</mi><mo>=</mo><mrow><mi>NP</mi></mrow></math>) by showing that for all spanning trees of bipartite graphs with height smaller than four we can solve both search tree recognition problems of LBFS in polynomial time. Finally, we give a linear-time algorithm that solves both problems for chordal bipartite graphs and fixed start vertices.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106483"},"PeriodicalIF":0.5,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000139/pdfft?md5=0a705320becd861a4100ad392710d19e&pid=1-s2.0-S0020019024000139-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139738315","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

Skolem and positivity completeness of ergodic Markov chains 遍历马尔可夫链的斯科莱姆和实在性完备性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-07 DOI: 10.1016/j.ipl.2024.106481

Mihir Vahanwala

{"title":"Skolem and positivity completeness of ergodic Markov chains","authors":"Mihir Vahanwala","doi":"10.1016/j.ipl.2024.106481","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106481","url":null,"abstract":"<div>We consider the following Markov Reachability decision problems that view Markov Chains as Linear Dynamical Systems: given a finite, rational Markov Chain, source and target states, and a rational threshold, does the probability of reaching the target from the source at the <math><msup><mrow><mi>n</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msup></math> step: (i) equal the threshold for some n? (ii) cross the threshold for some n? (iii) cross the threshold for infinitely many n? These problems are respectively known to be equivalent to the Skolem, Positivity, and Ultimate Positivity problems for Linear Recurrence Sequences (LRS), number-theoretic problems whose decidability has been open for decades. We present an elementary reduction from LRS Problems to Markov Reachability Problems that improves the state of the art as follows. (a) We map LRS to ergodic (irreducible and aperiodic) Markov Chains that are ubiquitous, not least by virtue of their spectral structure, and (b) our reduction maps LRS of order k to Markov Chains of order <math><mi>k</mi><mo>+</mo><mn>1</mn></math>: a substantial improvement over the previous reduction that mapped LRS of order k to reducible and periodic Markov chains of order <math><mn>4</mn><mi>k</mi><mo>+</mo><mn>5</mn></math>. This contribution is significant in view of the fact that the number-theoretic hardness of verifying Linear Dynamical Systems can often be mitigated by spectral assumptions and restrictions on order.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106481"},"PeriodicalIF":0.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000115/pdfft?md5=da39be99a4cd399e31f45e5c0e089132&pid=1-s2.0-S0020019024000115-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139738314","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

On size-independent sample complexity of ReLU networks 关于与规模无关的 ReLU 网络样本复杂性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-07 DOI: 10.1016/j.ipl.2024.106482

Mark Sellke

引用次数: 0

Expressive completeness by separation for discrete time interval temporal logic with expanding modalities 通过分离实现具有扩展模态的离散时间间隔时态逻辑的表达完备性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-02-05 DOI: 10.1016/j.ipl.2024.106480

Dimitar P. Guelev , Ben Moszkowski

引用次数: 0