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A Nearly Tight Lower Bound for the d-Dimensional Cow-Path Problem d维牛道问题的近紧下界
Inf. Process. Lett. Pub Date : 2022-09-17 DOI: 10.48550/arXiv.2209.08427
N. Bansal, John Kuszmaul, William Kuszmaul
{"title":"A Nearly Tight Lower Bound for the d-Dimensional Cow-Path Problem","authors":"N. Bansal, John Kuszmaul, William Kuszmaul","doi":"10.48550/arXiv.2209.08427","DOIUrl":"https://doi.org/10.48550/arXiv.2209.08427","url":null,"abstract":"In the $d$-dimensional cow-path problem, a cow living in $mathbb{R}^d$ must locate a $(d - 1)$-dimensional hyperplane $H$ whose location is unknown. The only way that the cow can find $H$ is to roam $mathbb{R}^d$ until it intersects $mathcal{H}$. If the cow travels a total distance $s$ to locate a hyperplane $H$ whose distance from the origin was $r ge 1$, then the cow is said to achieve competitive ratio $s / r$. It is a classic result that, in $mathbb{R}^2$, the optimal (deterministic) competitive ratio is $9$. In $mathbb{R}^3$, the optimal competitive ratio is known to be at most $approx 13.811$. But in higher dimensions, the asymptotic relationship between $d$ and the optimal competitive ratio remains an open question. The best upper and lower bounds, due to Antoniadis et al., are $O(d^{3/2})$ and $Omega(d)$, leaving a gap of roughly $sqrt{d}$. In this note, we achieve a stronger lower bound of $tilde{Omega}(d^{3/2})$.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"31 1","pages":"106389"},"PeriodicalIF":0.0,"publicationDate":"2022-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87141967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recognizing well-dominated graphs is coNP-complete 识别良好支配图是conp完备的
Inf. Process. Lett. Pub Date : 2022-08-18 DOI: 10.48550/arXiv.2208.08864
A. Agrawal, H. Fernau, P. Kindermann, Kevin Mann, U. Souza
{"title":"Recognizing well-dominated graphs is coNP-complete","authors":"A. Agrawal, H. Fernau, P. Kindermann, Kevin Mann, U. Souza","doi":"10.48550/arXiv.2208.08864","DOIUrl":"https://doi.org/10.48550/arXiv.2208.08864","url":null,"abstract":"A graph $G$ is well-covered if every minimal vertex cover of $G$ is minimum, and a graph $G$ is well-dominated if every minimal dominating set of $G$ is minimum. Studies on well-covered graphs were initiated in [Plummer, JCT 1970], and well-dominated graphs were first introduced in [Finbow, Hartnell and Nowakow, AC 1988]. Well-dominated graphs are well-covered, and both classes have been widely studied in the literature. The recognition of well-covered graphs was proved coNP-complete by [Chv'atal and Slater, AODM 1993] and by [Sankaranarayana and Stewart, Networks 1992], but the complexity of recognizing well-dominated graphs has been left open since their introduction. We close this complexity gap by proving that recognizing well-dominated graphs is coNP-complete. This solves a well-known open question (c.f. [Levit and Tankus, DM 2017] and [G\"{o}z\"{u}pek, Hujdurovic and Milaniv{c}, DMTCS 2017]), which was first asked in [Caro, SebH{o} and Tarsi, JAlg 1996]. Surprisingly, our proof is quite simple, although it was a long-standing open problem. Finally, we show that recognizing well-totally-dominated graphs is coNP-complete, answering a question of [Bahadir, Ekim, and G\"oz\"upek, AMC 2021].","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"43 1","pages":"106419"},"PeriodicalIF":0.0,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90617708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simplicity in Eulerian Circuits: Uniqueness and Safety 欧拉电路的简单性:唯一性和安全性
Inf. Process. Lett. Pub Date : 2022-08-17 DOI: 10.48550/arXiv.2208.08522
Nidia Obscura Acosta, Alexandru I. Tomescu
{"title":"Simplicity in Eulerian Circuits: Uniqueness and Safety","authors":"Nidia Obscura Acosta, Alexandru I. Tomescu","doi":"10.48550/arXiv.2208.08522","DOIUrl":"https://doi.org/10.48550/arXiv.2208.08522","url":null,"abstract":"An Eulerian circuit in a directed graph is one of the most fundamental Graph Theory notions. Detecting if a graph $G$ has a unique Eulerian circuit can be done in polynomial time via the BEST theorem by de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte, 1941-1951 (involving counting arborescences), or via a tailored characterization by Pevzner, 1989 (involving computing the intersection graph of simple cycles of $G$), both of which thus rely on overly complex notions for the simpler uniqueness problem. In this paper we give a new linear-time checkable characterization of directed graphs with a unique Eulerian circuit. This is based on a simple condition of when two edges must appear consecutively in all Eulerian circuits, in terms of cut nodes of the underlying undirected graph of $G$. As a by-product, we can also compute in linear-time all maximal $textit{safe}$ walks appearing in all Eulerian circuits, for which Nagarajan and Pop proposed in 2009 a polynomial-time algorithm based on Pevzner characterization.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"199 1","pages":"106421"},"PeriodicalIF":0.0,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75630682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The odd chromatic number of a toroidal graph is at most 9 环面图的奇色数不超过9
Inf. Process. Lett. Pub Date : 2022-06-12 DOI: 10.2139/ssrn.4162553
Fang Tian, Yuxue Yin
{"title":"The odd chromatic number of a toroidal graph is at most 9","authors":"Fang Tian, Yuxue Yin","doi":"10.2139/ssrn.4162553","DOIUrl":"https://doi.org/10.2139/ssrn.4162553","url":null,"abstract":"It's well known that every planar graph is $4$-colorable. A toroidal graph is a graph that can be embedded on a torus. It's proved that every toroidal graph is $7$-colorable. A proper coloring of a graph is called emph{odd} if every non-isolated vertex has at least one color that appears an odd number of times in its neighborhood. The smallest number of colors that admits an odd coloring of a graph $ G $ is denoted by $chi_{o}(G)$. In this paper, we prove that if $G$ is tortoidal, then $chi_{o}left({G}right)le9$; Note that $K_7$ is a toroidal graph, the upper bound is no less than $7$.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"48 1","pages":"106384"},"PeriodicalIF":0.0,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79535200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the Parameterized Complexity of the Maximum Exposure Problem 最大曝光问题的参数化复杂度
Inf. Process. Lett. Pub Date : 2022-03-21 DOI: 10.48550/arXiv.2203.11114
Remi Raman, S. ShahinJohnJ, R. Subashini, Subhasree Methirumangalath
{"title":"On the Parameterized Complexity of the Maximum Exposure Problem","authors":"Remi Raman, S. ShahinJohnJ, R. Subashini, Subhasree Methirumangalath","doi":"10.48550/arXiv.2203.11114","DOIUrl":"https://doi.org/10.48550/arXiv.2203.11114","url":null,"abstract":"We investigate the parameterized complexity of Maximum Exposure Problem (MEP). Given a range space (R, P ) where R is the set of ranges containing a set P of points, and an integer k, MEP asks for k ranges which on removal results in the maximum number of exposed points. A point p is said to be exposed when p is not contained in any of the ranges inR. The problem is known to be NP-hard. In this letter, we give fixed-parameter tractable results of MEP with respect to different parameterizations.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"34 1","pages":"106338"},"PeriodicalIF":0.0,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75073162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithms with improved delay for enumerating connected induced subgraphs of a large cardinality 具有改进延迟的大基数连通诱导子图枚举算法
Inf. Process. Lett. Pub Date : 2021-12-14 DOI: 10.2139/ssrn.4150167
Shanshan Wang, Chenglong Xiao, E. Casseau
{"title":"Algorithms with improved delay for enumerating connected induced subgraphs of a large cardinality","authors":"Shanshan Wang, Chenglong Xiao, E. Casseau","doi":"10.2139/ssrn.4150167","DOIUrl":"https://doi.org/10.2139/ssrn.4150167","url":null,"abstract":"The problem of enumerating all connected induced subgraphs of a given order $k$ from a given graph arises in many practical applications: bioinformatics, information retrieval, processor design,to name a few. The upper bound on the number of connected induced subgraphs of order $k$ is $ncdotfrac{(eDelta)^{k}}{(Delta-1)k}$, where $Delta$ is the maximum degree in the input graph $G$ and $n$ is the number of vertices in $G$. In this short communication, we first introduce a new neighborhood operator that is the key to design reverse search algorithms for enumerating all connected induced subgraphs of order $k$. Based on the proposed neighborhood operator, three algorithms with delay of $O(kcdot min{(n-k),kDelta}cdot(klog{Delta}+log{n}))$, $O(kcdot min{(n-k),kDelta}cdot n)$ and $O(k^2cdot min{(n-k),kDelta}cdot min{k,Delta})$ respectively are proposed. The first two algorithms require exponential space to improve upon the current best delay bound $O(k^2Delta)$cite{4} for this problem in the case $k>frac{nlog{Delta}-log{n}-Delta+sqrt{nlog{n}log{Delta}}}{log{Delta}}$ and $k>frac{n^2}{n+Delta}$ respectively.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"16 1","pages":"106425"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89440375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Instability results for Euclidean distance, nearest neighbor search on high dimensional Gaussian data 欧几里德距离的不稳定性结果，在高维高斯数据上的最近邻搜索
Inf. Process. Lett. Pub Date : 2021-08-01 DOI: 10.1016/J.IPL.2021.106115
C. Giannella
{"title":"Instability results for Euclidean distance, nearest neighbor search on high dimensional Gaussian data","authors":"C. Giannella","doi":"10.1016/J.IPL.2021.106115","DOIUrl":"https://doi.org/10.1016/J.IPL.2021.106115","url":null,"abstract":"","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"111 1","pages":"106115"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82922032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Tight FPT Approximation for Socially Fair Clustering 社会公平聚类的严格FPT近似
Inf. Process. Lett. Pub Date : 2021-06-12 DOI: 10.2139/ssrn.4226483
Dishant Goyal, Ragesh Jaiswal
{"title":"Tight FPT Approximation for Socially Fair Clustering","authors":"Dishant Goyal, Ragesh Jaiswal","doi":"10.2139/ssrn.4226483","DOIUrl":"https://doi.org/10.2139/ssrn.4226483","url":null,"abstract":"In this work, we study the socially fair $k$-median/$k$-means problem. We are given a set of points $P$ in a metric space $mathcal{X}$ with a distance function $d(.,.)$. There are $ell$ groups: $P_1,dotsc,P_{ell} subseteq P$. We are also given a set $F$ of feasible centers in $mathcal{X}$. The goal in the socially fair $k$-median problem is to find a set $C subseteq F$ of $k$ centers that minimizes the maximum average cost over all the groups. That is, find $C$ that minimizes the objective function $Phi(C,P) equiv max_{j} Big{ sum_{x in P_j} d(C,x)/|P_j| Big}$, where $d(C,x)$ is the distance of $x$ to the closest center in $C$. The socially fair $k$-means problem is defined similarly by using squared distances, i.e., $d^{2}(.,.)$ instead of $d(.,.)$. The current best approximation guarantee for both the problems is $Oleft( frac{log ell}{log log ell} right)$ due to Makarychev and Vakilian [COLT 2021]. In this work, we study the fixed parameter tractability of the problems with respect to parameter $k$. We design $(3+varepsilon)$ and $(9 + varepsilon)$ approximation algorithms for the socially fair $k$-median and $k$-means problems, respectively, in FPT (fixed parameter tractable) time $f(k,varepsilon) cdot n^{O(1)}$, where $f(k,varepsilon) = (k/varepsilon)^{{O}(k)}$ and $n = |P cup F|$. Furthermore, we show that if Gap-ETH holds, then better approximation guarantees are not possible in FPT time.","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"184 1","pages":"106383"},"PeriodicalIF":0.0,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75138993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A note on the concrete hardness of the shortest independent vector in lattices 关于格中最短独立向量的具体硬度的注释
Inf. Process. Lett. Pub Date : 2021-04-01 DOI: 10.1016/j.ipl.2020.106065
Divesh Aggarwal, E. Chung
{"title":"A note on the concrete hardness of the shortest independent vector in lattices","authors":"Divesh Aggarwal, E. Chung","doi":"10.1016/j.ipl.2020.106065","DOIUrl":"https://doi.org/10.1016/j.ipl.2020.106065","url":null,"abstract":"","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"16 1","pages":"106065"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81460169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
A lower bound for the coverability problem in acyclic pushdown VAS 非循环下推VAS可复性问题的下界
Inf. Process. Lett. Pub Date : 2021-04-01 DOI: 10.1016/j.ipl.2020.106079
Matthias Englert, Piotr Hofman, S. Lasota, R. Lazic, Jérôme Leroux, Juliusz Straszynski
{"title":"A lower bound for the coverability problem in acyclic pushdown VAS","authors":"Matthias Englert, Piotr Hofman, S. Lasota, R. Lazic, Jérôme Leroux, Juliusz Straszynski","doi":"10.1016/j.ipl.2020.106079","DOIUrl":"https://doi.org/10.1016/j.ipl.2020.106079","url":null,"abstract":"","PeriodicalId":13545,"journal":{"name":"Inf. Process. Lett.","volume":"6 1","pages":"106079"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84810556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
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