Electronic Notes in Theoretical Computer Science最新文献_第9页

FPT Algorithms to Enumerate and Count Acyclic and Totally Cyclic Orientations 列举和计数非循环和全循环定向的FPT算法

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.057

Farley Soares Oliveira, Hidefumi Hiraishi, Hiroshi Imai

引用次数: 1

A Multi-agent Transgenetic Algorithm for the Bi-objective Spanning Tree Problem 双目标生成树问题的多智能体转基因算法

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.040

Islame F.C. Fernandes , Silvia M.D.M. Maia, Elizabeth F.G. Goldbarg, Marco C. Goldbarg

引用次数: 3

On Computing the Path Number of a Graph 论图的路径数计算

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.017

F. Botler, R. Cano, M. Sambinelli

引用次数: 1

On Edge-magic Labelings of Forests 论森林的边缘魔法标签

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.027

Márcia R. Cerioli , Cristina G. Fernandes , Orlando Lee , Carla N. Lintzmayer , Guilherme O. Mota , Cândida N. da Silva

引用次数: 0

Adapting The Directed Grid Theorem into an FPT Algorithm 有向网格定理在FPT算法中的应用

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.021

Victor Campos, Raul Lopes, Ana Karolinna Maia, Ignasi Sau

{"title":"Adapting The Directed Grid Theorem into an FPT Algorithm","authors":"Victor Campos, Raul Lopes, Ana Karolinna Maia, Ignasi Sau","doi":"10.1016/j.entcs.2019.08.021","DOIUrl":"10.1016/j.entcs.2019.08.021","url":null,"abstract":"<div>Originally proved in 1986 by Robertson and Seymour, the Grid Theorem is one of the most important tools in the field of structural graph theory, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem isn directed graphs was conjectured by Johnson et al. in 2001, and proved recently by Kawarabayashi and Kreutzer in 2015. Namely, they showed that there is a function f(k) such that every directed graph of directed tree-width at least f(k) contains a cylindrical grid of size k as a butterfly minor. Moreover, they claim that their proof can be turned into an XP algorithm, with parameter k, that either constructs a decomposition of the appropriate width, or finds the claimed large cylindrical grid as a butterfly minor. In this article, we adapt some of the steps of the proof of Kawarabayashi and Kreutzer and we improve the XP algorithm into an FPT algorithm.The first step of the proof is an XP algorithm by Johnson et al. in 2001 that decides whether a directed graph D has directed tree-width at most 3k − 2 or admits a haven of order k. It is worth mentioning that a skecth of an FPT algorithm for this problem appears in Chapter 9 of the book ”Classes of Directed Graphs”, from 2018, with an approximation factor of 5k + 2. Our first contribution is to adapt the proof from Johnson et al. to find either an arboreal decomposition of width at most 3k − 2 or a haven of order k in a directed graph D in FPT time, by making use of important separators. We then follow the roadmap of the proof by Kawarabayashi and Kreutzer by locally improving the complexity at some steps, in particular concerning the problem of finding hitting sets for brambles of large order.</div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"346 ","pages":"Pages 229-240"},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2019.08.021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115168232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Metric Dimension: from Graphs to Oriented Graphs 度量维度:从图到有向图

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.011

Julien Bensmail , Fionn Mc Inerney , Nicolas Nisse

{"title":"Metric Dimension: from Graphs to Oriented Graphs","authors":"Julien Bensmail , Fionn Mc Inerney , Nicolas Nisse","doi":"10.1016/j.entcs.2019.08.011","DOIUrl":"10.1016/j.entcs.2019.08.011","url":null,"abstract":"<div>The metric dimension MD(G) of an undirected graph G is the cardinality of a smallest set of vertices that allows, through their distances to all vertices, to distinguish any two vertices of G. Many aspects of this notion have been investigated since its introduction in the 70's, including its generalization to digraphs. In this work, we study, for particular graph families, the maximum metric dimension over all strongly-connected orientations, by exhibiting lower and upper bounds on this value. We first exhibit general bounds for graphs with bounded maximum degree. In particular, we prove that, in the case of subcubic n-node graphs, all strongly-connected orientations asymptotically have metric dimension at most <math><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math>, and that there are such orientations having metric dimension <math><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mn>5</mn></mrow></mfrac></math>. We then consider strongly-connected orientations of grids. For a torus with n rows and m columns, we show that the maximum value of the metric dimension of a strongly-connected Eulerian orientation is asymptotically <math><mfrac><mrow><mi>n</mi><mi>m</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math> (the equality holding when n, m are even, which is best possible). For a grid with n rows and m columns, we prove that all strongly-connected orientations asymptotically have metric dimension at most <math><mfrac><mrow><mn>2</mn><mi>n</mi><mi>m</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math>, and that there are such orientations having metric dimension <math><mfrac><mrow><mi>n</mi><mi>m</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math>.</div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"346 ","pages":"Pages 111-123"},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2019.08.011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125490490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Two Problems on Interval Counting 关于区间计数的两个问题

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.055

Lívia Salgado Medeiros, Fabiano de Souza Oliveira , Jayme Luiz Szwarcfiter

{"title":"Two Problems on Interval Counting","authors":"Lívia Salgado Medeiros, Fabiano de Souza Oliveira , Jayme Luiz Szwarcfiter","doi":"10.1016/j.entcs.2019.08.055","DOIUrl":"10.1016/j.entcs.2019.08.055","url":null,"abstract":"<div>Let <math><mi>F</mi></math> be a family of intervals on the real line. An interval graph is the intersection graph of <math><mi>F</mi></math>. An interval order is a partial order <math><mo>(</mo><mi>F</mi><mo>,</mo><mo>≺</mo><mo>)</mo></math> such that for all <math><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>I</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>F</mi></math>, I1 ≺ I2 if and only if I1 lies entirely at the left of I2. Such a family <math><mi>F</mi></math> is called a model of the graph (order). The interval count of a given graph (resp. order) is the smallest number of interval lengths needed in any model of this graph (resp. order). The first problem we consider is related to the classes of graphs and orders which can be represented with two interval lengths, regarding to the inclusion hierarchy among such classes. The second problem is an extremal problem which consists of determining the smallest graph or order which has interval count at least k. In particular, we study a conjecture by Fishburn on this extremal problem, verifying its validity when such a conjecture is constrained to the classes of trivially perfect orders and split orders.</div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"346 ","pages":"Pages 625-643"},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2019.08.055","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131045458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Identifying Codes in the Complementary Prism of Cycles 互补环棱镜中的识别码

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.022

Márcia R. Cappelle , Erika M.M. Coelho , Hebert Coelho , Lucia D. Penso, Dieter Rautenbach

引用次数: 3

Aα-Spectrum of a Firefly Graph 萤火虫图的a α-谱

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.019

André Ebling Brondani, Carla Silva Oliveira, Francisca Andrea Macedo França, Leonardo de Lima

引用次数: 6

Linial's Conjecture for Arc-spine Digraphs 弧脊有向图的Linial猜想

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 Epub Date: 2019-09-30 DOI: 10.1016/j.entcs.2019.08.064

Lucas R. Yoshimura , Maycon Sambinelli , Cândida N. da Silva , Orlando Lee

{"title":"Linial's Conjecture for Arc-spine Digraphs","authors":"Lucas R. Yoshimura , Maycon Sambinelli , Cândida N. da Silva , Orlando Lee","doi":"10.1016/j.entcs.2019.08.064","DOIUrl":"10.1016/j.entcs.2019.08.064","url":null,"abstract":"<div>A path partition <math><mi>P</mi></math> of a digraph D is a collection of directed paths such that every vertex belongs to precisely one path. Given a positive integer k, the k-norm of a path partition <math><mi>P</mi></math> of D is defined as <math><msub><mrow><mo>∑</mo></mrow><mrow><mi>P</mi><mo>∈</mo><mi>P</mi></mrow></msub><mi>min</mi><mo>⁡</mo><mo>{</mo><mo>|</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>,</mo><mi>k</mi><mo>}</mo></math>. A path partition of a minimum k-norm is called k-optimal and its k-norm is denoted by πk(D). A stable set of a digraph D is a subset of pairwise non-adjacent vertices of V(D). Given a positive integer k, we denote by αk(D) the largest set of vertices of D that can be decomposed into k disjoint stable sets of D. In 1981, Linial conjectured that πk(D) ≤ αk(D) for every digraph. We say that a digraph D is arc-spine if V(D) can be partitioned into two sets X and Y where X is traceable and Y contains at most one arc in A(D). In this paper we show the validity of Linial's Conjecture for arc-spine digraphs.</div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"346 ","pages":"Pages 735-746"},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2019.08.064","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129153692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2