In this paper we present a modification of a technique by Chiba and Nishizeki
[Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J.
Comput. 14(1), pp. 210--223 (1985)]. Based on it, we design a data structure
suitable for dynamic graph algorithms. We employ the data structure to
formulate new algorithms for several problems, including counting subgraphs of
four vertices, recognition of diamond-free graphs, cop-win graphs and strongly
chordal graphs, among others. We improve the time complexity for graphs with
low arboricity or h-index.Comment: 19 pages, no figure

Alon

Bandelt

Bollobás

Chiba

Conforti

Coppersmith

Eisenbrand

Eppstein

Farber

Fonlupt

Francisco J. Soulignac

Jayme L. Szwarcfiter

Kloks

Mahadev

Min Chih Lin

Nowakowski

Paige

Spinrad

Szwarcfiter

Talmaciu

Tucker

English

arXiv

AbstractWe propose a new data structure for manipulating graphs, called h-graph, which is particularly suited for designing dynamic algorithms. The structure itself is simple, consisting basically of a triple of elements, for each vertex of the graph. The overall size of all triples is O(n+m), for a graph with n vertices and m edges. We describe algorithms for performing the basic operations related to dynamic applications, as insertions and deletions of vertices or edges, and adjacency queries. The data structure employs a technique first described by Chiba and Nishizeki [Chiba, Nishizeki, Arboricity and subgraph listing algorithms, SIAM J. Comput. 14 (1) (1985) 210–223], and relies on the arboricity of graphs. Using the proposed data structure, we describe several dynamic algorithms for solving problems as listing the cliques of a given size, recognizing diamond-free graphs, and finding simple, simplicial and dominated vertices. These algorithms are the first of their kind to be proposed in the literature. In fact, the dynamic algorithms for the above problems lead directly to new static algorithms, and using the data structure we also design new static algorithms for the problems of counting subgraphs of size 4, recognizing cop-win graphs and recognizing strongly chordal graphs. The complexities of all of the proposed static algorithms improve over the complexities of the so far existing algorithms, for graphs of low arboricity. In addition, for the problems of counting subgraphs of size 4 and recognizing diamond-free graphs, the improvement is general

Lin, Min Chih

Soulignac, Francisco J.

Szwarcfiter, Jayme L.

Elsevier - Publisher Connector 

Arboricity, h-index, and dynamic algorithms 

We propose a new data structure for manipulating graphs, called -graph, which is particularly suited for designing dynamic algorithms. The structure itself is simple, consisting basically of a triple of elements, for each vertex of the graph. The overall size of all triples is , for a graph with vertices and edges. We describe algorithms for performing the basic operations related to dynamic applications, as insertions and deletions of vertices or edges, and adjacency queries. The data structure employs a technique first described by Chiba and Nishizeki [Chiba, Nishizeki, Arboricity and subgraph listing algorithms, SIAM J. Comput. 14 (1) (1985) 210–223], and relies on the arboricity of graphs. Using the proposed data structure, we describe several dynamic algorithms for solving problems as listing the cliques of a given size, recognizing diamond-free graphs, and finding simple, simplicial and dominated vertices. These algorithms are the first of their kind to be proposed in the literature. In fact, the dynamic algorithms for the above problems lead directly to new static algorithms, and using the data structure we also design new static algorithms for the problems of counting subgraphs of size 4, recognizing cop-win graphs and recognizing strongly chordal graphs. The complexities of all of the proposed static algorithms improve over the complexities of the so far existing algorithms, for graphs of low arboricity. In addition, for the problems of counting subgraphs of size 4 and recognizing diamond-free graphs, the improvement is general. which is particularly suited for designing dynamic algorithms. The structure itself is simple, consisting basically of a triple of elements, for each vertex of the graph. The overall size of all triples is O(n+m), for a graph with n vertices and m edges. We describe algorithms for performing the basic operations related to dynamic applications, as insertions and deletions of vertices or edges, and adjacency queries. The data structure employs a technique first described by Chiba and Nishizeki [Chiba, Nishizeki, Arboricity and subgraph listing algorithms, SIAM J. Comput. 14 (1) (1985) 210–223], and relies on the arboricity of graphs. Using the proposed data structure, we describe several dynamic algorithms for solving problems as listing the cliques of a given size, recognizing diamond-free graphs, and finding simple, simplicial and dominated vertices. These algorithms are the first of their kind to be proposed in the literature. In fact, the dynamic algorithms for the above problems lead directly to new static algorithms, and using the data structure we also design new static algorithms for the problems of counting subgraphs of size 4, recognizing cop-win graphs and recognizing strongly chordal graphs. The complexities of all of the proposed static algorithms improve over the complexities of the so far existing algorithms, for graphs of low arboricity. In addition, for the problems of counting subgraphs of size 4 and recognizing diamond-free graphs, the improvement is general.Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Soulignac, Francisco Juan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasi

Soulignac, Francisco Juan

CONICET Digital

Theoretical Computer Science

Arboricity, h-Index, and Dynamic Algorithms

Crossref

Arboricity, <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>h</mml:mi></mml:math>-index, and dynamic algorithms

https://ri.conicet.gov.ar/bitstream/handle/11336/113567/CONICET_Digital_Nro.75dd6293-c44b-459c-9772-bc402f9ad3f7_A.pdf?sequence=2&isAllowed=y

Arboricity, h-Index, and Dynamic Algorithms

Abstract

Similar works

Full text

Available Versions

Elsevier - Publisher Connector

CONICET Digital

Crossref