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We 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) 210223], 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. © 2011 Elsevier B.V. All rights reserved.


Documento: Artículo
Título:Arboricity, h-index, and dynamic algorithms
Autor:Lin, M.C.; Soulignac, F.J.; Szwarcfiter, J.L.
Filiación:CONICET and Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Computación, Buenos Aires, Argentina
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Computación, Buenos Aires, Argentina
Universidade Federal Do Rio de Janeiro, Instituto de Matemática, NCE and COPPE, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brazil
Palabras clave:Arboricity; Cop-win graphs; Data structures; Diamond-free graphs; Dynamic algorithms; h-index; Strongly chordal graphs; Arboricity; Cop-win graphs; Diamond-free graphs; Dynamic algorithms; H indices; Strongly chordal graph; Algorithms; Data structures; Diamonds; Graphic methods; Indexing (of information); Problem solving; Graph theory
Página de inicio:75
Página de fin:90
Título revista:Theoretical Computer Science
Título revista abreviado:Theor Comput Sci


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---------- APA ----------
Lin, M.C., Soulignac, F.J. & Szwarcfiter, J.L. (2012) . Arboricity, h-index, and dynamic algorithms. Theoretical Computer Science, 426-427, 75-90.
---------- CHICAGO ----------
Lin, M.C., Soulignac, F.J., Szwarcfiter, J.L. "Arboricity, h-index, and dynamic algorithms" . Theoretical Computer Science 426-427 (2012) : 75-90.
---------- MLA ----------
Lin, M.C., Soulignac, F.J., Szwarcfiter, J.L. "Arboricity, h-index, and dynamic algorithms" . Theoretical Computer Science, vol. 426-427, 2012, pp. 75-90.
---------- VANCOUVER ----------
Lin, M.C., Soulignac, F.J., Szwarcfiter, J.L. Arboricity, h-index, and dynamic algorithms. Theor Comput Sci. 2012;426-427:75-90.