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Tytuł artykułu

Locally Derivable Graphs

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Języki publikacji
EN
Abstrakty
EN
In the paper a class of locally derivable graphs is defined and discussed. Well known particular cases of derivable graphs are (among others) trees, complete, and triangular graphs; in the paper a broader class of locally derivable graphs, called closed graphs, is defined. Nodes and edges of closed graphs can be partitioned into external and internal ones; the main property of such graphs their local reducibility: successive removing its external nodes leads eventually to a singleton, and removing its external edges leads to an a spanning tree of the graph. The class of closed graphs is then a class enabling structural reducing. This property can be applied in processor networks to design some local procedures leading to global results.
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Rocznik
Strony
335--355
Opis fizyczny
bibliogr. 11 poz., rys.
Twórcy
Bibliografia
  • [1] Angluin,D.: Local and global properties in networks of processors, in: Proc. of 12th Symp. on Theory of Computing (1980) 82-93
  • [2] Berge, C.: Theorie des graphes et ses applications, Dunod, Paris (1958)
  • [3] Courcelle,B., Métivier,Y.: Coverings and Minors: application to local computations in graphs, in: Europ. Journal of Combinatorics 15 (1994) 127-138
  • [4] Dijkstra,E.W.: Solution of a problem in concurrent programming control, Comm. of ACM 8 (1965) 569
  • [5] Fisher,M.J., Lynch,N.A., Merritt,A.: Easy impossibility proofs for distributed consensus problems, in: Distributed Computing 1 (1986) 26-29
  • [6] Godard,E.:(Ph.D. dissertation) A characterization of families of graphs in which election is possible, in: Proc. of Foundations of Software Sci. and Comp. Structures, LNCS 2303 (2002) 159-171
  • [7] Godard,E., Métivier,Y., MuscholL, A.: The power of local computations in graphs with initial knowledge, in: Proc. of Theory and Applications of Graph Transformations'98 1764 LNCS (2000) 71-84
  • [8] Le Lann,G.: Distributed systems - towards a formal approach, in: Information Processing 77 (IFIP), Gilchrist B., (editor), North-Holland (Amsterdam), (1977) 155-160.
  • [9] Litovsky,I., Métivier,Y., Sopena,E.: Graph relabelling systems and distributed algorithms, in: H.Ehrig, H.-J.Kreowski, U.Montanari, and G.Rozenberg (eds) Handbook of graph grammars and computing by graph transformation 3, World Scientific (1999) 1- 56
  • [10] Litovsky,I., Métivier,Y., Zielonka,W.: On the recognition of families of graphs with local computations, in: Information & Computation 118 (1995) 110-119
  • [11] Mazurkiewicz,A.: Local properties of triangular graphs, in: Proc. of CS&P'2006, vol.III, G. Lindemann V.Trzebiatowski, H.Schlingloff, eds. (2006) 400-409
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0009-0019
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