Inductive computations on graphs defined by clique-width expressions

Frédérique Carrère

RAIRO - Theoretical Informatics and Applications (2009)

  • Volume: 43, Issue: 3, page 625-651
  • ISSN: 0988-3754

Abstract

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Labelling problems for graphs consist in building distributed data structures, making it possible to check a given graph property or to compute a given function, the arguments of which are vertices. For an inductively computable function D, if G is a graph with n vertices and of clique-width at most k, where k is fixed, we can associate with each vertex x of G a piece of information (bit sequence) lab(x) of length O(log2(n)) such that we can compute D in constant time, using only the labels of its arguments. The preprocessing can be done in time O(h.n) where h is the height of the syntactic tree of G. We perform an inductive computation, without using the tools of monadic second order logic. This enables us to give an explicit labelling scheme and to avoid constants of exponential size.

How to cite

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Carrère, Frédérique. "Inductive computations on graphs defined by clique-width expressions." RAIRO - Theoretical Informatics and Applications 43.3 (2009): 625-651. <http://eudml.org/doc/250600>.

@article{Carrère2009,
abstract = { Labelling problems for graphs consist in building distributed data structures, making it possible to check a given graph property or to compute a given function, the arguments of which are vertices. For an inductively computable function D, if G is a graph with n vertices and of clique-width at most k, where k is fixed, we can associate with each vertex x of G a piece of information (bit sequence) lab(x) of length O(log2(n)) such that we can compute D in constant time, using only the labels of its arguments. The preprocessing can be done in time O(h.n) where h is the height of the syntactic tree of G. We perform an inductive computation, without using the tools of monadic second order logic. This enables us to give an explicit labelling scheme and to avoid constants of exponential size. },
author = {Carrère, Frédérique},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Terms; graphs; clique-width; labeling schemes; inductive computation.; terms; inductive computation},
language = {eng},
month = {4},
number = {3},
pages = {625-651},
publisher = {EDP Sciences},
title = {Inductive computations on graphs defined by clique-width expressions},
url = {http://eudml.org/doc/250600},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Carrère, Frédérique
TI - Inductive computations on graphs defined by clique-width expressions
JO - RAIRO - Theoretical Informatics and Applications
DA - 2009/4//
PB - EDP Sciences
VL - 43
IS - 3
SP - 625
EP - 651
AB - Labelling problems for graphs consist in building distributed data structures, making it possible to check a given graph property or to compute a given function, the arguments of which are vertices. For an inductively computable function D, if G is a graph with n vertices and of clique-width at most k, where k is fixed, we can associate with each vertex x of G a piece of information (bit sequence) lab(x) of length O(log2(n)) such that we can compute D in constant time, using only the labels of its arguments. The preprocessing can be done in time O(h.n) where h is the height of the syntactic tree of G. We perform an inductive computation, without using the tools of monadic second order logic. This enables us to give an explicit labelling scheme and to avoid constants of exponential size.
LA - eng
KW - Terms; graphs; clique-width; labeling schemes; inductive computation.; terms; inductive computation
UR - http://eudml.org/doc/250600
ER -

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