Handbook of theoretical computer science (vol. B)
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Node replacement graph grammars
Handbook of graph grammars and computing by graph transformation
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
Shortest paths in digraphs of small treewidth. Part II: optimal parallel algorithms
ESA '95 Selected papers from the third European symposium on Algorithms
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Efficient First-Order Model-Checking Using Short Labels
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Graph operations characterizing rank-width and balanced graph expressions
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Compact labelings for efficient first-order model-checking
Journal of Combinatorial Optimization
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Localized and compact data-structure for comparability graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Hi-index | 0.05 |
If P(x"1,...,x"k) is a graph property expressible in monadic second-order logic, where x"1,...,x"k denote vertices, if G is a graph with n vertices and of clique-width at most p where p is fixed, then we can associate with each vertex u of G a piece of information I(u) of size O(log(n)) such that, for all vertices x"1,...,x"k of G, one can decide whether P(x"1,...,x"k) holds in time O(log(n)) by using only I(x"1),...,I(x"k). The preprocessing can be done in time O(nlog(n)). One can do the same for any fixed monadic second-order optimization function (like distance) by using information of size O(log^2(n)) for each vertex and computation time O(log^2(n)). In this case preprocessing time is O(-log^2(n)). Clique-width is a complexity measure on graphs similar to tree-width, but more powerful since every set of graphs of bounded tree-width has bounded clique-width, but not conversely. Similar results apply to graphs of tree-width at most w and to properties and functions expressed in the version of monadic second-order logic allowing quantifications on sets of edges.