A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Exploiting hierarchy in VLSI design
Proc. of the Aegean workshop on computing on VLSI algorithms and architectures
Efficient solution to connectivity problems on hierarchically defined graphs
SIAM Journal on Computing
Journal of the ACM (JACM)
The Complexity of Problems Concerning Graphs with Regularities (Extended Abstract)
Proceedings of the Mathematical Foundations of Computer Science 1984
Efficient Analysis of Graph Properties on Context-free Graph Languages (Extended Abstract)
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Succinct representation of graphs
Succinct representation of graphs
Efficient decision procedures for graph properties on context-free graph languages
Journal of the ACM (JACM)
Approximation schemes for PSPACE-complete problems for succinct specifications (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The complexity of approximating pspace-complete problems for hierarchical specifications
Nordic Journal of Computing
On Radiocoloring Hierarchically Specified Planar Graphs: PSPACE-Completeness and Approximations
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On embedding a cycle in a plane graph
GD'05 Proceedings of the 13th international conference on Graph Drawing
Model-checking hierarchical structures
Journal of Computer and System Sciences
Fixpoint logics on hierarchical structures
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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Using hierarchical definitions, one can describe very large graphs in small space. The blow-up from the length of the hierarchical description to the size of the graph can be as large as exponential. If the efficiency of graph algorithms is measured in terms of the length of the hierarchical description rather than in terms of the graph size, algorithms that do not exploit the hierarchy become hopelessly inefficient. Whether the hierarchy can be exploited to speed up the solution of graph problems depends on the hierarchical graph model. In the literature, hierarchical graph models have been described that allow almost no exploitation of the hierarchy [ 16]. In this paper, a hierarchical graph model that permits taking advantage of the hierarchy is presented. For this model algorithms are given that test planarity of a hierarchically described graph in linear time in the length of the hierarchical description.