Average case complete problems
SIAM Journal on Computing
Journal of Computer and System Sciences
Fast detection and display of symmetry in outerplanar graphs
Discrete Applied Mathematics
Generating triangulations at random
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Random sampling of large planar maps and convex polyhedra
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximating the pathwidth of outerplanar graphs
Information Processing Letters
Uniform random generation of decomposable structures using floating-point arithmetic
Theoretical Computer Science - Special issue on Caen '97
Random maps, coalescing saddles, singularity analysis, and airy phenomena
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Proximity Drawings of Outerplanar Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Drawing Outer-Planar Graphs in O(n log n) Area
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Approximation of Pathwidth of Outerplanar Graphs
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
On random planar graphs, the number of planar graphs and their triangulations
Journal of Combinatorial Theory Series B
The first order definability of graphs with separators via the Ehrenfeucht game
Theoretical Computer Science - Game theory meets theoretical computer science
Generating labeled planar graphs uniformly at random
Theoretical Computer Science
An unbiased pointing operator for unlabeled structures, with applications to counting and sampling
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Generating unlabeled connected cubic planar graphs uniformly at random
Random Structures & Algorithms
Journal of Combinatorial Theory Series B
Boltzmann Samplers, Pólya Theory, and Cycle Pointing
SIAM Journal on Computing
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We show how to generate labelled and unlabelled outerplanar graphs with $n$ vertices uniformly at random in polynomial time in $n$. To generate labelled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block structure, and compute the exact number of labelled outerplanar graphs. This allows us to make the correct probabilistic choices in a recursive generation of uniformly distributed outerplanar graphs.Next we modify our formulas to also count rooted unlabelled graphs, and finally show how to use these formulas in a Las Vegas algorithm to generate unlabelled outerplanar graphs uniformly at random in expected polynomial time.