On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
On-line graph algorithms with SPQR-trees
Proceedings of the seventeenth international colloquium on Automata, languages and programming
SIAM Journal on Computing
Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Computing Orthogonal Drawings with the Minimum Number of Bends
IEEE Transactions on Computers
Inserting an edge into a planar graph
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Graph Drawing Algorithm Engineering with AGD
Revised Lectures on Software Visualization, International Seminar
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Drawing Graphs Symmetrically in Three Dimensions
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Advances in C-Planarity Testing of Clustered Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A Linear Time Algorithm to Recognize Clustered Graphs and Its Parallelization
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Finding Double Euler Trails of Planar Graphs in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Graph Drawing Software
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Testing planarity of partially embedded graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A kuratowski-type theorem for planarity of partially embedded graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
GD'04 Proceedings of the 12th international conference on Graph Drawing
Certifying 3-connectivity in linear time
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A Kuratowski-type theorem for planarity of partially embedded graphs
Computational Geometry: Theory and Applications
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The data structure SPQR-tree represents the decomposition of a biconnected graph with respect to its triconnected components. SPQR-trees have been introduced by Di Battista and Tamassia [13] based on ideas by Bienstock and Monma [9, 10]. For planar graphs, SPQR-trees have the nice property to represent the set of all its combinatorial embeddings. Therefore, the data structure has mainly (but not only) been used in the area of planar graph algorithms and graph layout. The techniques are quite manifold, reaching from special purpose algorithms that merge the solutions of the triconnected components in a clever way to a solution of the original graph, to general branch-andbound techniques and integer linear programming techniques. Applications reach from Steiner tree problems, to on-line problems in a dynamic setting as well as problems concerned with planarity and graph drawing. This paper gives a survey on the use of SPQR-trees in graph algorithms, with a focus on graph drawing.