Hierarchical planarity testing algorithms
Journal of the ACM (JACM)
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
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Inserting an edge into a planar graph
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Optimizing over All Combinatorial Embeddings of a Planar Graph
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Computing Orthogonal Drawings with the Minimum Number of Bends
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
A Linear Time Algorithm to Recognize Clustered Graphs and Its Parallelization
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Bend Minimization in Orthogonal Drawings Using Integer Programming
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Graph Drawing Algorithm Engineering with AGD
Revised Lectures on Software Visualization, International Seminar
Advances in C-Planarity Testing of Clustered Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
The Refined Process Structure Tree
BPM '08 Proceedings of the 6th International Conference on Business Process Management
On the Hardness and Approximability of Planar Biconnectivity Augmentation
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
The Triconnected Abstraction of Process Models
BPM '09 Proceedings of the 7th International Conference on Business Process Management
Unveiling Hidden Unstructured Regions in Process Models
OTM '09 Proceedings of the Confederated International Conferences, CoopIS, DOA, IS, and ODBASE 2009 on On the Move to Meaningful Internet Systems: Part I
ACM Transactions on Mathematical Software (TOMS)
A simple algorithm for triconnectivity of a multigraph
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Separator-based data reduction for signed graph balancing
Journal of Combinatorial Optimization
Testing planarity of partially embedded graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Progress on certifying algorithms
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Algorithms and theory of computation handbook
Semantic business process engineering
ReasoningWeb'10 Proceedings of the 6th international conference on Semantic technologies for software engineering
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
The biconnected verification of workflow nets
OTM'10 Proceedings of the 2010 international conference on On the move to meaningful internet systems - Volume Part I
GD'10 Proceedings of the 18th international conference on Graph drawing
Orthogonal graph drawing with flexibility constraints
GD'10 Proceedings of the 18th international conference on Graph drawing
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Simplified computation and generalization of the refined process structure tree
WS-FM'10 Proceedings of the 7th international conference on Web services and formal methods
A kuratowski-type theorem for planarity of partially embedded graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
A tighter insertion-based approximation of the crossing number
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Non-planar core reduction of graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
On graph crossing number and edge planarization
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fast and lossless graph division method for layout decomposition using SPQR-tree
Proceedings of the International Conference on Computer-Aided Design
Efficient computation of causal behavioural profiles using structural decomposition
PETRI NETS'10 Proceedings of the 31st international conference on Applications and Theory of Petri Nets
Advances in the planarization method: effective multiple edge insertions
GD'11 Proceedings of the 19th international conference on Graph Drawing
Journal of Discrete Algorithms
Computer Science Review
A branch-and-cut approach to the crossing number problem
Discrete Optimization
Brief announcement: speedups for parallel graph triconnectivity
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Certifying 3-connectivity in linear time
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Causal Behavioural Profiles - Efficient Computation, Applications, and Evaluation
Fundamenta Informaticae - Applications and Theory of Petri Nets and Other Models of Concurrency, 2010
The vulcan game of kal-toh: finding or making triconnected planar subgraphs
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
A Kuratowski-type theorem for planarity of partially embedded graphs
Computational Geometry: Theory and Applications
Disconnectivity and relative positions in simultaneous embeddings
GD'12 Proceedings of the 20th international conference on Graph Drawing
Implementing a partitioned 2-page book embedding testing algorithm
GD'12 Proceedings of the 20th international conference on Graph Drawing
Planar lombardi drawings for subcubic graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Decomposing a multigraph into split components
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Optimal orthogonal graph drawing with convex bend costs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Layout decomposition with pairwise coloring for multiple patterning lithography
Proceedings of the International Conference on Computer-Aided Design
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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 [8] and, since then, became quite important in the field of graph algorithms. Theoretical papers using SPQR-trees claim that they can be implemented in linear time using a modification of the algorithm by Hopcroft and Tarjan [15] for decomposing a graph into its triconnected components. So far no correct linear time implementation of either triconnectivity decomposition or SPQR-trees is known to us. Here, we show the incorrectness of the Hopcroft and Tarjan algorithm [15], and correct the faulty parts. We describe the relationship between SPQR-trees and triconnected components and apply the resulting algorithm to the computation of SPQR-trees. Our implementation is publically available in AGD [1].