Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric Separator Theorems and Applications
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Graph separators: a parameterized view
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Optimal branch-decomposition of planar graphs in O(n3) time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Exact algorithms for the Hamiltonian cycle problem in planar graphs
Operations Research Letters
Parameterized Complexity
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Computing branchwidth via efficient triangulations and blocks
Discrete Applied Mathematics
Semi-nice tree-decompositions: The best of branchwidth, treewidth and pathwidth with one algorithm
Discrete Applied Mathematics
On the minimum corridor connection problem and other generalized geometric problems
Computational Geometry: Theory and Applications
Computational study on planar dominating set problem
Theoretical Computer Science
Induced Packing of Odd Cycles in a Planar Graph
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
minimum dominating set of queens: A trivial programming exercise?
Discrete Applied Mathematics
A fast algorithm to generate open meandric systems and meanders
ACM Transactions on Algorithms (TALG)
Dynamic programming and planarity: Improved tree-decomposition based algorithms
Discrete Applied Mathematics
How to use planarity efficiently: new tree-decomposition based algorithms
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Computing branch decomposition of large planar graphs
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs
Journal of Discrete Algorithms
Dynamic programming for graphs on surfaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Faster algorithms on branch and clique decompositions
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Milling a graph with turn costs: a parameterized complexity perspective
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Computational study for planar connected dominating set problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
A local search algorithm for branchwidth
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
An exact algorithm for connected red-blue dominating set
Journal of Discrete Algorithms
Complexity and approximation of the Constrained Forest problem
Theoretical Computer Science
Generation of graphs with bounded branchwidth
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Fast subexponential algorithm for non-local problems on graphs of bounded genus
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Connectivity is not a limit for kernelization: planar connected dominating set
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the minimum corridor connection problem and other generalized geometric problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
An exact algorithm for connected red-blue dominating set
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Two birds with one stone: the best of branchwidth and treewidth with one algorithm
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Planar k-path in subexponential time and polynomial space
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Exploiting planarity in separation routines for the symmetric traveling salesman problem
Discrete Optimization
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
An improved exact algorithm for cubic graph TSP
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Divide-and-conquer strategy based on variations of the Lipton-Tarjan planar separator theorem has been one of the most common approaches for solving planar graph problems for more than 20 years. We present a new framework for designing fast subexponential exact and parameterized algorithms on planar graphs. Our approach is based on geometric properties of planar branch decompositions obtained by Seymour & Thomas, combined with new techniques of dynamic programming on planar graphs based on properties of non-crossing partitions. Compared to divide-and-conquer algorithms, the main advantages of our method are a) it is a generic method which allows to attack broad classes of problems; b) the obtained algorithms provide a better worst case analysis. To exemplify our approach we show how to obtain an $O(2^{6.903\sqrt{n}}n^{3/2}+n^{3})$ time algorithm solving weighted Hamiltonian Cycle. We observe how our technique can be used to solve Planar Graph TSP in time $O(2^{10.8224\sqrt{n}}n^{3/2}+n^{3})$. Our approach can be used to design parameterized algorithms as well. For example we introduce the first $2^{O\sqrt{k}}k^{O(1)}.n^{O(1)}$ time algorithm for parameterized Planar k–cycle by showing that for a given k we can decide if a planar graph on n vertices has a cycle of length ≥ k in time $O(2^{13.6\sqrt{k}}\sqrt{k}n+n^{3})$.