Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
SIAM Journal on Discrete Mathematics
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Graph Separator Algorithms: A Refined Analysis
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Bidimensional Parameters and Local Treewidth
SIAM Journal on Discrete Mathematics
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Optimal branch-decomposition of planar graphs in O(n3) Time
ACM Transactions on Algorithms (TALG)
New upper bounds on the decomposability of planar graphs
Journal of Graph Theory
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Genus characterizes the complexity of graph problems: some tight results
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Faster approximation schemes and parameterized algorithms on H-minor-free and odd-minor-free graphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Survey: Subexponential parameterized algorithms
Computer Science Review
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
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We provide a new theory, alternative to bidimensionality, of sub-exponential parameterized algorithms on planar graphs, which is based on the notion of compactness. Roughly speaking, a parameterized problem is (r, q)-compact when all the faces and vertices of its YES-instances are "r-radially dominated" by some vertex set whose size is at most q times the parameter. We prove that if a parameterized problem can be solved in cbranchwidth(G)nO(1) steps and is (r, q)-compact, then it can be solved by a crċ2.122ċ √ qċknO(1) step algorithm (where k is the parameter). Our framework is general enough to unify the analysis of almost all known sub-exponential parameterized algorithms on planar graphs and improves or matches their running times. Our results are based on an improved combinatorial bound on the branchwidth of planar graphs that bypasses the grid-minor exclusion theorem. That way, our approach encompasses new problems where bidimensionality theory do not directly provide sub-exponential parameterized algorithms.