Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
How to allocate network centers
Journal of Algorithms
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Approximation algorithms for independent sets in map graphs
Journal of Algorithms
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Small k-Dominating Sets in Planar Graphs with Applications
WG '01 Proceedings of the 27th 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
Exponential Speedup of Fixed-Parameter Algorithms on K3, 3-Minor-Free or K5-Minor-Free Graphs
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Parameterized Complexity
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized Complexity for Domination Problems on Degenerate Graphs
Graph-Theoretic Concepts in 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
Vertex fusion under distance constraints
European Journal of Combinatorics
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Approximation algorithm for the kinetic robust K-center problem
Computational Geometry: Theory and Applications
Extended dynamic subgraph statistics using h-index parameterized data structures
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Geometric clustering: Fixed-parameter tractability and lower bounds with respect to the dimension
ACM Transactions on Algorithms (TALG)
Implicit branching and parameterized partial cover problems
Journal of Computer and System Sciences
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Local search: Is brute-force avoidable?
Journal of Computer and System Sciences
Algorithmic graph minor theory: improved grid minor bounds and wagner's contraction
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Survey: Subexponential parameterized algorithms
Computer Science Review
Extended dynamic subgraph statistics using h-index parameterized data structures
Theoretical Computer Science
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Linear time algorithms for finding a dominating set of fixed size in degenerated graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Augmenting outerplanar graphs to meet diameter requirements
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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The (k, r)-center problem asks whether an input graph G has ≤k vertices (called centers) such that every vertex of G is within distance ≤r from some center. In this article, we prove that the (k, r)-center problem, parameterized by k and R, is fixed-parameter tractable (FPT) on planar graphs, i.e., it admits an algorithm of complexity f(k, r)nO(1) where the function f is independent of n. In particular, we show that f(k,r) = 2O(r log r) &ksqrt;, where the exponent of the exponential term grows sublinearly in the number of centers. Moreover, we prove that the same type of FPT algorithms can be designed for the more general class of map graphs introduced by Chen, Grigni, and Papadimitriou. Our results combine dynamic-programming algorithms for graphs of small branchwidth and a graph-theoretic result bounding this parameter in terms of k and r. Finally, a byproduct of our algorithm is the existence of a PTAS for the r-domination problem in both planar graphs and map graphs.Our approach builds on the seminal results of Robertson and Seymour on Graph Minors, and as a result is much more powerful than the previous machinery of Alber et al. for exponential speedup on planar graphs. To demonstrate the versatility of our results, we show how our algorithms can be extended to general parameters that are “large” on grids. In addition, our use of branchwidth instead of the usual treewidth allows us to obtain much faster algorithms, and requires more complicated dynamic programming than the standard leaf/introduce/forget/join structure of nice tree decompositions. Our results are also unique in that they apply to classes of graphs that are not minor-closed, namely, constant powers of planar graphs and map graphs.