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)
Journal of Combinatorial Theory Series B
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth 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)
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)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Reducing to independent set structure: the case of k-internal spanning tree
Nordic Journal of Computing
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Improved algorithms for feedback vertex set problems
Journal of Computer and System Sciences
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Minimum leaf out-branching and related problems
Theoretical Computer Science
Spanning Directed Trees with Many Leaves
SIAM Journal on Discrete Mathematics
FPT algorithms and kernels for the Directedk- Leaf problem
Journal of Computer and System Sciences
On Finding Directed Trees with Many Leaves
Parameterized and Exact Computation
A Linear Vertex Kernel for Maximum Internal Spanning Tree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximation Algorithms for Treewidth
Algorithmica
Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem
Journal of Computer and System Sciences
Improved upper bounds for vertex cover
Theoretical Computer Science
Contraction obstructions for treewidth
Journal of Combinatorial Theory Series B
Tight bounds and a fast FPT algorithm for directed Max-Leaf Spanning Tree
ACM Transactions on Algorithms (TALG)
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
A New Algorithm for Finding Trees with Many Leaves
Algorithmica
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
The dag-width of directed graphs
Journal of Combinatorial Theory Series B
Survey: Subexponential parameterized algorithms
Computer Science Review
Finding odd cycle transversals
Operations Research Letters
Kernel(s) for problems with no kernel: On out-trees with many leaves
ACM Transactions on Algorithms (TALG)
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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In this paper we make the first step beyond bidimensionality by obtaining subexponential time algorithms for problems on directed graphs. We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, k-Leaf Out-Branching, which is to find an oriented spanning tree with at least k leaves, we obtain an algorithm solving the problem in time 2^O^(^k^l^o^g^k^)n+n^O^(^1^) on directed graphs whose underlying undirected graph excludes some fixed graph H as a minor. For the special case when the input directed graph is planar, the running time can be improved to 2^O^(^k^)n+n^O^(^1^). The second example is a generalization of the Directed Hamiltonian Path problem, namely k-Internal Out-Branching, which is to find an oriented spanning tree with at least k internal vertices. We obtain an algorithm solving the problem in time 2^O^(^k^l^o^g^k^)+n^O^(^1^) on directed graphs whose underlying undirected graph excludes some fixed apex graph H as a minor. Finally, we observe that on these classes of graphs, the k-Directed Path problem is solvable in time O((1+@e)^kn^f^(^@e^)), for any @e0, where f is some function of @e. Our methods are based on non-trivial combinations of obstruction theorems for undirected graphs, kernelization, problem-specific combinatorial structures, and a layering technique similar to the one employed by Baker to obtain PTAS for planar graphs.