#### DMCA

## Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs

### Cached

### Download Links

Citations: | 7 - 6 self |

### Citations

639 | Parameterized Complexity Theory - Flum, Grohe - 2006 |

447 | Invitation to Fixed-Parameter Algorithms
- Niedermeier
- 2006
(Show Context)
Citation Context ...rithm, that reduces the input instance down to an instance with size bounded by a polynomial p(k) in k, while preserving the answer. This reduced instance is called a p(k) kernel for the problem. See =-=[29]-=- for an introduction to kernelization. 3 Method I – Quasi Bidimensionality In this section we present our first approach. In general, a subexponential time algorithm using bidimensionality is obtained... |

375 |
Approximation algorithms for NP-complete problems on planar graphs.
- BAKER
- 1994
(Show Context)
Citation Context ...elization and dynamic programming over graphs of bounded treewidth. Here, using a combination of kernelization and a Baker style layering technique for obtaining polynomial time approximation schemes =-=[5]-=-, we reduce the instance of a given problem to 2 o(k) n O(1) many new instances of the same problem. These new instances have the following properties: (a) the treewidth of the underlying undirected g... |

242 | Which Problems Have Strongly Exponential Complexity
- Impagliazzo, Paturi, et al.
- 2001
(Show Context)
Citation Context ...an we have algorithms with running time 2 o(k) n O(1) . It is now possible to show that these problems do not admit algorithms with running time 2 o(k) n O(1) unless Exponential Time Hypothesis (ETH) =-=[22, 27]-=- fails. Finding algorithms with subexponential running time on general undirected graphs is a trait uncommon to parameterized algorithms. However, the situation changes completely when we consider pro... |

150 |
Quickly excluding a planar graph.
- ROBERTSON, SEYMOUR, et al.
- 1994
(Show Context)
Citation Context ...s almost all known previous subexponential algorithms on spare graphs. The theory is based on algorithmic and combinatorial extensions to various parts of Graph Minors Theory of Robertson and Seymour =-=[32]-=- and provides a simple criteria for checking whether a parameterized problem is solvable in subexponential time on sparse graphs. The theory applies to graph problems that are bidimensional in the sen... |

111 | Fixed parameter algorithms for dominating set and related problems on planar graphs.
- ALBER, BODLAENDER, et al.
- 2002
(Show Context)
Citation Context ...mmon to parameterized algorithms. However, the situation changes completely when we consider problems on topological graph classes like planar graphs or graphs of bounded genus. In 2000, Alber et al. =-=[1]-=- obtained the first parameterized subexponential algorithm on undirected planar graphs by showing that k-DOMINATING SET is solvable in time 2 O(√ k) n O(1) . This result triggered an extensive study o... |

96 | Finding odd cycle transversals.
- Reed, Smith, et al.
- 2004
(Show Context)
Citation Context ...ssible. This has led to the development of various graph algorithms with running time 2 O(k) n O(1) — notable ones include kFEEDBACK VERTEX SET [7], k-LEAF SPANNING TREE [28], k-ODD CYCLE TRANSVERSAL =-=[31]-=-, k-PATH [4], and k-VERTEX COVER [8] in undirected graphs. A natural question was whether we can get subexponential time algorithms for these problems, that is, can we have algorithms with running tim... |

68 | Dominating sets in planar graphs: branch-width and exponential speed-up,
- Fomin, Thilikos
- 2006
(Show Context)
Citation Context ...ial time algorithms for several fundamental problems like k-FEEDBACK VERTEX SET, k-EDGE DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER to name a few on planar graphs =-=[1, 12, 25]-=-, and more generally, on H-minor-free graphs [13, 15, 16]. These algorithms are obtained by showing a combinatorial relation between the parameter and the structure of the input graph and proofs requi... |

56 | Algorithmic graph minor theory: Decomposition, approximation, and coloring.
- Demaine, Hajiaghayi, et al.
- 2005
(Show Context)
Citation Context ...leaves in D or find a digraph D ′ with UG(D ′ ) excluding a fixed graph H as a minor and tw(UG(D ′ )) = O( √ k). In the later case, using the constant factor approximation algorithm of Demaine et al. =-=[17]-=- for computing the treewidth of a H-minor free graph, we find a tree decomposition of width O( √ k) for UG(D ′ ) in time n O(1) . With the previous observation that we can find an r-out-branching with... |

50 | Improved parameterized upper bounds for vertex cover. In:
- Chen, Kanj, et al.
- 2006
(Show Context)
Citation Context ...nt of various graph algorithms with running time 2 O(k) n O(1) — notable ones include kFEEDBACK VERTEX SET [7], k-LEAF SPANNING TREE [28], k-ODD CYCLE TRANSVERSAL [31], k-PATH [4], and k-VERTEX COVER =-=[8]-=- in undirected graphs. A natural question was whether we can get subexponential time algorithms for these problems, that is, can we have algorithms with running time 2 o(k) n O(1) . It is now possible... |

48 | Efficient exact algorithms on planar graphs: Exploiting sphere cut decompositions
- Dorn, Penninkx, et al.
(Show Context)
Citation Context ...treewidth has led to 2 O(√ k) n O(1) time algorithm for k-FEEDBACK VERTEX SET, k-EDGE DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER and many others on planar graphs =-=[12, 13, 20]-=- and in some cases like kDOMINATING SET and k-PATH on H-minor free graphs [13, 18]. We refer to surveys by Demaine and Hajiaghayi [15] and Dorn et al. [19] for further details on bidimensionality and ... |

47 | The bidimensionality theory and its algorithmic applications.
- Demaine, Hajiaghayi
- 2008
(Show Context)
Citation Context ...e k-FEEDBACK VERTEX SET, k-EDGE DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER to name a few on planar graphs [1, 12, 25], and more generally, on H-minor-free graphs =-=[13, 15, 16]-=-. These algorithms are obtained by showing a combinatorial relation between the parameter and the structure of the input graph and proofs require strong graph theoretic arguments. This graph-theoretic... |

42 | Improved algorithms for the feedback vertex set problems.
- Chen, Fomin, et al.
- 2007
(Show Context)
Citation Context ...) · n O(1) such that f is as slow growing function as possible. This has led to the development of various graph algorithms with running time 2 O(k) n O(1) — notable ones include kFEEDBACK VERTEX SET =-=[7]-=-, k-LEAF SPANNING TREE [28], k-ODD CYCLE TRANSVERSAL [31], k-PATH [4], and k-VERTEX COVER [8] in undirected graphs. A natural question was whether we can get subexponential time algorithms for these p... |

40 |
Thilikos. Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs
- Demaine, Fomin, et al.
(Show Context)
Citation Context ...e k-FEEDBACK VERTEX SET, k-EDGE DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER to name a few on planar graphs [1, 12, 25], and more generally, on H-minor-free graphs =-=[13, 15, 16]-=-. These algorithms are obtained by showing a combinatorial relation between the parameter and the structure of the input graph and proofs require strong graph theoretic arguments. This graph-theoretic... |

34 | Subexponential parameterized algorithms
- Dorn, Fomin, et al.
- 2007
(Show Context)
Citation Context ...VER and many others on planar graphs [12, 13, 20] and in some cases like kDOMINATING SET and k-PATH on H-minor free graphs [13, 18]. We refer to surveys by Demaine and Hajiaghayi [15] and Dorn et al. =-=[19]-=- for further details on bidimensionality and subexponential parameterized algorithms. While bidimensionality theory is a powerful algorithmic framework on undirected graphs, it remains unclear how to ... |

33 | Linearity of grid minors in treewidth with applications through bidimensionality.
- Demaine, Hajiaghayi
- 2008
(Show Context)
Citation Context ...e k-FEEDBACK VERTEX SET, k-EDGE DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER to name a few on planar graphs [1, 12, 25], and more generally, on H-minor-free graphs =-=[13, 15, 16]-=-. These algorithms are obtained by showing a combinatorial relation between the parameter and the structure of the input graph and proofs require strong graph theoretic arguments. This graph-theoretic... |

31 | Thilikos, Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
- Demaine, Fomin, et al.
(Show Context)
Citation Context ...ial time algorithms for several fundamental problems like k-FEEDBACK VERTEX SET, k-EDGE DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER to name a few on planar graphs =-=[1, 12, 25]-=-, and more generally, on H-minor-free graphs [13, 15, 16]. These algorithms are obtained by showing a combinatorial relation between the parameter and the structure of the input graph and proofs requi... |

31 | Equivalence of local treewidth and linear local treewidth and its algorithmic applications
- Demaine, Hajiaghayi
- 2004
(Show Context)
Citation Context ..., we obtain a minor M of UG(D ′ ). This minor M has diameter at most ⌈ √ k⌉ + 2 and contains Ci as an induced subgraph. Since UG(D ′ ) ∈ G ′ , we have that M ∈ G . Furthermore, Demaine and Hajiaghayi =-=[14]-=- have shown that for any fixed apex graph H, every H-minor-free graph of diameter d has treewidth O(d). This implies that the tw(Ci) ≤ tw(M) ≤ O( √ k). Notice that since every connected component of G... |

21 |
Catalan structures and dynamic programming in H-minor-free graphs
- Dorn, Fomin, et al.
- 2008
(Show Context)
Citation Context ...DOMINATING SET, k-LEAF SPANNING TREE, k-PATH, k-r-DOMINATING SET, k-VERTEX COVER and many others on planar graphs [12, 13, 20] and in some cases like kDOMINATING SET and k-PATH on H-minor free graphs =-=[13, 18]-=-. We refer to surveys by Demaine and Hajiaghayi [15] and Dorn et al. [19] for further details on bidimensionality and subexponential parameterized algorithms. While bidimensionality theory is a powerf... |

19 | Kernel(s) for Problems With No Kernels: On Out-Trees with Many Leaves.
- Fernau, Fomin, et al.
- 2009
(Show Context)
Citation Context ...rithm. Recently, Kneis et al. [28] provided a parameterized algorithm solving the problem in time 4 k n O(1) . This result was further improved to 3.72 k n O(1) by Daligaut et al. [10]. Fernau et al. =-=[21]-=- showed that for the rooted version of the problem, where apart from the input instance we are also given a root r and one asks for a k-leaf out-branching rooted at r, admits a O(k 3 ) kernel. Further... |

16 | Fast fast
- Alon, Lokshtanov, et al.
- 2009
(Show Context)
Citation Context ... for digraphs is not unique 2and several alternative definitions have been proposed. Only recently the first non-trivial subexponential parameterized algorithms on digraphs was obtained. Alon et al. =-=[3]-=- introduced the method of chromatic coding, a variant of color coding [4], and combined it with divide and conquer to obtain 2 O(√ k log k) n O(1) for k-FEEDBACK ARC SET in tournaments. Our contributi... |

14 |
Reducing to Independent Set Structure: The Case of k-Internal Spanning Tree.
- Prieto, Sloper
- 2005
(Show Context)
Citation Context ...NG (k-IOB): Given a digraph D with the vertex set V (D) and the arc set A(D) and a positive integer k, check whether there exists an out-branching with at least k internal vertices. Prieto and Sloper =-=[30]-=- studied the undirected version of this problem and gave an algorithm with running time 2 4k log k n O(1) and obtained a kernel of size O(k 2 ). Recently, Fomin et al. [23] obtained a vertex kernel of... |

13 | A.: Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem
- Cohen, Fomin, et al.
- 2010
(Show Context)
Citation Context ... k n O(1) . Gutin et al. [26] obtained an algorithm of running time 2 O(k log k) n O(1) for k-IOB and gave a kernel of size of O(k 2 ) using the well known method of crown-decomposition. Cohen et al. =-=[9]-=- improved the algorithm for k-IOB and gave an algorithm with running time 49.4 k n O(1) . Here, we obtain a subexponential time algorithm for k-IOB with running time 2 O(√ k log k) + n O(1) on directe... |

13 | A new algorithm for finding trees with many leaves
- Kneis, Langer, et al.
- 2008
(Show Context)
Citation Context ...as slow growing function as possible. This has led to the development of various graph algorithms with running time 2 O(k) n O(1) — notable ones include kFEEDBACK VERTEX SET [7], k-LEAF SPANNING TREE =-=[28]-=-, k-ODD CYCLE TRANSVERSAL [31], k-PATH [4], and k-VERTEX COVER [8] in undirected graphs. A natural question was whether we can get subexponential time algorithms for these problems, that is, can we ha... |

11 | Minimum leaf out-branching problems, in
- Gutin, Razgon, et al.
(Show Context)
Citation Context ... obtained a kernel of size O(k 2 ). Recently, Fomin et al. [23] obtained a vertex kernel of size 3k and gave an algorithm for the undirected version of k-IOB running in time 8 k n O(1) . Gutin et al. =-=[26]-=- obtained an algorithm of running time 2 O(k log k) n O(1) for k-IOB and gave a kernel of size of O(k 2 ) using the well known method of crown-decomposition. Cohen et al. [9] improved the algorithm fo... |

9 | FPT-Algorithms and Kernels for the Directed k-Leaf Problem.
- Daligault, Gutin, et al.
- 2010
(Show Context)
Citation Context ...ing time of the algorithm. Recently, Kneis et al. [28] provided a parameterized algorithm solving the problem in time 4 k n O(1) . This result was further improved to 3.72 k n O(1) by Daligaut et al. =-=[10]-=-. Fernau et al. [21] showed that for the rooted version of the problem, where apart from the input instance we are also given a root r and one asks for a k-leaf out-branching rooted at r, admits a O(k... |

9 | Contraction Bidimensionality: The Accurate Picture. - Fomin, Golovach, et al. - 2009 |

8 | A Linear Vertex Kernel for Maximum Internal Spanning Tree.
- Fomin, Gaspers, et al.
- 2009
(Show Context)
Citation Context ...vertices. Prieto and Sloper [30] studied the undirected version of this problem and gave an algorithm with running time 2 4k log k n O(1) and obtained a kernel of size O(k 2 ). Recently, Fomin et al. =-=[23]-=- obtained a vertex kernel of size 3k and gave an algorithm for the undirected version of k-IOB running in time 8 k n O(1) . Gutin et al. [26] obtained an algorithm of running time 2 O(k log k) n O(1) ... |

7 | Spanning directed trees with many leaves - Alon, Fomin, et al. |

5 |
On finding directed trees with many leaves. In:
- Daligault, Thomasse
- 2009
(Show Context)
Citation Context ...hing rooted at r, admits a O(k 3 ) kernel. Furthermore they also show that k-LOB does not admit polynomial kernel unless polynomial hierarchy collapses to third level. Finally, Daligault and Thomassé =-=[11]-=- obtained a O(k 2 ) kernel for the rooted version of the k-LOB problem and gave a constant factor approximation algorithm for k-LOB. Using our new technique in combination with kernelization result of... |

3 |
Tight bounds and a fast FPT algorithm for directed max-leaf spanning tree
- Bonsma, Dorn
(Show Context)
Citation Context ...wed that the problem is fixed parameter tractable by giving an algorithm that decides in time O(f(k)n) whether a strongly connected digraph has an outbranching with at least k leaves. Bonsma and Dorn =-=[6]-=- extended this result to all digraphs, and improved the running time of the algorithm. Recently, Kneis et al. [28] provided a parameterized algorithm solving the problem in time 4 k n O(1) . This resu... |