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Linear kernels on graphs excluding topological minors
"... We show that problems that have finite integer index and satisfy a requirement we call treewidthbounding admit linear kernels on the class ofHtopologicalminor free graphs, for an arbitrary fixed graphH. This builds on earlier results by Bodlaender et al. on graphs of bounded genus [2] and by Fom ..."
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We show that problems that have finite integer index and satisfy a requirement we call treewidthbounding admit linear kernels on the class ofHtopologicalminor free graphs, for an arbitrary fixed graphH. This builds on earlier results by Bodlaender et al. on graphs of bounded genus [2
Turing kernelization for finding long paths and cycles in restricted graph classes
 In Proc. 22nd ESA
, 2014
"... Abstract. We analyze the potential for provably effective preprocessing for the problems of finding paths and cycles with at least k edges. Several years ago, the question was raised whether the existing superpolynomial kernelization lower bounds for kPath and kCycle can be circumvented by relaxin ..."
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Cited by 4 (1 self)
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by relaxing the requirement that the preprocessing algorithm outputs a single instance. To this date, very few examples are known where the relaxation to Turing kernelization is fruitful. We provide a novel example by giving polynomialsize Turing kernels for kPath and kCycle on planar graphs, graphs
Polynomial Kernels and Faster Algorithms for the Dominating Set Problem on Graphs with an Excluded Minor
"... Abstract. The domination number of a graph G = (V,E) is the minimum size of a dominating set U ⊆ V, which satisfies that every vertex in V \U is adjacent to at least one vertex in U. The notion of a problem kernel refers to a polynomial time algorithm that achieves some provable reduction of the in ..."
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be used to obtain efficient approximation and exact algorithms for the domination number, and are also useful in practical settings. In this paper, we present the first nontrivial result for the general case of graphs with an excluded minor, as follows. For every fixed h, given a graph G with n vertices
Polynomial Kernels and Faster Algorithms for the Dominating Set Problem on Graphs with an Excluded Minor
 In Proceedings of IWPEC 2009
, 2009
"... Abstract. The domination number of a graph G = (V, E) is the minimum size of a dominating set U ⊆ V, which satisfies that every vertex in V \ U is adjacent to at least one vertex in U. The notion of a problem kernel refers to a polynomial time algorithm that achieves some provable reduction of the i ..."
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Cited by 6 (0 self)
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is improved for graphs that do not contain K3,h as a topological minor, using a simpler algorithm that constructs a subgraph with at most ck vertices, where c is a constant that depends only on h. Our results imply that there is a problem kernel of polynomial size for graphs with an excluded minor and a
Turing
"... The techniques described in this paper have been developed and applied on a series of major systems engineering projects, most recently including the BOWMAN programme. BOWMAN will encompass the design, development, manufacture, conversion (rollout) and support of the new communications systems for t ..."
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for the British Army. The BOWMAN contract will be valued in excess of £1.5 Billion and be delivered and installed over a period of 6 years. Thread Analysis is a technique that enables systems design to be systematically inspected with respect to a number of desirable properties. Threads analysis finds application
ON THE RELATIVE IMPORTANCE OF EXCLUDED MINORS
"... ABSTRACT. If E is a set of matroids, then Ex(E) denotes the set of matroids that have no minor isomorphic to a member of E. If E ′ ⊆ E, we say that E ′ is superfluous if Ex(E − E ′) − Ex(E) contains only finitely many 3connected matroids. We determine the superfluous subsets of six wellknown coll ..."
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ABSTRACT. If E is a set of matroids, then Ex(E) denotes the set of matroids that have no minor isomorphic to a member of E. If E ′ ⊆ E, we say that E ′ is superfluous if Ex(E − E ′) − Ex(E) contains only finitely many 3connected matroids. We determine the superfluous subsets of six well
Kernel on graphs based on dictionary of paths for image retrieval
 in: IAPR International Conference on Pattern Recognition
, 2010
"... Recent approaches of graph comparison consider graphs as sets of paths [6, 5]. Kernels on graphs are then computed from kernels on paths. A common strategy for graph retrieval is to perform pairwise comparisons. In this paper, we propose to follow a different strategy, where we collect a set of pa ..."
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Cited by 2 (0 self)
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Recent approaches of graph comparison consider graphs as sets of paths [6, 5]. Kernels on graphs are then computed from kernels on paths. A common strategy for graph retrieval is to perform pairwise comparisons. In this paper, we propose to follow a different strategy, where we collect a set
EXCLUDING SUBDIVISIONS OF Bounded Degree Graphs
, 2014
"... Let H be a fixed graph. What can be said about graphs G that have no subgraph isomorphic to a subdivision of H? Grohe and Marx proved that such graphs G satisfy a certain structure theorem that is not satisfied by graphs that contain a subdivision of a (larger) graph H1. Dvořák found a clever stre ..."
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Let H be a fixed graph. What can be said about graphs G that have no subgraph isomorphic to a subdivision of H? Grohe and Marx proved that such graphs G satisfy a certain structure theorem that is not satisfied by graphs that contain a subdivision of a (larger) graph H1. Dvořák found a clever
Results 1  10
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