• Publications
  • Influence
Invitation to fixed-parameter algorithms
  • D. Thilikos
  • Computer Science
  • Comput. Sci. Rev.
  • 1 December 2007
This is a review of the recent book by Rolf Niedermeier on fixed-parameter algorithms. It contains a critical description of the covered material, a comparison with other books dedicated to the sameExpand
Dominating sets in planar graphs: branch-width and exponential speed-up
TLDR
This paper shows how very deep min-max and duality theorems from Graph Minors can be used to obtain essential speed-up to many known algorithms on different domination problems. Expand
(Meta) Kernelization
TLDR
The theorems unify and extend all previously known kernelization results for planar graph problems and show that all problems expressible in Counting Monadic Second Order Logic and satisfying a compactness property admit a polynomial kernel on graphs of bounded genus. Expand
On Graph Powers for Leaf-Labeled Trees
TLDR
By discovering hidden combinatorial structure of cliques and neighborhoods, this work has developed polynomial-time algorithms that identify whether or not a given graph G is a k-leaf power of a tree T, and if so, produce aTree T for which G isA k- leaf power. Expand
Parameterized complexity of finding regular induced subgraphs
TLDR
This paper examines the parameterized complexity of the dual parameterized problem, namely, the k-Almostr-Regular Graph problem, which asks for a given graph G and a non-negative integer k whether G can be made r-regular by deleting at most k vertices and proves the existence of a problem kernel of size O(kr(r+k)^2). Expand
Constructive Linear Time Algorithms for Branchwidth
TLDR
This paper proves that one can construct a linear time algorithm that checks if a graph belongs to G k and, if so, outputs a branch decomposition of minimum width and finds the obstruction set for G k. Expand
Searching Is Not Jumping
TLDR
This paper provides a complete characterization of the set of trees that can be cleared by a given number of searchers and shows that, in trees, there is exactly one obstruction for monotone internal search, as well as for connected search, and this obstruction is the same for the two problems. Expand
Bidimensionality and kernels
TLDR
It is shown that "essentially" all bidimensional problems not only have sub-exponential time algorithms and PTASs but they also have linear kernels, affirmatively answering an open question from ACM 2005, where the existence of linear kernels was conjectured for the first time. Expand
Fast Parameterized Algorithms for Graphs on Surfaces: Linear Kernel and Exponential Speed-Up
TLDR
It is proved that the same rules, applied to any graph G of genus g, reduce the k-dominating set problem to a kernel of size O(k+g), i.e. linear kernel, and drastically the best so far combinatorial bound to the branchwidth of a graph in terms of its minimum dominating set and its genus is improved. Expand
D-cores: measuring collaboration of directed graphs based on degeneracy
TLDR
This paper defines a novel D-core framework and devise a wealth of novel metrics used to evaluate graph collaboration features of directed graphs, extending the classic graph-theoretic notion of $$k$$-cores for undirected graphs to directed ones. Expand
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