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Improved upper bounds for vertex cover
TLDR
This paper presents an O(1.2738^k+kn)-time polynomial-space algorithm for Vertex Cover improving the previous O( 1.286^k) time upper bound by Chen, Kanj, and Jia. Expand
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The Stretch Factor of the Delaunay Triangulation Is Less than 1.998
  • Ge Xia
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 22 March 2011
TLDR
We show that the stretch factor of the Delaunay triangulation is less than $\rho = 1.998$, significantly improving the current best upper bound of 2.42 by Keil and Gutwin. Expand
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Strong computational lower bounds via parameterized complexity
TLDR
We develop new techniques for deriving strong computational lower bounds for a class of well-known NP-hard problems in the above class. Expand
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Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
TLDR
We develop new techniques to derive lower bounds on the kernel size for certain parameterized problems. Expand
  • 63
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Improved Parameterized Upper Bounds for Vertex Cover
TLDR
This paper presents an O(1.2738k + kn)-time polynomial-space parameterized algorithm for Vertex Cover improving the previous O(2kk2k+2) time upper bound by Chen, Kanj, and Jia. Expand
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Seeing the trees and their branches in the network is hard
TLDR
We prove that the problem of deciding whether a given tree is contained inside a network is NP-complete and provide a parameterized algorithm that runs in time O(2^k^/^2n^2). Expand
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Linear FPT reductions and computational lower bounds
TLDR
We develop new techniques for deriving very strong computational lower bounds for a class of well-known NP-hard problems, including weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. Expand
  • 120
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Tight lower bounds for certain parameterized NP-hard problems
  • J. Chen, B. Chor, +4 authors Ge Xia
  • Computer Science, Mathematics
  • Proceedings. 19th IEEE Annual Conference on…
  • 15 September 2005
TLDR
A group of parameterized NP-hard problems, including weighted SAT, dominating set, hitting set, set cover, and feature set, cannot be solved in time n/sup o(k)/poly(m), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[l] of the W-hierarchy collapses to FPT. Expand
  • 111
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Improved upper bound on the stretch factor of delaunay triangulations
  • Ge Xia
  • Mathematics, Computer Science
  • SoCG '11
  • 13 June 2011
TLDR
We prove that the stretch factor of the Delaunay triangulation of a set of points in the plane is less than ρ = 1.998, improving the previous best upper bound of 2.42. Expand
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Tight Lower Bounds for Certain Parameterized NP-Hard Problems
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