470 research outputs found
Improved FPT algorithms for weighted independent set in bull-free graphs
Very recently, Thomass\'e, Trotignon and Vuskovic [WG 2014] have given an FPT
algorithm for Weighted Independent Set in bull-free graphs parameterized by the
weight of the solution, running in time . In this article
we improve this running time to . As a byproduct, we also
improve the previous Turing-kernel for this problem from to .
Furthermore, for the subclass of bull-free graphs without holes of length at
most for , we speed up the running time to . As grows, this running time is
asymptotically tight in terms of , since we prove that for each integer , Weighted Independent Set cannot be solved in time in the class of -free graphs unless the
ETH fails.Comment: 15 page
Lossy Kernels for Hitting Subgraphs
In this paper, we study the Connected H-hitting Set and Dominating Set problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the Connected H-hitting set problem, we obtain an alpha-approximate kernel for every alpha>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the Dominating Set problem on d-degenerate graphs and provide an interpolation of approximate kernels between the known d^2-approximate kernel of constant size and 1-approximate kernel of size k^{O(d^2)}
Improved Linear Cryptanalysis of Reduced-Round MIBS
MIBS is a 32-round lightweight block cipher with 64-bit block size and two different key sizes, namely 64-bit and 80-bit keys. Bay et al. provided the first impossible differential, differential and linear cryptanalyses of MIBS. Their best attack was a linear attack on the 18-round MIBS-80. In this paper, we significantly improve their attack by discovering more approximations and mounting Hermelin et al.'s multidimensional linear cryptanalysis. We also use Nguyen et al.'s technique to have less time complexity. We attack on 19 rounds of MIBS-80 with a time complexity of 2^{74.23} 19-round MIBS-80 encryptions by using 2^{57.87} plaintext-ciphertext pairs. To the best of our knowledge, the result proposed in this paper is the best cryptanalytic result for MIBS, so far
Transmission Phase in the Kondo Regime Revealed in a Two-Path Interferometer
We report on the direct observation of the transmission phase shift through a
Kondo correlated quantum dot by employing a new type of two-path
interferometer. We observed a clear -phase shift, which persists up to
the Kondo temperature . Above this temperature, the phase shifts by
more than at each Coulomb peak, approaching the behavior observed for
the standard Coulomb blockade regime. These observations are in remarkable
agreement with 2-level numerical renormalization group calculations. The unique
combination of experimental and theoretical results presented here fully
elucidates the phase evolution in the Kondo regime.Comment: 4 pages, 3 figure
Modifications of filament spectra by shaped octave-spanning laser pulses
In this paper we examine the spectral changes in a white light laser filament due to different pulse shapes generated by a pulse-shaping setup. We particularly explore how the properties of the filament spectra can be controlled by parametrically tailored white light pulses. The experiments are carried out in a gas cell with up to 9 bars of argon. Plasma generation and self-phase modulation strongly affect the pulse in the spectral and temporal domains. By exploiting these effects we show that the pulse spectrum can be modified in a desired way by either using second-order parametric chirp functions to shift the filament spectrum to higher or lower wavelengths, or by optimizing pulse shapes with a genetic algorithm to generate more complex filament spectra. This paper is an example of the application of complex, parametrically shaped white light pulses
Polynomial kernelization for removing induced claws and diamonds
A graph is called (claw,diamond)-free if it contains neither a claw (a
) nor a diamond (a with an edge removed) as an induced subgraph.
Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of
triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex
is in at most two maximal cliques and every edge is in exactly one maximal
clique.
In this paper we consider the parameterized complexity of the
(claw,diamond)-free Edge Deletion problem, where given a graph and a
parameter , the question is whether one can remove at most edges from
to obtain a (claw,diamond)-free graph. Our main result is that this problem
admits a polynomial kernel. We complement this finding by proving that, even on
instances with maximum degree , the problem is NP-complete and cannot be
solved in time unless the Exponential Time
Hypothesis fai
Finding secluded places of special interest in graphs.
Finding a vertex subset in a graph that satisfies a certain property is one of the most-studied topics
in algorithmic graph theory. The focus herein is often on minimizing or maximizing the size
of the solution, that is, the size of the desired vertex set. In several applications, however, we also
want to limit the “exposure” of the solution to the rest of the graph. This is the case, for example,
when the solution represents persons that ought to deal with sensitive information or a segregated
community. In this work, we thus explore the (parameterized) complexity of finding such secluded
vertex subsets for a wide variety of properties that they shall fulfill. More precisely, we study the
constraint that the (open or closed) neighborhood of the solution shall be bounded by a parameter
and the influence of this constraint on the complexity of minimizing separators, feedback vertex
sets, F-free vertex deletion sets, dominating sets, and the maximization of independent sets
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