218 research outputs found
Parameterization Above a Multiplicative Guarantee
Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given an instance (I,k) of some (parameterized) problem ? with a guarantee g(I), decide whether I admits a solution of size at least (at most) k+g(I). Here, g(I) is usually a lower bound (resp. upper bound) on the maximum (resp. minimum) size of a solution. Since its introduction in 1999 for Max SAT and Max Cut (with g(I) being half the number of clauses and half the number of edges, respectively, in the input), analysis of parameterization above a guarantee has become a very active and fruitful topic of research.
We highlight a multiplicative form of parameterization above a guarantee: Given an instance (I,k) of some (parameterized) problem ? with a guarantee g(I), decide whether I admits a solution of size at least (resp. at most) k ? g(I). In particular, we study the Long Cycle problem with a multiplicative parameterization above the girth g(I) of the input graph, and provide a parameterized algorithm for this problem. Apart from being of independent interest, this exemplifies how parameterization above a multiplicative guarantee can arise naturally. We also show that, for any fixed constant ?>0, multiplicative parameterization above g(I)^(1+?) of Long Cycle yields para-NP-hardness, thus our parameterization is tight in this sense. We complement our main result with the design (or refutation of the existence) of algorithms for other problems parameterized multiplicatively above girth
Transmission through a n interacting quantum dot in the Coulomb blockade regime
The influence of electron-electron (e-e) interactions on the transmission
through a quantum dot is investigated numerically for the Coulomb blockade
regime. For vanishing magnetic fields, the conductance peak height statistics
is found to be independent of the interactions strength. It is identical to the
statistics predicted by constant interaction single electron random matrix
theory and agrees well with recent experiments. However, in contrast to these
random matrix theories, our calculations reproduces the reduced sensitivity to
magnetic flux observed in many experiments. The relevant physics is traced to
the short range Coulomb correlations providing thus a unified explanation for
the transmission statistics as well as for the large conductance peak spacing
fluctuations observed in other experiments.Comment: Final version as publishe
Cognitive Analytic Therapy in People with Learning Disability: An investigation into the common reciprocal roles found within this client group
Developments over the last twenty years have shown that, contrary to previous opinion, people with learning disabilities can benefit from psychotherapy (Sinason 1992; Kroese, Dagnan & Loumidia, 1997). Cognitive Analytic Therapy (CAT) has been adapted for use with a learning disability population (Ryle 2002). CAT collaboratively examines the Reciprocal Roles (RRs) a client plays in relationships. These are impacted by clients’ experiences of the world. The aim of this research is to identify which RRs may become apparent in working with people with learning disabilities. The therapy notes of participants (n=16) who had undergone CAT were examined and analysed using content analysis. Twenty-two different RRs were found. Four common Reciprocal Roles and two common idealised Reciprocal Roles were identified. Other observations about the data are presented. The limitations and clinical implications of the study are discussed
Kernelization for Spreading Points
We consider the following problem about dispersing points. Given a set of
points in the plane, the task is to identify whether by moving a small number
of points by small distance, we can obtain an arrangement of points such that
no pair of points is ``close" to each other. More precisely, for a family of
points, an integer , and a real number , we ask whether at most
points could be relocated, each point at distance at most from its
original location, such that the distance between each pair of points is at
least a fixed constant, say . A number of approximation algorithms for
variants of this problem, under different names like distant representatives,
disk dispersing, or point spreading, are known in the literature. However, to
the best of our knowledge, the parameterized complexity of this problem remains
widely unexplored. We make the first step in this direction by providing a
kernelization algorithm that, in polynomial time, produces an equivalent
instance with points. As a byproduct of this result, we also design
a non-trivial fixed-parameter tractable (FPT) algorithm for the problem,
parameterized by and . Finally, we complement the result about
polynomial kernelization by showing a lower bound that rules out the existence
of a kernel whose size is polynomial in alone, unless
Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
The fluctuations and the distribution of the conductance peak spacings of a
quantum dot in the Coulomb-blockade regime are studied and compared with the
predictions of random matrix theory (RMT). The experimental data were obtained
in transport measurements performed on a semiconductor quantum dot fabricated
in a GaAs-AlGaAs heterostructure. It is found that the fluctuations in the peak
spacings are considerably larger than the mean level spacing in the quantum
dot. The distribution of the spacings appears Gaussian both for zero and for
non-zero magnetic field and deviates strongly from the RMT-predictions.Comment: 7 pages, 4 figure
Covering Vectors by Spaces in Perturbed Graphic Matroids and Their Duals
Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, an r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P, where I is the incidence matrix of some graph and P is a binary matrix of rank at most r. Such matroids naturally appear in a number of theoretical and applied settings. The main motivation behind our work is an attempt to understand which parameterized algorithms for various problems on graphs could be lifted to perturbed graphic matroids.
We study the parameterized complexity of a natural generalization (for matroids) of the following fundamental problems on graphs: Steiner Tree and Multiway Cut. In this generalization, called the Space Cover problem, we are given a binary matroid M with a ground set E, a set of terminals T subseteq E, and a non-negative integer k. The task is to decide whether T can be spanned by a subset of E T of size at most k.
We prove that on graphic matroid perturbations, for every fixed r, Space Cover is fixed-parameter tractable parameterized by k. On the other hand, the problem becomes W[1]-hard when parameterized by r+k+|T| and it is NP-complete for r <= 2 and |T|<= 2.
On cographic matroids, that are the duals of graphic matroids, Space Cover generalizes another fundamental and well-studied problem, namely Multiway Cut. We show that on the duals of perturbed graphic matroids the Space Cover problem is fixed-parameter tractable parameterized by r+k
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