1,935 research outputs found
Linear Time Parameterized Algorithms via Skew-Symmetric Multicuts
A skew-symmetric graph is a directed graph with an
involution on the set of vertices and arcs. In this paper, we
introduce a separation problem, -Skew-Symmetric Multicut, where we are given
a skew-symmetric graph , a family of of -sized subsets of
vertices and an integer . The objective is to decide if there is a set
of arcs such that every set in the family has a vertex
such that and are in different connected components of
. In this paper, we give an algorithm for
this problem which runs in time , where is the
number of arcs in the graph, the number of vertices and the length
of the family given in the input.
Using our algorithm, we show that Almost 2-SAT has an algorithm with running
time and we obtain algorithms for {\sc Odd Cycle Transversal}
and {\sc Edge Bipartization} which run in time and
respectively. This resolves an open problem posed by Reed,
Smith and Vetta [Operations Research Letters, 2003] and improves upon the
earlier almost linear time algorithm of Kawarabayashi and Reed [SODA, 2010].
We also show that Deletion q-Horn Backdoor Set Detection is a special case of
3-Skew-Symmetric Multicut, giving us an algorithm for Deletion q-Horn Backdoor
Set Detection which runs in time . This gives the first
fixed-parameter tractable algorithm for this problem answering a question posed
in a paper by a superset of the authors [STACS, 2013]. Using this result, we
get an algorithm for Satisfiability which runs in time where
is the size of the smallest q-Horn deletion backdoor set, with being
the length of the input formula
Sharp weighted estimates for multi-frequency Calder\'on-Zygmund operators
In this paper we study weighted estimates for the multi-frequency
Calder\'{o}n-Zygmund operators associated with the frequency set
and modulus of continuity
satisfying the usual Dini condition. We use the modern method of domination by
sparse operators and obtain bounds for the exponents of and characteristic
Radiatively Generated Oscillations: General Analysis, Textures and Models
We study the consequences of assuming that the mass scale
corresponding to the solar neutrino oscillations and mixing angle
corresponding to the electron neutrino oscillation at CHOOZ are radiatively
generated through the standard electroweak gauge interactions. All the leptonic
mass matrices having zero and at a high scale lead to
a unique low energy value for the which is determined by the
(known) size of the radiative corrections, solar and the atmospheric mixing
angle and the Majorana mass of the neutrino observed in neutrinoless double
beta decay. This prediction leads to the following consequences: () The MSSM
radiative corrections generate only the dark side of the solar neutrino
solutions. () The inverted mass hierarchy () at the high scale
fails in generating the LMA solution but it can lead to the LOW or vacuum
solutions. () The generated in models with maximal solar
mixing at a high scale is zero to the lowest order in the radiative parameter.
It tends to get suppressed as a result of this and lies in the vacuum region.
We discuss specific textures which can lead to the LMA solution in the present
framework and provide a gauge theoretical realization of this in the context of
the seesaw model.Comment: 19 pages, LATE
Fast Neutrino Decay in the Minimal Seesaw Model
Neutrino decay in the minimal seesaw model containing three right handed
neutrinos and a complex singlet Higgs in addition to the
standard model fields is considered. A global horizontal symmetry is
imposed, which on spontaneous breaking gives rise to a Goldstone boson. This
symmetry is chosen in a way that makes a) the contribution of heavy (
MeV) majorana neutrinos to the neutrinoless double beta decay amplitude
vanish and b) allows the heavy neutrino to decay to a lighter neutrino and the
Goldstone boson. It is shown that this decay can occur at a rate much faster
than in the original Majoron model even if one does not introduce any
additional Higgs fields as is done in the literature. Possibility of describing
the 17 keV neutrino in this minimal seesaw model is investigated. While most of
the cosmological and astrophysical constraints on the 17 keV neutrino can be
satisfied in this model, the laboratory limits coming from the neutrino
oscillations cannot be easily met. An extension which removes this inadequacy
and offers a consistent description of the 17 keV neutrino is discussed.Comment: 16 pages, PRL-TH/92-1
A Linear Time Parameterized Algorithm for Node Unique Label Cover
The optimization version of the Unique Label Cover problem is at the heart of
the Unique Games Conjecture which has played an important role in the proof of
several tight inapproximability results. In recent years, this problem has been
also studied extensively from the point of view of parameterized complexity.
Cygan et al. [FOCS 2012] proved that this problem is fixed-parameter tractable
(FPT) and Wahlstr\"om [SODA 2014] gave an FPT algorithm with an improved
parameter dependence. Subsequently, Iwata, Wahlstr\"om and Yoshida [2014]
proved that the edge version of Unique Label Cover can be solved in linear
FPT-time. That is, there is an FPT algorithm whose dependence on the input-size
is linear. However, such an algorithm for the node version of the problem was
left as an open problem. In this paper, we resolve this question by presenting
the first linear-time FPT algorithm for Node Unique Label Cover
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