46,988 research outputs found
Heuristic algorithms for the min-max edge 2-coloring problem
In multi-channel Wireless Mesh Networks (WMN), each node is able to use
multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004,
INFOCOM 2005) propose and study several such architectures in which a computer
can have multiple network interface cards. These architectures are modeled as a
graph problem named \emph{maximum edge -coloring} and studied in several
papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016).
Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an
alternative variant, named the \emph{min-max edge -coloring}.
The above mentioned graph problems, namely the maximum edge -coloring and
the min-max edge -coloring are studied mainly from the theoretical
perspective. In this paper, we study the min-max edge 2-coloring problem from a
practical perspective. More precisely, we introduce, implement and test four
heuristic approximation algorithms for the min-max edge -coloring problem.
These algorithms are based on a \emph{Breadth First Search} (BFS)-based
heuristic and on \emph{local search} methods like basic \emph{hill climbing},
\emph{simulated annealing} and \emph{tabu search} techniques, respectively.
Although several algorithms for particular graph classes were proposed by
Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques,
hypergraphs), we design the first algorithms for general graphs.
We study and compare the running data for all algorithms on Unit Disk Graphs,
as well as some graphs from the DIMACS vertex coloring benchmark dataset.Comment: This is a post-peer-review, pre-copyedit version of an article
published in International Computing and Combinatorics Conference
(COCOON'18). The final authenticated version is available online at:
http://www.doi.org/10.1007/978-3-319-94776-1_5
When Catalysis is Useful for Probabilistic Entanglement Transformation
We determine all quantum states that can serve as useful
catalysts for a given probabilistic entanglement transformation, in the sense
that they can increase the maximal transformation probability. When
higher-dimensional catalysts are considered, a sufficient and necessary
condition is derived under which a certain probabilistic transformation has
useful catalysts.Comment: 5 pages, journal versio
Superconductivity in Inhomogeneous Hubbard Models
We present a controlled perturbative approach to the low temperature phase
diagram of highly inhomogeneous Hubbard models in the limit of small coupling,
, between clusters. We apply this to the dimerized and checkerboard models.
The dimerized model is found to behave like a doped semiconductor, with a
Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which
are smooth functions of the Hubbard interaction, . By contrast, the
checkerboard model has a nodeless d-wave superconducting state (preformed pair
condensate, -BEC) for , which smoothly crosses over to an
intermediate BCS-like superconducting phase (-BCS), also with no nodal
quasi-particles, for , which gives way to a
Fermi liquid phase at large .Comment: 7 pages, a sign error in Eq.(3) has been corrected and its
consequence has been discussed with updated figure
Residual Symmetries for Neutrino Mixing with a Large theta_13 and Nearly Maximal delta_D
The residual Z^s_2(k) and bar Z^s_2(k) symmetries induce a direct and unique
phenomenological relation with theta_x (= theta_13) expressed in terms of the
other two mixing angles, theta_s (= theta_12) and theta_a (= theta_23), and the
Dirac CP phase delta_D. Z^s_2(k) predicts a theta_x probability distribution
centered around 3^o ~ 6^o with an uncertainty of 2^o to 4^o while those from
bar Z^s_2(k) are approximately a factor of two larger. Either result fits the
T2K, MINOS and Double CHOOZ measurements. Alternately a prediction for the
Dirac CP phase delta_D results in a peak at +-74^o (+-106^o) for Z^s_2(k) or
+-123^o (+-57^o) for bar Z^s_2(k) which is consistent with the latest global
fit. We also give a distribution for the leptonic Jarslkog invariant J_v which
can provide further tests from measurements at T2K and NOvA.Comment: Accepted for publication in PR
On the tau-functions of the Degasperis-Procesi equation
The DP equation is investigated from the point of view of
determinant-pfaffian identities. The reciprocal link between the
Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the
two-dimensional Toda system is used to construct the N-soliton solution of the
DP equation. The N-soliton solution of the DP equation is presented in the form
of pfaffian through a hodograph (reciprocal) transformation. The bilinear
equations, the identities between determinants and pfaffians, and the
-functions of the DP equation are obtained from the pseudo 3-reduction of
the two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and
Theoretical, to be publishe
Time-dependent universal conductance fluctuations in mesoscopic Au wires: implications
In cold, mesoscopic conductors, two-level fluctuators lead to time-dependent
universal conductance fluctuations (TDUCF) manifested as noise. In Au
nanowires, we measure the magnetic field dependence of TDUCF, weak localization
(WL), and magnetic field-driven (MF) UCF before and after treatments that alter
magnetic scattering and passivate surface fluctuators. Inconsistencies between
and strongly suggest either that the
theory of these mesoscopic phenomena in weakly disordered, highly pure Au is
incomplete, or that the assumption that the TDUCF frequency dependence remains
to very high frequencies is incorrect. In the latter case, TDUCF in
excess of expectations may have implications for decoherence in
solid-state qubits.Comment: 8 pages, 9 figures, accepted to PR
Non-local Matching Condition and Scale-invariant Spectrum in Bouncing Cosmology
In cosmological scenarios such as the pre-big bang scenario or the ekpyrotic
scenario, a matching condition between the metric perturbations in the pre-big
bang phase and those in the post big-bang phase is often assumed. Various
matching conditions have been considered in the literature. Nevertheless
obtaining a scale invariant CMB spectrum via a concrete mechanism remains
impossible. In this paper, we examine this problem from the point of view of
local causality. We begin with introducing the notion of local causality and
explain how it constrains the form of the matching condition. We then prove a
no-go theorem: independent of the details of the matching condition, a scale
invariant spectrum is impossible as long as the local causality condition is
satisfied. In our framework, it is easy to show that a violation of local
causality around the bounce is needed in order to give a scale invariant
spectrum. We study a specific scenario of this possibility by considering a
nonlocal effective theory inspired by noncommutative geometry around the bounce
and show that a scale invariant spectrum is possible. Moreover we demonstrate
that the magnitude of the spectrum is compatible with observations if the
bounce is assumed to occur at an energy scale which is a few orders of
magnitude below the Planckian energy scale.Comment: 15 pages, 2 figures; v3: clarifications added, changes in references,
version to appear in PR
Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities
The construction of brane setups for the exceptional series E6,E7,E8 of SU(2)
orbifolds remains an ever-haunting conundrum. Motivated by techniques in some
works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic
outlook, a method which we call stepwise projection, that may shed some light
on this puzzle. We exemplify this method, consisting of transformation rules
for obtaining complex quivers and brane setups from more elementary ones, to
the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we
demonstrate the generality of the stepwise procedure by appealing to Frobenius'
theory of Induced Representations. Our algorithm suggests the existence of
generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure
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