1,925 research outputs found
Fine-Grained Complexity of k-OPT in Bounded-Degree Graphs for Solving TSP
The Traveling Salesman Problem asks to find a minimum-weight Hamiltonian cycle in an edge-weighted complete graph. Local search is a widely-employed strategy for finding good solutions to TSP. A popular neighborhood operator for local search is k-opt, which turns a Hamiltonian cycle C into a new Hamiltonian cycle C\u27 by replacing k edges. We analyze the problem of determining whether the weight of a given cycle can be decreased by a k-opt move. Earlier work has shown that (i) assuming the Exponential Time Hypothesis, there is no algorithm that can detect whether or not a given Hamiltonian cycle C in an n-vertex input can be improved by a k-opt move in time f(k) n^o(k / log k) for any function f, while (ii) it is possible to improve on the brute-force running time of O(n^k) and save linear factors in the exponent. Modern TSP heuristics are very successful at identifying the most promising edges to be used in k-opt moves, and experiments show that very good global solutions can already be reached using only the top-O(1) most promising edges incident to each vertex. This leads to the following question: can improving k-opt moves be found efficiently in graphs of bounded degree? We answer this question in various regimes, presenting new algorithms and conditional lower bounds. We show that the aforementioned ETH lower bound also holds for graphs of maximum degree three, but that in bounded-degree graphs the best improving k-move can be found in time O(n^((23/135+epsilon_k)k)), where lim_{k -> infty} epsilon_k = 0. This improves upon the best-known bounds for general graphs. Due to its practical importance, we devote special attention to the range of k in which improving k-moves in bounded-degree graphs can be found in quasi-linear time. For k <= 7, we give quasi-linear time algorithms for general weights. For k=8 we obtain a quasi-linear time algorithm when the weights are bounded by O(polylog n). On the other hand, based on established fine-grained complexity hypotheses about the impossibility of detecting a triangle in edge-linear time, we prove that the k = 9 case does not admit quasi-linear time algorithms. Hence we fully characterize the values of k for which quasi-linear time algorithms exist for polylogarithmic weights on bounded-degree graphs
Transport through a single Anderson impurity coupled to one normal and two superconducting leads
We study the interplay between the Kondo and Andreev-Josephson effects in a
quantum dot coupled to one normal and two superconducting (SC) leads. In the
large gap limit, the low-energy states of this system can be described exactly
by a local Fermi liquid for the interacting Bogoliubov particles. The phase
shift and the renormalized parameters for the Bogoliubov particles vary
depending on the Josephson phase between the two SC leads. We explore the
precise features of a crossover that occurs between the Kondo singlet and local
Cooper-pairing states as the Josephson phase varies, using the numerical
renormalization group approach.Comment: 4 pages, 4 figures, contribution to SCES 201
Chemical potential jump between hole- and electron-doped sides of ambipolar high-Tc cuprate
In order to study an intrinsic chemical potential jump between the hole- and
electron-doped high-Tc superconductors, we have performed core-level X-ray
photoemission spectroscopy (XPS) measurements of Y0.38La0.62Ba1.74La0.26Cu3Oy
(YLBLCO), into which one can dope both holes and electrons with maintaining the
same crystal structure. Unlike the case between the hole-doped system
La_2-xSrxCuO4 and the electron-doped system Nd_2-xCexCuO4, we have estimated
the true chemical potential jump between the hole- and electron-doped YLBLCO to
be ~0.8 eV, which is much smaller than the optical gaps of 1.4-1.7 eV reported
for the parent insulating compounds. We attribute the reduced jump to the
indirect nature of the charge-excitation gap as well as to the polaronic nature
of the doped carriers.Comment: 4 pages, 3 figure
Bulk superconducting phase with a full energy gap in the doped topological insulator Cu_xBi_2Se_3
The superconductivity recently found in the doped topological insulator
Cu_xBi_2Se_3 offers a great opportunity to search for a topological
superconductor. We have successfully prepared a single-crystal sample with a
large shielding fraction and measured the specific-heat anomaly associated with
the superconductivity. The temperature dependence of the specific heat suggests
a fully-gapped, strong-coupling superconducting state, but the BCS theory is
not in full agreement with the data, which hints at a possible unconventional
pairing in Cu_xBi_2Se_3. Also, the evaluated effective mass of 2.6m_e (m_e is
the free electron mass) points to a large mass enhancement in this material.Comment: 4 pages, 3 figure
Low Energy Action of "Covariant" Superstring Field Theory in the NS-NS pp-Wave Background
Exact construction of superstring field theory in some background fields is
very important. We construct the low energy NS-NS sector of superstring field
action in the pp-wave background with the flux of NS-NS antisymmetric tensor
field (NS-NS pp-wave) without gauge fixing up to the second-order where the
action is world-sheet BRST invariant. Here we use the word "covariant" in a
invariant theory for a symmetric transformation of the pp-wave background which
is not the Lorentz transformation in the flat background. Moreover we prove the
exact correspondence between this low energy action and the second-order
perturbation of supergravity action in the same background. We also prove the
correspondence of the gauge transformation in both the actions. This
construction is based on the BRST first quantization of superstrings in the
pp-wave background in our previous paper.Comment: 34 page
Oscillatory angular dependence of the magnetoresistance in a topological insulator Bi_{1-x}Sb_{x}
The angular-dependent magnetoresistance and the Shubnikov-de Haas
oscillations are studied in a topological insulator Bi_{0.91}Sb_{0.09}, where
the two-dimensional (2D) surface states coexist with a three-dimensional (3D)
bulk Fermi surface (FS). Two distinct types of oscillatory phenomena are
discovered in the angular-dependence: The one observed at lower fields is shown
to originate from the surface state, which resides on the (2\bar{1}\bar{1})
plane, giving a new way to distinguish the 2D surface state from the 3D FS. The
other one, which becomes prominent at higher fields, probably comes from the
(111) plane and is obviously of unknown origin, pointing to new physics in
transport properties of topological insulators.Comment: 4 pages, 5 figures, revised version with improved data and analysi
Magic Doping Fractions in High-Temperature Superconductors
We report hole-doping dependence of the in-plane resistivity \rho_{ab} in a
cuprate superconductor La_{2-x}Sr_{x}CuO_{4}, carefully examined using a series
of high-quality single crystals. Our detailed measurements find a tendency
towards charge ordering at particular rational hole doping fractions of 1/16,
3/32, 1/8, and 3/16. This observation appears to suggest a specific form of
charge order and is most consistent with the recent theoretical prediction of
the checkerboard-type ordering of the Cooper pairs at rational doping fractions
x = (2m+1)/2^n, with integers m and n.Comment: 5 pages, 3 figure, resubmitted to Phys. Rev. Lett. The Tc vs. x
diagram has been added and the discussions have been modified to focus more
on the experimental result
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