234 research outputs found
Greedy Algorithms for Steiner Forest
In the Steiner Forest problem, we are given terminal pairs ,
and need to find the cheapest subgraph which connects each of the terminal
pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson
gave primal-dual constant-factor approximation algorithms for this problem;
until now, the only constant-factor approximations we know are via linear
programming relaxations.
We consider the following greedy algorithm: Given terminal pairs in a metric
space, call a terminal "active" if its distance to its partner is non-zero.
Pick the two closest active terminals (say ), set the distance
between them to zero, and buy a path connecting them. Recompute the metric, and
repeat. Our main result is that this algorithm is a constant-factor
approximation.
We also use this algorithm to give new, simpler constructions of cost-sharing
schemes for Steiner forest. In particular, the first "group-strict" cost-shares
for this problem implies a very simple combinatorial sampling-based algorithm
for stochastic Steiner forest
Tunneling resonances in quantum dots: Coulomb interaction modifies the width
Single-electron tunneling through a zero-dimensional state in an asymmetric
double-barrier resonant-tunneling structure is studied. The broadening of steps
in the -- characteristics is found to strongly depend on the polarity of
the applied bias voltage. Based on a qualitative picture for the
finite-life-time broadening of the quantum dot states and a quantitative
comparison of the experimental data with a non-equilibrium transport theory, we
identify this polarity dependence as a clear signature of Coulomb interaction.Comment: 4 pages, 4 figure
Measurement of the energy dependence of phase relaxation by single electron tunneling
Single electron tunneling through a single impurity level is used to probe
the fluctuations of the local density of states in the emitter. The energy
dependence of quasi-particle relaxation in the emitter can be extracted from
the damping of the fluctuations of the local density of states (LDOS). At
larger magnetic fields Zeeman splitting is observed.Comment: 2 pages, 4 figures; 25th International Conference on the Physics of
Semiconductors, Osaka, Japan, September 17-22, 200
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
A -Vertex Kernel for Maximum Internal Spanning Tree
We consider the parameterized version of the maximum internal spanning tree
problem, which, given an -vertex graph and a parameter , asks for a
spanning tree with at least internal vertices. Fomin et al. [J. Comput.
System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a
simple application of this rule is sufficient to yield a -vertex kernel.
Here we propose a novel way to use the same reduction rule, resulting in an
improved -vertex kernel. Our algorithm applies first a greedy procedure
consisting of a sequence of local exchange operations, which ends with a
local-optimal spanning tree, and then uses this special tree to find a
reducible structure. As a corollary of our kernel, we obtain a deterministic
algorithm for the problem running in time
Impurity effects in quantum dots: Toward quantitative modeling
We have studied the single-electron transport spectrum of a quantum dot in GaAs/AlGaAs resonant tunneling device. The measured spectrum has irregularities indicating a broken circular symmetry. We model the system with an external potential consisting of a parabolic confinement and a negatively charged Coulombic impurity placed in the vicinity of the quantum dot. The model leads to good agreement between the calculated single-electron eigenenergies and the experimental spectrum. Furthermore, we use the spin-density-functional theory to study the energies and angular momenta when the system contains many interacting electrons. In the high magnetic field regime the increasing electron number is shown to reduce the distortion induced by the impurity.Peer reviewe
Approximating the minimum directed tree cover
Given a directed graph with non negative cost on the arcs, a directed
tree cover of is a rooted directed tree such that either head or tail (or
both of them) of every arc in is touched by . The minimum directed tree
cover problem (DTCP) is to find a directed tree cover of minimum cost. The
problem is known to be -hard. In this paper, we show that the weighted Set
Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to
approximate DTCP with the same ratio as for SCP. We show that this expectation
can be satisfied in some way by designing a purely combinatorial approximation
algorithm for the DTCP and proving that the approximation ratio of the
algorithm is with is the maximum outgoing degree of
the nodes in .Comment: 13 page
Radix heaps an efficient implementation for priority queues
We describe the implementation of a data structure called radix heap, which is a priority queue with restricted functionality. Its restrictions are observed by Dijkstra's algorithm, which uses priority queues to solve the single source shortest path problem in graphs with nonnegative edge costs. For a graph with nodes and edges and real-valued edge costs, the best known theoretical bound for the algorithm is . This bound is attained by using Fibonacci heaps to implement priority queues. If the edge costs are integers in the range , then using our implementation of radix heaps for Dijkstra's algorithm leads to a running time of . We compare our implementation of radix heaps with an existing implementation of Fibonacci heaps in the framework of Dijkstra's algorithm. Our experiments exhibit a tangible advantage for radix heaps over Fibonacci heaps and confirm the positive influence of small edge costs on the running time
Zeeman energy and spin relaxation in a one-electron quantum dot
We have measured the relaxation time, T1, of the spin of a single electron
confined in a semiconductor quantum dot (a proposed quantum bit). In a magnetic
field, applied parallel to the two-dimensional electron gas in which the
quantum dot is defined, Zeeman splitting of the orbital states is directly
observed by measurements of electron transport through the dot. By applying
short voltage pulses, we can populate the excited spin state with one electron
and monitor relaxation of the spin. We find a lower bound on T1 of 50
microseconds at 7.5 T, only limited by our signal-to-noise ratio. A continuous
measurement of the charge on the dot has no observable effect on the spin
relaxation.Comment: Replaced with the version published in Phys. Rev. Let
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