12,377 research outputs found
Fully Dynamic Matching in Bipartite Graphs
Maximum cardinality matching in bipartite graphs is an important and
well-studied problem. The fully dynamic version, in which edges are inserted
and deleted over time has also been the subject of much attention. Existing
algorithms for dynamic matching (in general graphs) seem to fall into two
groups: there are fast (mostly randomized) algorithms that do not achieve a
better than 2-approximation, and there slow algorithms with \O(\sqrt{m})
update time that achieve a better-than-2 approximation. Thus the obvious
question is whether we can design an algorithm -- deterministic or randomized
-- that achieves a tradeoff between these two: a approximation
and a better-than-2 approximation simultaneously. We answer this question in
the affirmative for bipartite graphs.
Our main result is a fully dynamic algorithm that maintains a 3/2 + \eps
approximation in worst-case update time O(m^{1/4}\eps^{/2.5}). We also give
stronger results for graphs whose arboricity is at most \al, achieving a (1+
\eps) approximation in worst-case time O(\al (\al + \log n)) for constant
\eps. When the arboricity is constant, this bound is and when the
arboricity is polylogarithmic the update time is also polylogarithmic.
The most important technical developement is the use of an intermediate graph
we call an edge degree constrained subgraph (EDCS). This graph places
constraints on the sum of the degrees of the endpoints of each edge: upper
bounds for matched edges and lower bounds for unmatched edges. The main
technical content of our paper involves showing both how to maintain an EDCS
dynamically and that and EDCS always contains a sufficiently large matching. We
also make use of graph orientations to help bound the amount of work done
during each update.Comment: Longer version of paper that appears in ICALP 201
Achievable efficiencies for probabilistically cloning the states
We present an example of quantum computational tasks whose performance is
enhanced if we distribute quantum information using quantum cloning.
Furthermore we give achievable efficiencies for probabilistic cloning the
quantum states used in implemented tasks for which cloning provides some
enhancement in performance.Comment: 9 pages, 8 figure
Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems
The Biconjugate A-Orthogonal Residual (BiCOR) method carried out in finite precision arithmetic by means of the biconjugate A-orthonormalization procedure may possibly tend to suffer from two sources of numerical instability, known as two kinds of breakdowns, similarly to those of the Biconjugate Gradient (BCG) method. This paper naturally exploits the composite step strategy employed in the development of the composite step BCG (CSBCG) method into the BiCOR method to cure one of the breakdowns called as pivot breakdown. Analogously to the CSBCG method, the resulting interesting variant, with only a minor modification to the usual implementation of the BiCOR method, is able to avoid near pivot breakdowns and compute all the well-defined BiCOR iterates stably on the assumption that the underlying biconjugate A-orthonormalization procedure does not break down. Another benefit acquired is that it seems to be a viable algorithm providing some further practically desired smoothing of the convergence history of the norm of the residuals, which is justified by numerical experiments. In addition, the exhibited method inherits the promising advantages of the empirically observed stability and fast convergence rate of the BiCOR method over the BCG method so that it outperforms the CSBCG method to some extent
Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing
We consider the problem of deciding if a given three-party entangled pure
state can be converted, with a non-zero success probability, into a given
two-party pure state through local quantum operations and classical
communication. We show that this question is equivalent to the well-known
computational problem of deciding if a multivariate polynomial is identically
zero. Efficient randomized algorithms developed to study the latter can thus be
applied to the question of tripartite to bipartite entanglement
transformations
Evaluation of bistable systems versus matched filters in detecting bipolar pulse signals
This paper presents a thorough evaluation of a bistable system versus a
matched filter in detecting bipolar pulse signals. The detectability of the
bistable system can be optimized by adding noise, i.e. the stochastic resonance
(SR) phenomenon. This SR effect is also demonstrated by approximate statistical
detection theory of the bistable system and corresponding numerical
simulations. Furthermore, the performance comparison results between the
bistable system and the matched filter show that (a) the bistable system is
more robust than the matched filter in detecting signals with disturbed pulse
rates, and (b) the bistable system approaches the performance of the matched
filter in detecting unknown arrival times of received signals, with an
especially better computational efficiency. These significant results verify
the potential applicability of the bistable system in signal detection field.Comment: 15 pages, 9 figures, MikTex v2.
Global Optimization by Energy Landscape Paving
We introduce a novel heuristic global optimization method, energy landscape
paving (ELP), which combines core ideas from energy surface deformation and
tabu search. In appropriate limits, ELP reduces to existing techniques. The
approach is very general and flexible and is illustrated here on two protein
folding problems. For these examples, the technique gives faster convergence to
the global minimum than previous approaches.Comment: to appear in Phys. Rev. Lett. (2002
Pulse Control of Decoherence with Population Decay
The pulse control of decoherence in a qubit interacting with a quantum
environment is studied with focus on a general case where decoherence is
induced by both pure dephasing and population decay. To observe how the
decoherence is suppressed by periodic pi pulses, we present a simple method to
calculate the time evolution of a qubit under arbitrary pulse sequences
consisting of bit-flips and/or phase-flips. We examine the effectiveness of the
two typical sequences: bb sequence consisting of only bit-flips, and bp
sequence consisting of both bit- and phase-flips. It is shown that the
effectiveness of the pulse sequences depends on a relative strength of the two
decoherence processes especially when a pulse interval is slightly shorter than
qubit-environment correlation times. In the short-interval limit, however, the
bp sequence is always more effective than, or at least as effective as, the bb
sequence.Comment: 11 pages, 7 figure
Detecting the inseparability and distillability of continuous variable states in Fock space
The partial transposition(PT) operation is an effecient tool in detecting the
inseparability of a mixed state. We give an explicit formula for the PT
operation for the continuous variable states in Fock space. We then give the
necessary and sufficient condition for the positivity of Gaussian operators.
Based on this, a number of creterions on the inseparability and distillability
for the multimode Gaussian states are naturally drawn. We finally give an
explicit formula for the state in a subspace of a global Gaussian state. This
formula, together with the known results for Gaussian states, gives the
criterions for the inseparability and distillability in a subspace of the
global Gaussian state.Comment: 8 pages, no figure, some typing errors correcte
The separability of tripartite Gaussian state with amplification and amplitude damping
Tripartite three mode Gaussian state undergoes parametric amplification and
amplitude damping as well as thermal noise is studied. In the case of a state
totally symmetrically interacting with the environment, the time dependent
correlation matrix of the state in evolution is given. The conditions for fully
separability and fully entanglement of the final tripartite three mode Gaussian
state are worked out.Comment: 9 pages, 3 figure
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