2,084 research outputs found
Almost Optimal Stochastic Weighted Matching With Few Queries
We consider the {\em stochastic matching} problem. An edge-weighted general
(i.e., not necessarily bipartite) graph is given in the input, where
each edge in is {\em realized} independently with probability ; the
realization is initially unknown, however, we are able to {\em query} the edges
to determine whether they are realized. The goal is to query only a small
number of edges to find a {\em realized matching} that is sufficiently close to
the maximum matching among all realized edges. This problem has received a
considerable attention during the past decade due to its numerous real-world
applications in kidney-exchange, matchmaking services, online labor markets,
and advertisements.
Our main result is an {\em adaptive} algorithm that for any arbitrarily small
, finds a -approximation in expectation, by
querying only edges per vertex. We further show that our approach leads
to a -approximate {\em non-adaptive} algorithm that also
queries only edges per vertex. Prior to our work, no nontrivial
approximation was known for weighted graphs using a constant per-vertex budget.
The state-of-the-art adaptive (resp. non-adaptive) algorithm of Maehara and
Yamaguchi [SODA 2018] achieves a -approximation (resp.
-approximation) by querying up to edges per
vertex where denotes the maximum integer edge-weight. Our result is a
substantial improvement over this bound and has an appealing message: No matter
what the structure of the input graph is, one can get arbitrarily close to the
optimum solution by querying only a constant number of edges per vertex.
To obtain our results, we introduce novel properties of a generalization of
{\em augmenting paths} to weighted matchings that may be of independent
interest
Reentrant Adhesion Behavior in Nanocluster Deposition
We simulate the collision of atomic clusters with a weakly attractive surface
using molecular dynamics in a regime between soft-landing and fragmentation,
where the cluster undergoes large deformation but remains intact. As a function
of incident kinetic energy, we find a transition from adhesion to reflection at
low kinetic energies. We also identify a second adhesive regime at intermediate
kinetic energies, where strong deformation of the cluster leads to an increase
in contact area and adhesive energy.Comment: 7 pages, 6 figure
Ignorance is Almost Bliss: Near-Optimal Stochastic Matching With Few Queries
The stochastic matching problem deals with finding a maximum matching in a
graph whose edges are unknown but can be accessed via queries. This is a
special case of stochastic -set packing, where the problem is to find a
maximum packing of sets, each of which exists with some probability. In this
paper, we provide edge and set query algorithms for these two problems,
respectively, that provably achieve some fraction of the omniscient optimal
solution.
Our main theoretical result for the stochastic matching (i.e., -set
packing) problem is the design of an \emph{adaptive} algorithm that queries
only a constant number of edges per vertex and achieves a
fraction of the omniscient optimal solution, for an arbitrarily small
. Moreover, this adaptive algorithm performs the queries in only a
constant number of rounds. We complement this result with a \emph{non-adaptive}
(i.e., one round of queries) algorithm that achieves a
fraction of the omniscient optimum. We also extend both our results to
stochastic -set packing by designing an adaptive algorithm that achieves a
fraction of the omniscient optimal solution, again
with only queries per element. This guarantee is close to the best known
polynomial-time approximation ratio of for the
\emph{deterministic} -set packing problem [Furer and Yu, 2013]
We empirically explore the application of (adaptations of) these algorithms
to the kidney exchange problem, where patients with end-stage renal failure
swap willing but incompatible donors. We show on both generated data and on
real data from the first 169 match runs of the UNOS nationwide kidney exchange
that even a very small number of non-adaptive edge queries per vertex results
in large gains in expected successful matches
Molecular dynamics simulations of reflection and adhesion behavior in Lennard-Jones cluster deposition
We conduct molecular dynamics simulations of the collision of atomic clusters
with a weakly-attractive surface. We focus on an intermediate regime, between
soft-landing and fragmentation, where the cluster undergoes deformation on
impact but remains largely intact, and will either adhere to the surface (and
possibly slide), or be reflected. We find that the outcome of the collision is
determined by the Weber number, We i.e. the ratio of the kinetic energy to the
adhesion energy, with a transition between adhesion and reflection occurring as
We passes through unity. We also identify two distinct collision regimes: in
one regime the collision is largely elastic and deformation of the cluster is
relatively small but in the second regime the deformation is large and the
adhesion energy starts to depend on the kinetic energy. If the transition
between these two regimes occurs at a similar kinetic energy to that of the
transition between reflection and adhesion, then we find that the probability
of adhesion for a cluster can be bimodal. In addition we investigate the
effects of the angle of incidence on adhesion and reflection. Finally we
compare our findings both with recent experimental results and with macroscopic
theories of particle collisions.Comment: 18 pages, 13 figure
Break-down of the single-active-electron approximation for one-photon ionization of the B state of H exposed to intense laser fields
Ionization, excitation, and de-excitation to the ground state is studied
theoretically for the first excited singlet state B of H
exposed to intense laser fields with photon energies in between about 3 eV and
13 eV. A parallel orientation of a linear polarized laser and the molecular
axis is considered. Within the dipole and the fixed-nuclei approximations the
time-dependent Schr\"odinger equation describing the electronic motion is
solved in full dimensionality and compared to simpler models. A dramatic
break-down of the single-active-electron approximation is found and explained
to be due to the inadequate description of the final continuum states.Comment: 9 pages, 4 figure
Biochemical composition of promising leaves genotypes of buckwheat grown in Himachal Pradesh
Buckwheat originated from China and being cultivated all over the world, and has become a prominent pseudocereal. Among the pseudocereals (amaranthus, buckwheat and quinoa), buckwheat plant is economically important primarily due to their carbohydrate and protein rich grains, short growth span; besides foliage being used as a green vegetable and commercial source of the glycoside rutin used in medicine. In the present study, an attempt was made to evaluate the biochemical constituents of nutritional and nutraceutical significance of fourteen promising leaves genotypes of common buckwheat grown in Sangla region by following standard procedures. Wide variations in moisture content, crude protein, fat, ash, crude fiber, carbohydrates, ascorbic acid, oxalate and in vitro protein digestibility were observed to range from 87.4 to 92.2 %, 22.4 to 30.4 %, 1.8 to 3.7 %, 10.6 to 15.4 %, 12.0 to 13.9 %, 34.8 to 42.4 %, 25.0 to 29.2 mg/100g, 1375 to 1390 mg/100g and 53.4 to 65.1 % in that order. The content of minerals such as potassium, phosphorus, calcium, magnesium, zinc, manganese and copper varied from 1767.5 to 2035.0 mg/100g, 808 to 910 mg/100g, 394 to 409 mg/100g, 232.0 to 248.2 mg/100g, 3.1 to 6.1 mg/100g, 20.4 to 29.8 mg/100g and 0.2 to 1.4 mg/100g respectively. Based on cumulative grading done in respect of nutritionally desirable quality i.e., protein, ash, crude fiber, carbohydrates, ascorbic acid, in vitro protein digestibility, calcium, phosphorus, iron and oxalate content, the genotype IC-323731 followed by Kullugangetri and VL-27 emerged out to be overall superior versatile cultivars for cultivation under dry temperate climate
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