54 research outputs found
On the Approximability of Digraph Ordering
Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute
a labeling maximizing the number of forward edges, i.e.
edges (u,v) such that (u) < (v). For different values of k, this
reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work
studies the approximability of Max-k-Ordering and its generalizations,
motivated by their applications to job scheduling with soft precedence
constraints. We give an LP rounding based 2-approximation algorithm for
Max-k-Ordering for any k={2,..., n}, improving on the known
2k/(k-1)-approximation obtained via random assignment. The tightness of this
rounding is shown by proving that for any k={2,..., n} and constant
, Max-k-Ordering has an LP integrality gap of 2 -
for rounds of the
Sherali-Adams hierarchy.
A further generalization of Max-k-Ordering is the restricted maximum acyclic
subgraph problem or RMAS, where each vertex v has a finite set of allowable
labels . We prove an LP rounding based
approximation for it, improving on the
approximation recently given by Grandoni et al.
(Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact,
our approximation algorithm also works for a general version where the
objective counts the edges which go forward by at least a positive offset
specific to each edge.
The minimization formulation of digraph ordering is DAG edge deletion or
DED(k), which requires deleting the minimum number of edges from an n-vertex
directed acyclic graph (DAG) to remove all paths of length k. We show that
both, the LP relaxation and a local ratio approach for DED(k) yield
k-approximation for any .Comment: 21 pages, Conference version to appear in ESA 201
History of EISCAT – Part 6: the participation of Japan in the EISCAT Scientific Association
In Sect. 1, the original planning of Japanese Svalbard IS (incoherent scatter) radar with phased-array antennas is described. In 1988, this plan was proposed as one of the major projects for the forthcoming Solar–Terrestrial Environment Laboratory, Nagoya University, Japan, to be reorganized by the Research Institute of Atmospherics at Nagoya University. On the other hand, in 1989, UK scientists proposed a plan of polar cap radar with parabolic dish antennas in Longyearbyen to the EISCAT (European incoherent scatter) Council. In Sect. 2, the circumstances leading to Japan's participation in the EISCAT Scientific Association, with details of its processes with strong collaborations with Norwegian scientists and the EISCAT Scientific Association are described. In 1995, Japan participated EISCAT Scientific Association as the seventh member country with funds contributing to the second dish antenna of the EISCAT Svalbard Radar. In Sect. 3, a summary of the EISCAT-related achievement by Japanese scientists is described, where major interests are the lower thermosphere wind dynamics, the
magnetosphere–ionosphere–thermosphere coupling, characteristics, and driving mechanisms of ion upflow, electrodynamics of current, electric field and particles, characteristics and production mechanisms of auroras, such as pulsating aurora, and aurora tomography. In Sect. 4, a summary of the scientific collaborations between Japan and Europe, particularly those between Japan and Norway, and hopes for the forthcoming EISCAT_3D and further collaboration with EISCAT community are described.</p
Fast Distributed Approximation for Max-Cut
Finding a maximum cut is a fundamental task in many computational settings.
Surprisingly, it has been insufficiently studied in the classic distributed
settings, where vertices communicate by synchronously sending messages to their
neighbors according to the underlying graph, known as the or
models. We amend this by obtaining almost optimal
algorithms for Max-Cut on a wide class of graphs in these models. In
particular, for any , we develop randomized approximation
algorithms achieving a ratio of to the optimum for Max-Cut on
bipartite graphs in the model, and on general graphs in the
model.
We further present efficient deterministic algorithms, including a
-approximation for Max-Dicut in our models, thus improving the best known
(randomized) ratio of . Our algorithms make non-trivial use of the greedy
approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing
an unconstrained (non-monotone) submodular function, which may be of
independent interest
ALMA observations of molecules in Supernova 1987A
Supernova (SN) 1987A has provided a unique opportunity to study how SN ejecta evolve in 30 years time scale. We report our ALMA spectral observations of SN 1987A, taken in 2014, 2015 and 2016, with detections of CO, 28SiO, HCO+ and SO, with weaker lines of 29SiO.
We find a dip in the SiO line profiles, suggesting that the ejecta morphology is likely elongated. The difference of the CO and SiO line profiles is consistent with hydrodynamic simulations, which show that Rayleigh-Taylor instabilities causes mixing of gas, with heavier elements much more disturbed, making more elongated structure.
Using 28SiO and its isotopologues, Si isotope ratios were estimated for the first time in SN 1987A. The estimated ratios appear to be consistent with theoretical predictions of inefficient formation of neutron rich atoms at lower metallicity, such as observed in the Large Magellanic Cloud (about half a solar metallicity).
The deduced large HCO+ mass and small SiS mass, which are inconsistent to the predictions of chemical model, might be explained by some mixing of elements immediately after the explosion. The mixing might have made some hydrogen from the envelope to sink into carbon and oxygen-rich zone during early days after the explosion, enabling the formation of a substantial mass of HCO+. Oxygen atoms may penetrate into silicon and sulphur zone, suppressing formation of SiS.
Our ALMA observations open up a new window to investigate chemistry, dynamics and explosive-nucleosynthesis in supernovae
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