306 research outputs found
Skyline Identification in Multi-Armed Bandits
We introduce a variant of the classical PAC multi-armed bandit problem. There
is an ordered set of arms , each with some stochastic
reward drawn from some unknown bounded distribution. The goal is to identify
the of the set , consisting of all arms such that
has larger expected reward than all lower-numbered arms . We
define a natural notion of an -approximate skyline and prove
matching upper and lower bounds for identifying an -skyline.
Specifically, we show that in order to identify an -skyline from
among arms with probability , samples are necessary and sufficient. When , our results improve over the naive algorithm, which draws enough samples
to approximate the expected reward of every arm; the algorithm of (Auer et al.,
AISTATS'16) for Pareto-optimal arm identification is likewise superseded. Our
results show that the sample complexity of the skyline problem lies strictly in
between that of best arm identification (Even-Dar et al., COLT'02) and that of
approximating the expected reward of every arm.Comment: 18 pages, 2 Figures; an ALT'18/ISIT'18 submissio
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
Spanning trees short or small
We study the problem of finding small trees. Classical network design
problems are considered with the additional constraint that only a specified
number of nodes are required to be connected in the solution. A
prototypical example is the MST problem in which we require a tree of
minimum weight spanning at least nodes in an edge-weighted graph. We show
that the MST problem is NP-hard even for points in the Euclidean plane. We
provide approximation algorithms with performance ratio for the
general edge-weighted case and for the case of points in the
plane. Polynomial-time exact solutions are also presented for the class of
decomposable graphs which includes trees, series-parallel graphs, and bounded
bandwidth graphs, and for points on the boundary of a convex region in the
Euclidean plane. We also investigate the problem of finding short trees, and
more generally, that of finding networks with minimum diameter. A simple
technique is used to provide a polynomial-time solution for finding -trees
of minimum diameter. We identify easy and hard problems arising in finding
short networks using a framework due to T. C. Hu.Comment: 27 page
The essential oil constituents of Artabotrys species – A review
Artabotrys species which belongs to Annonaceae family are pleasant smelling and it is attributed to the presence of mono and sesquiterpenoids present in the essential oil of the plant. The objective of the present work is to review the chemical composition of the essential oils reported from twenty different Artabotrys species from various parts of the world. In the various Artabotrys species, the major compounds are monoterpene and sesquiterpene hydrocarbons and oxygenated sesquiterpenes. The frequently and most commonly identified constituents are β-caryophyllene, caryophyllene oxide, 3-Carene, cyperene, cyperenone and 1,5-epoxy-salvial4(14)-ene. Other constituents seems to be more specific to the respective Artabotrys species
Behavior of Dune Sands of the Thar Desert Under Dynamic Loading
Forced vibration test were conducted on concrete blocks for a power project in north-western Rajasthan (India). The site is in the Thar desert and has meta-stable aeolian sand deposits. At shallow depth, the amplitude versus frequency curves shows two peaks, suggesting that the soil structure was probably collapsing and settling under the dynamic load. Tests conducted on the deeper, relatively more stable soils confirm a good response to dynamic loads. The instability under static loading conditions is also highlighted and correlated to the dune morphology
Designing Overlapping Networks for Publish-Subscribe Systems
From the publish-subscribe systems of the early days of the Internet to the recent emergence of Web 3.0 and IoT (Internet of Things), new problems arise in the design of networks centered at producers and consumers of constantly evolving information. In a typical problem, each terminal is a source or sink of information and builds a physical network in the form of a tree or an overlay network in the form of a star rooted at itself. Every pair of pub-sub terminals that need to be coordinated (e.g. the source and sink of an important piece of control information) define an edge in a bipartite demand graph; the solution must ensure that the corresponding networks rooted at the endpoints of each demand edge overlap at some node. This simple overlap constraint, and the requirement that each network is a tree or a star, leads to a variety of new questions on the design of overlapping networks.
In this paper, for the general demand case of the problem, we show that a natural LP formulation has a non-constant integrality gap; on the positive side, we present a logarithmic approximation for the general demand case. When the demand graph is complete, however, we design approximation algorithms with small constant performance ratios, irrespective of whether the pub networks and sub networks are required to be trees or stars
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