537,938 research outputs found
Approximation algorithms for stochastic clustering
We consider stochastic settings for clustering, and develop provably-good
approximation algorithms for a number of these notions. These algorithms yield
better approximation ratios compared to the usual deterministic clustering
setting. Additionally, they offer a number of advantages including clustering
which is fairer and has better long-term behavior for each user. In particular,
they ensure that *every user* is guaranteed to get good service (on average).
We also complement some of these with impossibility results
Multi-level stochastic approximation algorithms
This paper studies multi-level stochastic approximation algorithms. Our aim
is to extend the scope of the multilevel Monte Carlo method recently introduced
by Giles (Giles 2008) to the framework of stochastic optimization by means of
stochastic approximation algorithm. We first introduce and study a two-level
method, also referred as statistical Romberg stochastic approximation
algorithm. Then, its extension to multi-level is proposed. We prove a central
limit theorem for both methods and describe the possible optimal choices of
step size sequence. Numerical results confirm the theoretical analysis and show
a significant reduction in the initial computational cost.Comment: 44 pages, 9 figure
Approximation algorithms for stochastic and risk-averse optimization
We present improved approximation algorithms in stochastic optimization. We
prove that the multi-stage stochastic versions of covering integer programs
(such as set cover and vertex cover) admit essentially the same approximation
algorithms as their standard (non-stochastic) counterparts; this improves upon
work of Swamy \& Shmoys which shows an approximability that depends
multiplicatively on the number of stages. We also present approximation
algorithms for facility location and some of its variants in the -stage
recourse model, improving on previous approximation guarantees. We give a
-approximation algorithm in the standard polynomial-scenario model and
an algorithm with an expected per-scenario -approximation guarantee,
which is applicable to the more general black-box distribution model.Comment: Extension of a SODA'07 paper. To appear in SIAM J. Discrete Mat
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