11,881 research outputs found
Lower Bounds for On-Line Two-Dimensional Packing Algorithms
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAG-29-78-C-001
Lower bounds for several online variants of bin packing
We consider several previously studied online variants of bin packing and
prove new and improved lower bounds on the asymptotic competitive ratios for
them. For that, we use a method of fully adaptive constructions. In particular,
we improve the lower bound for the asymptotic competitive ratio of online
square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201
Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization via Information Theory
We present an information-theoretic approach to lower bound the oracle
complexity of nonsmooth black box convex optimization, unifying previous lower
bounding techniques by identifying a combinatorial problem, namely string
guessing, as a single source of hardness. As a measure of complexity we use
distributional oracle complexity, which subsumes randomized oracle complexity
as well as worst-case oracle complexity. We obtain strong lower bounds on
distributional oracle complexity for the box , as well as for the
-ball for (for both low-scale and large-scale regimes),
matching worst-case upper bounds, and hence we close the gap between
distributional complexity, and in particular, randomized complexity, and
worst-case complexity. Furthermore, the bounds remain essentially the same for
high-probability and bounded-error oracle complexity, and even for combination
of the two, i.e., bounded-error high-probability oracle complexity. This
considerably extends the applicability of known bounds
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