364 research outputs found
Lower Bounds for Oblivious Near-Neighbor Search
We prove an lower bound on the dynamic
cell-probe complexity of statistically
approximate-near-neighbor search () over the -dimensional
Hamming cube. For the natural setting of , our result
implies an lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
. This is the first super-logarithmic
lower bound for against general (non black-box) data structures.
We also show that any oblivious data structure for
decomposable search problems (like ) can be obliviously dynamized
with overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page
Ramsey-type theorems for metric spaces with applications to online problems
A nearly logarithmic lower bound on the randomized competitive ratio for the
metrical task systems problem is presented. This implies a similar lower bound
for the extensively studied k-server problem. The proof is based on Ramsey-type
theorems for metric spaces, that state that every metric space contains a large
subspace which is approximately a hierarchically well-separated tree (and in
particular an ultrametric). These Ramsey-type theorems may be of independent
interest.Comment: Fix an error in the metadata. 31 pages, 0 figures. Preliminary
version in FOCS '01. To be published in J. Comput. System Sc
The achievable region method in the optimal control of queueing systems : formulations, bounds and policies
Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas
The achievable region method in the optimal control of queueing systems : formulations, bounds and policies
Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas
On metric Ramsey-type phenomena
The main question studied in this article may be viewed as a nonlinear
analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey
theory in combinatorics. Given a finite metric space on n points, we seek its
subspace of largest cardinality which can be embedded with a given distortion
in Hilbert space. We provide nearly tight upper and lower bounds on the
cardinality of this subspace in terms of n and the desired distortion. Our main
theorem states that for any epsilon>0, every n point metric space contains a
subset of size at least n^{1-\epsilon} which is embeddable in Hilbert space
with O(\frac{\log(1/\epsilon)}{\epsilon}) distortion. The bound on the
distortion is tight up to the log(1/\epsilon) factor. We further include a
comprehensive study of various other aspects of this problem.Comment: 67 pages, published versio
The Predicted-Deletion Dynamic Model: Taking Advantage of ML Predictions, for Free
The main bottleneck in designing efficient dynamic algorithms is the unknown
nature of the update sequence. In particular, there are some problems, like
3-vertex connectivity, planar digraph all pairs shortest paths, and others,
where the separation in runtime between the best partially dynamic solutions
and the best fully dynamic solutions is polynomial, sometimes even exponential.
In this paper, we formulate the predicted-deletion dynamic model, motivated
by a recent line of empirical work about predicting edge updates in dynamic
graphs. In this model, edges are inserted and deleted online, and when an edge
is inserted, it is accompanied by a "prediction" of its deletion time. This
models real world settings where services may have access to historical data or
other information about an input and can subsequently use such information make
predictions about user behavior. The model is also of theoretical interest, as
it interpolates between the partially dynamic and fully dynamic settings, and
provides a natural extension of the algorithms with predictions paradigm to the
dynamic setting.
We give a novel framework for this model that "lifts" partially dynamic
algorithms into the fully dynamic setting with little overhead. We use our
framework to obtain improved efficiency bounds over the state-of-the-art
dynamic algorithms for a variety of problems. In particular, we design
algorithms that have amortized update time that scales with a partially dynamic
algorithm, with high probability, when the predictions are of high quality. On
the flip side, our algorithms do no worse than existing fully-dynamic
algorithms when the predictions are of low quality. Furthermore, our algorithms
exhibit a graceful trade-off between the two cases. Thus, we are able to take
advantage of ML predictions asymptotically "for free.'
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