2,872 research outputs found
Secondary Indexing in One Dimension: Beyond B-trees and Bitmap Indexes
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string
over S. A "secondary index" for x answers alphabet range queries of the form:
Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in
[a_l; a_r]}. Secondary indexes are heavily used in relational databases and
scientific data analysis. It is well-known that the obvious solution, storing a
dictionary for the position set associated with each character, does not always
give optimal query time. In this paper we give the first theoretically optimal
data structure for the secondary indexing problem. In the I/O model, the amount
of data read when answering a query is within a constant factor of the minimum
space needed to represent I_{[a_l;a_r]}, assuming that the size of internal
memory is (|S| log n)^{delta} blocks, for some constant delta > 0. The space
usage of the data structure is O(n log |S|) bits in the worst case, and we
further show how to bound the size of the data structure in terms of the 0-th
order entropy of x. We show how to support updates achieving various time-space
trade-offs.
We also consider an approximate version of the basic secondary indexing
problem where a query reports a superset of I_{[a_l;a_r]} containing each
element not in I_{[a_l;a_r]} with probability at most epsilon, where epsilon >
0 is the false positive probability. For this problem the amount of data that
needs to be read by the query algorithm is reduced to O(|I_{[a_l;a_r]}|
log(1/epsilon)) bits.Comment: 16 page
A Partition Theorem for a Randomly Selected Large Population
We state and prove a proposition on partitioning of a randomly selected large
population into stationary and non-stationary populations by using a property
of stationary population identity. Applicability of this theorem for practical
purposes is summarized at the end.Comment: 7 pages, a new result in population dynamic
Shared Autonomy via Hindsight Optimization
In shared autonomy, user input and robot autonomy are combined to control a
robot to achieve a goal. Often, the robot does not know a priori which goal the
user wants to achieve, and must both predict the user's intended goal, and
assist in achieving that goal. We formulate the problem of shared autonomy as a
Partially Observable Markov Decision Process with uncertainty over the user's
goal. We utilize maximum entropy inverse optimal control to estimate a
distribution over the user's goal based on the history of inputs. Ideally, the
robot assists the user by solving for an action which minimizes the expected
cost-to-go for the (unknown) goal. As solving the POMDP to select the optimal
action is intractable, we use hindsight optimization to approximate the
solution. In a user study, we compare our method to a standard
predict-then-blend approach. We find that our method enables users to
accomplish tasks more quickly while utilizing less input. However, when asked
to rate each system, users were mixed in their assessment, citing a tradeoff
between maintaining control authority and accomplishing tasks quickly
Compressing Binary Decision Diagrams
The paper introduces a new technique for compressing Binary Decision Diagrams
in those cases where random access is not required. Using this technique,
compression and decompression can be done in linear time in the size of the BDD
and compression will in many cases reduce the size of the BDD to 1-2 bits per
node. Empirical results for our compression technique are presented, including
comparisons with previously introduced techniques, showing that the new
technique dominate on all tested instances.Comment: Full (tech-report) version of ECAI 2008 short pape
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