78,833 research outputs found
On Searching a Table Consistent with Division Poset
Suppose is a partially ordered set with the partial order
defined by divisibility, that is, for any two distinct elements
satisfying divides , . A table of
distinct real numbers is said to be \emph{consistent} with , provided for
any two distinct elements satisfying divides ,
. Given an real number , we want to determine whether ,
by comparing with as few entries of as possible. In this paper we
investigate the complexity , measured in the number of comparisons, of
the above search problem. We present a search
algorithm for and prove a lower bound on
by using an adversary argument.Comment: 16 pages, no figure; same results, representation improved, add
reference
A trivariate interpolation algorithm using a cube-partition searching procedure
In this paper we propose a fast algorithm for trivariate interpolation, which
is based on the partition of unity method for constructing a global interpolant
by blending local radial basis function interpolants and using locally
supported weight functions. The partition of unity algorithm is efficiently
implemented and optimized by connecting the method with an effective
cube-partition searching procedure. More precisely, we construct a cube
structure, which partitions the domain and strictly depends on the size of its
subdomains, so that the new searching procedure and, accordingly, the resulting
algorithm enable us to efficiently deal with a large number of nodes.
Complexity analysis and numerical experiments show high efficiency and accuracy
of the proposed interpolation algorithm
A proposal for founding mistrustful quantum cryptography on coin tossing
A significant branch of classical cryptography deals with the problems which
arise when mistrustful parties need to generate, process or exchange
information. As Kilian showed a while ago, mistrustful classical cryptography
can be founded on a single protocol, oblivious transfer, from which general
secure multi-party computations can be built.
The scope of mistrustful quantum cryptography is limited by no-go theorems,
which rule out, inter alia, unconditionally secure quantum protocols for
oblivious transfer or general secure two-party computations. These theorems
apply even to protocols which take relativistic signalling constraints into
account. The best that can be hoped for, in general, are quantum protocols
computationally secure against quantum attack. I describe here a method for
building a classically certified bit commitment, and hence every other
mistrustful cryptographic task, from a secure coin tossing protocol. No
security proof is attempted, but I sketch reasons why these protocols might
resist quantum computational attack.Comment: Title altered in deference to Physical Review's fear of question
marks. Published version; references update
Antimatroids and Balanced Pairs
We generalize the 1/3-2/3 conjecture from partially ordered sets to
antimatroids: we conjecture that any antimatroid has a pair of elements x,y
such that x has probability between 1/3 and 2/3 of appearing earlier than y in
a uniformly random basic word of the antimatroid. We prove the conjecture for
antimatroids of convex dimension two (the antimatroid-theoretic analogue of
partial orders of width two), for antimatroids of height two, for antimatroids
with an independent element, and for the perfect elimination antimatroids and
node search antimatroids of several classes of graphs. A computer search shows
that the conjecture is true for all antimatroids with at most six elements.Comment: 16 pages, 5 figure
Improving 6D Pose Estimation of Objects in Clutter via Physics-aware Monte Carlo Tree Search
This work proposes a process for efficiently searching over combinations of
individual object 6D pose hypotheses in cluttered scenes, especially in cases
involving occlusions and objects resting on each other. The initial set of
candidate object poses is generated from state-of-the-art object detection and
global point cloud registration techniques. The best-scored pose per object by
using these techniques may not be accurate due to overlaps and occlusions.
Nevertheless, experimental indications provided in this work show that object
poses with lower ranks may be closer to the real poses than ones with high
ranks according to registration techniques. This motivates a global
optimization process for improving these poses by taking into account
scene-level physical interactions between objects. It also implies that the
Cartesian product of candidate poses for interacting objects must be searched
so as to identify the best scene-level hypothesis. To perform the search
efficiently, the candidate poses for each object are clustered so as to reduce
their number but still keep a sufficient diversity. Then, searching over the
combinations of candidate object poses is performed through a Monte Carlo Tree
Search (MCTS) process that uses the similarity between the observed depth image
of the scene and a rendering of the scene given the hypothesized pose as a
score that guides the search procedure. MCTS handles in a principled way the
tradeoff between fine-tuning the most promising poses and exploring new ones,
by using the Upper Confidence Bound (UCB) technique. Experimental results
indicate that this process is able to quickly identify in cluttered scenes
physically-consistent object poses that are significantly closer to ground
truth compared to poses found by point cloud registration methods.Comment: 8 pages, 4 figure
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