23,091 research outputs found
Bounding right-arm rotation distances
Rotation distance measures the difference in shape between binary trees of
the same size by counting the minimum number of rotations needed to transform
one tree to the other. We describe several types of rotation distance where
restrictions are put on the locations where rotations are permitted, and
provide upper bounds on distances between trees with a fixed number of nodes
with respect to several families of these restrictions. These bounds are sharp
in a certain asymptotic sense and are obtained by relating each restricted
rotation distance to the word length of elements of Thompson's group F with
respect to different generating sets, including both finite and infinite
generating sets.Comment: 30 pages, 11 figures. This revised version corrects some typos and
has some clearer proofs of the results for the lower bounds and better
figure
On Rotation Distance of Rank Bounded Trees
Computing the rotation distance between two binary trees with internal
nodes efficiently (in time) is a long standing open question in the
study of height balancing in tree data structures. In this paper, we initiate
the study of this problem bounding the rank of the trees given at the input
(defined by Ehrenfeucht and Haussler (1989) in the context of decision trees).
We define the rank-bounded rotation distance between two given binary trees
and (with internal nodes) of rank at most , denoted by
, as the length of the shortest sequence of rotations that
transforms to with the restriction that the intermediate trees must
be of rank at most . We show that the rotation distance problem reduces in
polynomial time to the rank bounded rotation distance problem. This motivates
the study of the problem in the combinatorial and algorithmic frontiers.
Observing that trees with rank coincide exactly with skew trees (binary
trees where every internal node has at least one leaf as a child), we show the
following results in this frontier :
We present an time algorithm for computing . That is,
when the given trees are skew trees (we call this variant as skew rotation
distance problem) - where the intermediate trees are restricted to be skew as
well. In particular, our techniques imply that for any two skew trees
.
We show the following upper bound : for any two trees and of rank
at most and respectively, we have that: where . This bound is asymptotically
tight for .
En route our proof of the above theorems, we associate binary trees to
permutations and bivariate polynomials, and prove several characterizations in
the case of skew trees.Comment: 25 pages, 2 figures, Abstract shortened to meet arxiv requirement
Robust Procedures for Obtaining Assembly Contact State Extremal Configurations
Two important components in the selection of an admittance that facilitates force-guided assembly are the identification of: 1) the set of feasible contact states, and 2) the set of configurations that span each contact state, i.e., the extremal configurations. We present a procedure to automatically generate both sets from CAD models of the assembly parts. In the procedure, all possible combinations of principle contacts are considered when generating hypothesized contact states. The feasibility of each is then evaluated in a genetic algorithm based optimization procedure. The maximum and minimum value of each of the 6 configuration variables spanning each contact state are obtained by again using genetic algorithms. Together, the genetic algorithm approach, the hierarchical data structure containing the states, the relationships among the states, and the extremals within each state are used to provide a reliable means of identifying all feasible contact states and their associated extremal configurations
Factoring Shape, Pose, and Layout from the 2D Image of a 3D Scene
The goal of this paper is to take a single 2D image of a scene and recover
the 3D structure in terms of a small set of factors: a layout representing the
enclosing surfaces as well as a set of objects represented in terms of shape
and pose. We propose a convolutional neural network-based approach to predict
this representation and benchmark it on a large dataset of indoor scenes. Our
experiments evaluate a number of practical design questions, demonstrate that
we can infer this representation, and quantitatively and qualitatively
demonstrate its merits compared to alternate representations.Comment: Project url with code: https://shubhtuls.github.io/factored3
Rigid motion revisited: rigid quasilocal frames
We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically
natural way to define a "system" in general relativity. An RQF is defined as a
two-parameter family of timelike worldlines comprising the worldtube boundary
of the history of a finite spatial volume, with the rigidity conditions that
the congruence of worldlines is expansion-free (constant size) and shear-free
(constant shape). This definition of a system is anticipated to yield simple,
exact geometrical insights into the problem of motion in general relativity. It
begins by answering the questions what is in motion (a rigid two-dimensional
system boundary), and what motions of this rigid boundary are possible. Nearly
a century ago Herglotz and Noether showed that a three-parameter family of
timelike worldlines in Minkowski space satisfying Born's 1909 rigidity
conditions has only three degrees of freedom instead of the six we are familiar
with from Newtonian mechanics. We argue that in fact we can implement Born's
notion of rigid motion in both flat spacetime (this paper) and arbitrary curved
spacetimes containing sources (subsequent papers) - with precisely the expected
three translational and three rotational degrees of freedom - provided the
system is defined quasilocally as the two-dimensional set of points comprising
the boundary of a finite spatial volume, rather than the three-dimensional set
of points within the volume.Comment: 10 pages (two column), 24 pages (preprint), 1 figur
Novel CMOS RFIC Layout Generation with Concurrent Device Placement and Fixed-Length Microstrip Routing
With advancing process technologies and booming IoT markets, millimeter-wave
CMOS RFICs have been widely developed in re- cent years. Since the performance
of CMOS RFICs is very sensi- tive to the precision of the layout, precise
placement of devices and precisely matched microstrip lengths to given values
have been a labor-intensive and time-consuming task, and thus become a major
bottleneck for time to market. This paper introduces a progressive
integer-linear-programming-based method to gener- ate high-quality RFIC layouts
satisfying very stringent routing requirements of microstrip lines, including
spacing/non-crossing rules, precise length, and bend number minimization,
within a given layout area. The resulting RFIC layouts excel in both per-
formance and area with much fewer bends compared with the simulation-tuning
based manual layout, while the layout gener- ation time is significantly
reduced from weeks to half an hour.Comment: ACM/IEEE Design Automation Conference (DAC), 201
Self-Selective Correlation Ship Tracking Method for Smart Ocean System
In recent years, with the development of the marine industry, navigation
environment becomes more complicated. Some artificial intelligence
technologies, such as computer vision, can recognize, track and count the
sailing ships to ensure the maritime security and facilitates the management
for Smart Ocean System. Aiming at the scaling problem and boundary effect
problem of traditional correlation filtering methods, we propose a
self-selective correlation filtering method based on box regression (BRCF). The
proposed method mainly include: 1) A self-selective model with negative samples
mining method which effectively reduces the boundary effect in strengthening
the classification ability of classifier at the same time; 2) A bounding box
regression method combined with a key points matching method for the scale
prediction, leading to a fast and efficient calculation. The experimental
results show that the proposed method can effectively deal with the problem of
ship size changes and background interference. The success rates and precisions
were higher than Discriminative Scale Space Tracking (DSST) by over 8
percentage points on the marine traffic dataset of our laboratory. In terms of
processing speed, the proposed method is higher than DSST by nearly 22 Frames
Per Second (FPS)
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