39,394 research outputs found
Cache-Oblivious Selection in Sorted X+Y Matrices
Let X[0..n-1] and Y[0..m-1] be two sorted arrays, and define the mxn matrix A
by A[j][i]=X[i]+Y[j]. Frederickson and Johnson gave an efficient algorithm for
selecting the k-th smallest element from A. We show how to make this algorithm
IO-efficient. Our cache-oblivious algorithm performs O((m+n)/B) IOs, where B is
the block size of memory transfers
Adaptive neuro-fuzzy technique for autonomous ground vehicle navigation
This article proposes an adaptive neuro-fuzzy inference system (ANFIS) for solving navigation problems of an autonomous ground vehicle (AGV). The system consists of four ANFIS controllers; two of which are used for regulating both the left and right angular velocities of the AGV in order to reach the target position; and other two ANFIS controllers are used for optimal heading adjustment in order to avoid obstacles. The two velocity controllers receive three sensor inputs: front distance (FD); right distance (RD) and left distance (LD) for the low-level motion control. Two heading controllers deploy the angle difference (AD) between the heading of AGV and the angle to the target to choose the optimal direction. The simulation experiments have been carried out under two different scenarios to investigate the feasibility of the proposed ANFIS technique. The simulation results have been presented using MATLAB software package; showing that ANFIS is capable of performing the navigation and path planning task safely and efficiently in a workspace populated with static obstacles
Fat Polygonal Partitions with Applications to Visualization and Embeddings
Let be a rooted and weighted tree, where the weight of any node
is equal to the sum of the weights of its children. The popular Treemap
algorithm visualizes such a tree as a hierarchical partition of a square into
rectangles, where the area of the rectangle corresponding to any node in
is equal to the weight of that node. The aspect ratio of the
rectangles in such a rectangular partition necessarily depends on the weights
and can become arbitrarily high.
We introduce a new hierarchical partition scheme, called a polygonal
partition, which uses convex polygons rather than just rectangles. We present
two methods for constructing polygonal partitions, both having guarantees on
the worst-case aspect ratio of the constructed polygons; in particular, both
methods guarantee a bound on the aspect ratio that is independent of the
weights of the nodes.
We also consider rectangular partitions with slack, where the areas of the
rectangles may differ slightly from the weights of the corresponding nodes. We
show that this makes it possible to obtain partitions with constant aspect
ratio. This result generalizes to hyper-rectangular partitions in
. We use these partitions with slack for embedding ultrametrics
into -dimensional Euclidean space: we give a -approximation algorithm for embedding -point ultrametrics
into with minimum distortion, where denotes the spread
of the metric, i.e., the ratio between the largest and the smallest distance
between two points. The previously best-known approximation ratio for this
problem was polynomial in . This is the first algorithm for embedding a
non-trivial family of weighted-graph metrics into a space of constant dimension
that achieves polylogarithmic approximation ratio.Comment: 26 page
Models of Non-Well-Founded Sets via an Indexed Final Coalgebra Theorem
The paper uses the formalism of indexed categories to recover the proof of a
standard final coalgebra theorem, thus showing existence of final coalgebras
for a special class of functors on categories with finite limits and colimits.
As an instance of this result, we build the final coalgebra for the powerclass
functor, in the context of a Heyting pretopos with a class of small maps. This
is then proved to provide a model for various non-well-founded set theories,
depending on the chosen axiomatisation for the class of small maps
Can we always sweep the details of RNA-processing under the carpet?
RNA molecules follow a succession of enzyme-mediated processing steps from
transcription until maturation. The participating enzymes, for example the
spliceosome for mRNAs and Drosha and Dicer for microRNAs, are also produced in
the cell and their copy-numbers fluctuate over time. Enzyme copy-number changes
affect the processing rate of the substrate molecules; high enzyme numbers
increase the processing probability, low enzyme numbers decrease it. We study
different RNA processing cascades where enzyme copy-numbers are either fixed or
fluctuate. We find that for fixed enzyme-copy numbers the substrates at
steady-state are Poisson-distributed, and the whole RNA cascade dynamics can be
understood as a single birth-death process of the mature RNA product. In this
case, solely fluctuations in the timing of RNA processing lead to variation in
the number of RNA molecules. However, we show analytically and numerically that
when enzyme copy-numbers fluctuate, the strength of RNA fluctuations increases
linearly with the RNA transcription rate. This linear effect becomes stronger
as the speed of enzyme dynamics decreases relative to the speed of RNA
dynamics. Interestingly, we find that under certain conditions, the RNA cascade
can reduce the strength of fluctuations in the expression level of the mature
RNA product. Finally, by investigating the effects of processing polymorphisms
we show that it is possible for the effects of transcriptional polymorphisms to
be enhanced, reduced, or even reversed. Our results provide a framework to
understand the dynamics of RNA processing
Using Entropy-Based Methods to Study General Constrained Parameter Optimization Problems
In this letter we propose the use of physics techniques for entropy
determination on constrained parameter optimization problems. The main feature
of such techniques, the construction of an unbiased walk on energy space,
suggests their use on the quest for optimal solutions of an optimization
problem. Moreover, the entropy, and its associated density of states, give us
information concerning the feasibility of solutions.Comment: 10 pages, 3 figures, references correcte
Snapping Graph Drawings to the Grid Optimally
In geographic information systems and in the production of digital maps for
small devices with restricted computational resources one often wants to round
coordinates to a rougher grid. This removes unnecessary detail and reduces
space consumption as well as computation time. This process is called snapping
to the grid and has been investigated thoroughly from a computational-geometry
perspective. In this paper we investigate the same problem for given drawings
of planar graphs under the restriction that their combinatorial embedding must
be kept and edges are drawn straight-line. We show that the problem is NP-hard
for several objectives and provide an integer linear programming formulation.
Given a plane graph G and a positive integer w, our ILP can also be used to
draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
The Homogeneous Broadcast Problem in Narrow and Wide Strips
Let be a set of nodes in a wireless network, where each node is modeled
as a point in the plane, and let be a given source node. Each node
can transmit information to all other nodes within unit distance, provided
is activated. The (homogeneous) broadcast problem is to activate a minimum
number of nodes such that in the resulting directed communication graph, the
source can reach any other node. We study the complexity of the regular and
the hop-bounded version of the problem (in the latter, must be able to
reach every node within a specified number of hops), with the restriction that
all points lie inside a strip of width . We almost completely characterize
the complexity of both the regular and the hop-bounded versions as a function
of the strip width .Comment: 50 pages, WADS 2017 submissio
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