2,165 research outputs found
An Algorithmic Study of Manufacturing Paperclips and Other Folded Structures
We study algorithmic aspects of bending wires and sheet metal into a
specified structure. Problems of this type are closely related to the question
of deciding whether a simple non-self-intersecting wire structure (a
carpenter's ruler) can be straightened, a problem that was open for several
years and has only recently been solved in the affirmative.
If we impose some of the constraints that are imposed by the manufacturing
process, we obtain quite different results. In particular, we study the variant
of the carpenter's ruler problem in which there is a restriction that only one
joint can be modified at a time. For a linkage that does not self-intersect or
self-touch, the recent results of Connelly et al. and Streinu imply that it can
always be straightened, modifying one joint at a time. However, we show that
for a linkage with even a single vertex degeneracy, it becomes NP-hard to
decide if it can be straightened while altering only one joint at a time. If we
add the restriction that each joint can be altered at most once, we show that
the problem is NP-complete even without vertex degeneracies.
In the special case, arising in wire forming manufacturing, that each joint
can be altered at most once, and must be done sequentially from one or both
ends of the linkage, we give an efficient algorithm to determine if a linkage
can be straightened.Comment: 28 pages, 14 figures, Latex, to appear in Computational Geometry -
Theory and Application
The Lazy Bureaucrat Scheduling Problem
We introduce a new class of scheduling problems in which the optimization is
performed by the worker (single ``machine'') who performs the tasks. A typical
worker's objective is to minimize the amount of work he does (he is ``lazy''),
or more generally, to schedule as inefficiently (in some sense) as possible.
The worker is subject to the constraint that he must be busy when there is work
that he can do; we make this notion precise both in the preemptive and
nonpreemptive settings. The resulting class of ``perverse'' scheduling
problems, which we denote ``Lazy Bureaucrat Problems,'' gives rise to a rich
set of new questions that explore the distinction between maximization and
minimization in computing optimal schedules.Comment: 19 pages, 2 figures, Latex. To appear, Information and Computatio
Probabilistic Bounds on the Length of a Longest Edge in Delaunay Graphs of Random Points in d-Dimensions
Motivated by low energy consumption in geographic routing in wireless
networks, there has been recent interest in determining bounds on the length of
edges in the Delaunay graph of randomly distributed points. Asymptotic results
are known for random networks in planar domains. In this paper, we obtain upper
and lower bounds that hold with parametric probability in any dimension, for
points distributed uniformly at random in domains with and without boundary.
The results obtained are asymptotically tight for all relevant values of such
probability and constant number of dimensions, and show that the overhead
produced by boundary nodes in the plane holds also for higher dimensions. To
our knowledge, this is the first comprehensive study on the lengths of long
edges in Delaunay graphsComment: 10 pages. 2 figures. In Proceedings of the 23rd Canadian Conference
on Computational Geometry (CCCG 2011). Replacement of version 1106.4927,
reference [5] adde
RegPrecise web services interface: programmatic access to the transcriptional regulatory interactions in bacteria reconstructed by comparative genomics.
Web services application programming interface (API) was developed to provide a programmatic access to the regulatory interactions accumulated in the RegPrecise database (http://regprecise.lbl.gov), a core resource on transcriptional regulation for the microbial domain of the Department of Energy (DOE) Systems Biology Knowledgebase. RegPrecise captures and visualize regulogs, sets of genes controlled by orthologous regulators in several closely related bacterial genomes, that were reconstructed by comparative genomics. The current release of RegPrecise 2.0 includes >1400 regulogs controlled either by protein transcription factors or by conserved ribonucleic acid regulatory motifs in >250 genomes from 24 taxonomic groups of bacteria. The reference regulons accumulated in RegPrecise can serve as a basis for automatic annotation of regulatory interactions in newly sequenced genomes. The developed API provides an efficient access to the RegPrecise data by a comprehensive set of 14 web service resources. The RegPrecise web services API is freely accessible at http://regprecise.lbl.gov/RegPrecise/services.jsp with no login requirements
Adaptive finite element method assisted by stochastic simulation of chemical systems
Stochastic models of chemical systems are often analysed by solving the corresponding\ud
Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability\ud
distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density
Stochastic Gene Expression in a Lentiviral Positive Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity
Stochastic gene expression has been implicated in a variety of cellular
processes, including cell differentiation and disease. In this issue of Cell,
Weinberger et al. (2005) take an integrated computational-experimental approach
to study the Tat transactivation feedback loop in HIV-1 and show that
fluctuations in a key regulator, Tat, can result in a phenotypic bifurcation.
This phenomenon is observed in an isogenic population where individual cells
display two distinct expression states corresponding to latent and productive
infection by HIV-1. These findings demonstrate the importance of stochastic
gene expression in molecular "decision-making."Comment: Supplemental data available as q-bio.MN/060800
Algorithms for Rapidly Dispersing Robot Swarms in Unknown Environments
We develop and analyze algorithms for dispersing a swarm of primitive robots
in an unknown environment, R. The primary objective is to minimize the
makespan, that is, the time to fill the entire region. An environment is
composed of pixels that form a connected subset of the integer grid.
There is at most one robot per pixel and robots move horizontally or
vertically at unit speed. Robots enter R by means of k>=1 door pixels
Robots are primitive finite automata, only having local communication, local
sensors, and a constant-sized memory.
We first give algorithms for the single-door case (i.e., k=1), analyzing the
algorithms both theoretically and experimentally. We prove that our algorithms
have optimal makespan 2A-1, where A is the area of R.
We next give an algorithm for the multi-door case (k>1), based on a
wall-following version of the leader-follower strategy. We prove that our
strategy is O(log(k+1))-competitive, and that this bound is tight for our
strategy and other related strategies.Comment: 17 pages, 4 figures, Latex, to appear in Workshop on Algorithmic
Foundations of Robotics, 200
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