180 research outputs found
Conditional Lower Bounds for Space/Time Tradeoffs
In recent years much effort has been concentrated towards achieving
polynomial time lower bounds on algorithms for solving various well-known
problems. A useful technique for showing such lower bounds is to prove them
conditionally based on well-studied hardness assumptions such as 3SUM, APSP,
SETH, etc. This line of research helps to obtain a better understanding of the
complexity inside P.
A related question asks to prove conditional space lower bounds on data
structures that are constructed to solve certain algorithmic tasks after an
initial preprocessing stage. This question received little attention in
previous research even though it has potential strong impact.
In this paper we address this question and show that surprisingly many of the
well-studied hard problems that are known to have conditional polynomial time
lower bounds are also hard when concerning space. This hardness is shown as a
tradeoff between the space consumed by the data structure and the time needed
to answer queries. The tradeoff may be either smooth or admit one or more
singularity points.
We reveal interesting connections between different space hardness
conjectures and present matching upper bounds. We also apply these hardness
conjectures to both static and dynamic problems and prove their conditional
space hardness.
We believe that this novel framework of polynomial space conjectures can play
an important role in expressing polynomial space lower bounds of many important
algorithmic problems. Moreover, it seems that it can also help in achieving a
better understanding of the hardness of their corresponding problems in terms
of time
Modeling and simulating the stick-slip motion of the μWalker, a MEMS-based device for μSPAM
In this paper, the accent is on modeling the stick–slip phenomenon of micro devices, where a case shall be presented from the field of scanning probe microactuators. The case is about the lWalker, an electrostatic stepper motor which can deliver forces up to 1.7 mN and has ranges up to 140 lm. For the sake of a reliable operation, it is very important to control the stick–slip effects at the sliding surfaces. In order to introduce the stick–slip effect, a basic model of a mass, spring and sliding surface is presented, accompanied by simulation results. The total model of the device is then shown, again stressing the stick–slip phenomenon at the two sliding surfaces. Simulations from the model presented fit the measurements and can also predict step sizes as a function of varying inputs. Using a model for predictions is very attractive when looking for a way to decrease development cost and time
Stick-slip actuation of electrostatic stepper micropositioners for data storage-the µWalker
This paper is about the /spl mu/Walker, an electrostatic stepper motor mainly intended for positioning the data probes with respect to the storage medium in a data storage device. It can deliver forces up to 1.7 mN for ranges as large as 140 /spl mu/m. Controlling the stick-slip effects at the sliding surfaces is of central importance for reliable operation. A model is introduced to estimate the operating voltage of the actuator plate, which is an essential part of the /spl mu/Walker. Several methods to obtain displacements smaller than one nominal step (/spl ap/ 50 nm) are discussed, as well as how to increase the step repeatability and accuracy
Dynamic Connectivity: Connecting to Networks and Geometry
Dynamic connectivity is a well-studied problem, but so far the most
compelling progress has been confined to the edge-update model: maintain an
understanding of connectivity in an undirected graph, subject to edge
insertions and deletions. In this paper, we study two more challenging, yet
equally fundamental problems.
Subgraph connectivity asks to maintain an understanding of connectivity under
vertex updates: updates can turn vertices on and off, and queries refer to the
subgraph induced by "on" vertices. (For instance, this is closer to
applications in networks of routers, where node faults may occur.)
We describe a data structure supporting vertex updates in O (m^{2/3})
amortized time, where m denotes the number of edges in the graph. This greatly
improves over the previous result [Chan, STOC'02], which required fast matrix
multiplication and had an update time of O(m^0.94). The new data structure is
also simpler.
Geometric connectivity asks to maintain a dynamic set of n geometric objects,
and query connectivity in their intersection graph. (For instance, the
intersection graph of balls describes connectivity in a network of sensors with
bounded transmission radius.)
Previously, nontrivial fully dynamic results were known only for special
cases like axis-parallel line segments and rectangles. We provide similarly
improved update times, O (n^{2/3}), for these special cases. Moreover, we show
how to obtain sublinear update bounds for virtually all families of geometric
objects which allow sublinear-time range queries, such as arbitrary 2D line
segments, d-dimensional simplices, and d-dimensional balls.Comment: Full version of a paper to appear in FOCS 200
Succinct Partial Sums and Fenwick Trees
We consider the well-studied partial sums problem in succint space where one
is to maintain an array of n k-bit integers subject to updates such that
partial sums queries can be efficiently answered. We present two succint
versions of the Fenwick Tree - which is known for its simplicity and
practicality. Our results hold in the encoding model where one is allowed to
reuse the space from the input data. Our main result is the first that only
requires nk + o(n) bits of space while still supporting sum/update in O(log_b
n) / O(b log_b n) time where 2 <= b <= log^O(1) n. The second result shows how
optimal time for sum/update can be achieved while only slightly increasing the
space usage to nk + o(nk) bits. Beyond Fenwick Trees, the results are primarily
based on bit-packing and sampling - making them very practical - and they also
allow for simple optimal parallelization
Oscillator-Based Volatile Detection System Using Doubly- Clamped Micromechanical Resonators
AbstractIn this paper, we demonstrate a functionalized and resonant piezo-actuated volatile sensor which is interfaced by electronics for frequency shift detection. Enhanced signal sensing is achieved via the effective feed-through capacitance cancellation scheme. The closed-loop oscillator, realized with off-the-shelf components, attains a frequency stability of 2.7Hz for the 1.8MHz resonant mode of the gas sensor. The sensor was exposed to pulses of water and ethanol vapor mixtures, yielding a temporary dip in resonance frequency as well as volatile-specific recovery times
Nanometer range closed-loop control of a stepper micro-motor for data storage
We present a nanometer range, closed-loop control study for MEMS stepper actuators. Although generically applicable to other types of stepper motors, the control design presented here was particularly intended for one dimensional shuffle actuators fabricated by surface micromachining technology. The stepper actuator features 50 nm or smaller step sizes. It can deliver forces up to 5 mN (measured) and has a typical range of about 20 μm. The target application is probe storage, where positioning accuracies of about 10 nm are required. The presence of inherent actuator stiction, load disturbances, and other effects make physical modeling and control studies necessary. Performed experiments include measurements with openand closed-loop control, where a positioning accuracy in the order of tens of nm or better is obtained from image data of a conventional fire-wire camera at 30 fps
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