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