Super-linear time-space tradeoff lower bounds for randomized computation

2002 ◽  
Author(s):  
P. Beame ◽  
M. Saks ◽  
Xiaodong Sun ◽  
E. Vee
Keyword(s):  
Lower Bounds ◽  
Linear Time ◽  
Time Space ◽  
Randomized Computation

Time-space trade-off lower bounds for randomized computation of decision problems

2003 ◽  
Vol 50 (2) ◽  
pp. 154-195 ◽  
Author(s):  
Paul Beame ◽  
Michael Saks ◽  
Xiaodong Sun ◽  
Erik Vee
Keyword(s):  
Lower Bounds ◽  
Decision Problems ◽  
Trade Off ◽  
Time Space ◽  
Randomized Computation

The Principle and Structure of Novel High-Precision Linear Time Grating Displacement Sensors

2012 ◽  
Vol 236-237 ◽  
pp. 1216-1221
Author(s):  
Dong Lin Peng ◽  
Ji Sen Yang ◽  
Xi Hou Chen ◽  
Zi Ran Chen
Keyword(s):  
Linear Time ◽  
Theoretical Concept ◽  
Electrical Machine ◽  
Displacement Sensors ◽  
Time Space ◽  
Optical Grating ◽  
Testing Technology ◽  
Measurement And Testing ◽  
Space Coordinate ◽  
Physical And Mathematical Models

The existing grating type sensors such as optical grating sensor, have long been designed to rely on the precise mechanical space division technology, which is hard to develop without heavy investment. A theoretical concept, time-space coordinate transformation, was presented to realize measuring spatial displacement with time difference. Similar to the principle of circular time grating based on rotating electrical machine, linear time grating is designed based on the principle of linear motor, with which the physical and mathematical models of linear time grating are established. Based on these models linear time grating mechanical structure is designed, which has commercialization value. The resolution of linear time grating can achieve 0.1μm tested by National Institute of Measurement and Testing Technology.

Limits on Alternation Trading Proofs for Time–Space Lower Bounds

2015 ◽  
Vol 24 (3) ◽  
pp. 533-600 ◽  
Author(s):  
Samuel R. Buss ◽  
Ryan Williams
Keyword(s):  
Lower Bounds ◽  
Time Space

scholarly journals Time-space lower bounds for satisfiability

2005 ◽  
Vol 52 (6) ◽  
pp. 835-865 ◽  
Author(s):  
Lance Fortnow ◽  
Richard Lipton ◽  
Dieter van Melkebeek ◽  
Anastasios Viglas
Keyword(s):  
Lower Bounds ◽  
Time Space

scholarly journals On Ajtai’s Lower Bound Technique for R-way Branching Programs and the Hamming Distance Problem

2000 ◽  
Vol 7 (11) ◽  
Author(s):  
Jakob Pagter
Keyword(s):  
Lower Bound ◽  
Hamming Distance ◽  
Linear Time ◽  
Program Model ◽  
Branching Programs ◽  
Original Proof ◽  
Trade Off ◽  
Time Space ◽  
Distance Problem ◽  
With Memory

In this report we study the proof employed by Miklos Ajtai<br />[Determinism versus Non-Determinism for Linear Time RAMs<br />with Memory Restrictions, 31st Symposium on Theory of <br />Computation (STOC), 1999] when proving a non-trivial lower bound<br />in a general model of computation for the Hamming Distance<br />problem: given n elements: decide whether any two of them have<br />"small" Hamming distance. Specifically, Ajtai was able to show<br />that any R-way branching program deciding this problem using<br />time O(n) must use space Omega(n lg n).<br />We generalize Ajtai's original proof allowing us to prove a<br />time-space trade-off for deciding the Hamming Distance problem<br /> in the R-way branching program model for time between n<br />and alpha n lg n / lg lg n, for some suitable 0 < alpha < 1. In particular we prove<br />that if space is O(n^(1−epsilon)), then time is Omega(n lg n / lg lg n).

scholarly journals Place, Non-Place, Multi-Place and the (Non)Possibilities of Identity: Philosophical, Social, and Communicational Aspects

2016 ◽  
Vol 24 (2) ◽  
pp. 83-84
Author(s):  
Basia Nikiforova
Keyword(s):  
Immanuel Kant ◽  
Human Activity ◽  
Social Research ◽  
Linear Time ◽  
A Priori ◽  
Department Stores ◽  
Place And Space ◽  
Collective Identification ◽  
Time Space ◽  
Social Product

Michel Foucault in the text “Of Other Spaces: Utopias and Heterotopias” wrote that “the present epoch will perhaps be above all the epoch of space”. Space, place, and territories are social productions. Territory is a polysemic concept. Place is “events” created by territories, fluid areas of control produced by territorial negotiation (horizontal dynamics) and negotiations between places (vertical dynamics). Space produces places and is produced by places. Moreover, space, place and territories can be seen as the waves of territorialization and deterritorialization in an endless process. It is a form of seizure in the world, an a priori for Immanuel Kant, an ontological need for Martin Heidegger. Territory is a space, governed by a set of rules, named “code”. Territorialization is then synonymous of a certain codification, or the symbolical organization of space. Places are created by territorializational dynamics. They are the sum of “events”. The place and its territory is not “natural”, but it is a cultural artifact, a social product linked to desire, power and identity. The changes of the functions of places (what Foucault called heterotopy) are an important subject of contemporary studies. There are also many new temporary uses of these spaces and different emerging functions, including new forms of control, access, surveillance, new forms of openness and closeness (passwords, access profiles, etc.). Informational territory creates new heterotopias, new functions for places and a redefinition of social and communicational practices. It is not the end of a concrete place and its territory, but rather, a new meaning, sense, and a function for these spaces. The contemporary meaning of place and space has a visible tendency in creating ambivalence of sacrum and profanum, which means the secularization of the sacred and the sacralization of the secular. One of the sides of this tendency is sacralizing market and marketing the sacral. At the same time space has become a powerful tool of the ideological mobilization of people. The case which is analyzed in some articles in this issue of non-places (factories, department stores, sport complexes, etc.) is an example of absence of cultural references, its denial of a place. Also, the cases of textile factory Drobė and supermarket Prisma which are found in the above-mentioned papers are good examples of a situation when one version of the non-place was changed by another. Place is an essential dimension of human activity and existence. The place and territory are requirements for such a kind of human activity as subsidiarity, struggle for human rights, relation to Others, public experiences, personal and collective identification (“subjective” aspects of the object of identification) including some new aspects of gender, arts, performance in various contexts, the images and dreams about planning environment, borders disappearance and strengthening, the realization of the biopolitical mechanism. At the same time, the borders of a place are particularly revealing a line and a space for a social research, especially in the present era of a growing globalization. Border is a place where “past” and “future” are permanently clashed. On the borders of different places there is no inherently determinated relationship between the past, the present, and the future. Foucault’s idea corresponds with our understanding of space over time and contests the traditional notion of linear time, asserting that concepts of time have been understood in various ways, under varying historical circumstances. A closer analysis of the concept of space and all form of human activity there, is a central focus for contemporary social and humanitarian studies.

scholarly journals Improved Approximation for Fréchet Distance on c-Packed Curves Matching Conditional Lower Bounds

2017 ◽  
Vol 27 (01n02) ◽  
pp. 85-119 ◽  
Author(s):  
Karl Bringmann ◽  
Marvin Künnemann
Keyword(s):  
Lower Bounds ◽  
Time Complexity ◽  
Linear Time ◽  
High Dimensions ◽  
Fréchet Distance ◽  
Worst Case ◽  
One Dimensional ◽  
Dimension Formula ◽  
Frechet Distance ◽  
Special Case

The Fréchet distance is a well studied and very popular measure of similarity of two curves. The best known algorithms have quadratic time complexity, which has recently been shown to be optimal assuming the Strong Exponential Time Hypothesis (SETH) [Bringmann, FOCS'14]. To overcome the worst-case quadratic time barrier, restricted classes of curves have been studied that attempt to capture realistic input curves. The most popular such class are [Formula: see text]-packed curves, for which the Fréchet distance has a [Formula: see text]-approximation in time [Formula: see text] [Driemel et al., DCG'12]. In dimension [Formula: see text] this cannot be improved to [Formula: see text] for any [Formula: see text] unless SETH fails [Bringmann, FOCS'14]. In this paper, exploiting properties that prevent stronger lower bounds, we present an improved algorithm with time complexity [Formula: see text]. This improves upon the algorithm by Driemel et al. for any [Formula: see text]. Moreover, our algorithm's dependence on [Formula: see text], [Formula: see text] and [Formula: see text] is optimal in high dimensions apart from lower order factors, unless SETH fails. Our main new ingredients are as follows: For filling the classical free-space diagram we project short subcurves onto a line, which yields one-dimensional separated curves with roughly the same pairwise distances between vertices. Then we tackle this special case in near-linear time by carefully extending a greedy algorithm for the Fréchet distance of one-dimensional separated curves.

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