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#* [[随机算法 (Fall 2011)/Cover Time|Cover Time]] # Coupling and Mixing Time ...

...(1)</math> in total variation distance, when <math>d=o(n^{1/2})</math>. If time permits, I will describe how to use this new method to generate uniformly r ...develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming alg ...

...time in <math>\left(\frac{\text{distance}}{\text{time}}\right)\times\text{time}</math>. This is done by adding small slices of the rate graph together. Th Another time integration is helpful is when finding the [[volume]] of a solid. It can ad ...

...s accept the fact that there are at least 11 dimensions in our universe: 1 time dimension and 10 spacial dimensions.) The length of the strings would be de ...

* Analyze the mixing time of the random walk by coupling. * Prove that the mixing time is <math>O(k\log k)</math> by coupling. ...

...ge [[speed]] of the runner if we divide the distance they travelled by the time it took. But this does not say what speed the person was running at exactly ...1.5 seconds. This was a very long and hard process and had to be done each time people wanted to work something out. Imagine a driver trying to figure out ...

...he two decks with probability proportional to the size of the deck at that time. :The mixing time of inverse riffle shuffle of a deck of <math>n</math> cards is <math>\tau_{ ...

...f electric resistance present in the conductor, and ''t'' is the amount of time that this happens for. ...

...'' consists of all decision problems <math>f</math> that have a polynomial time deterministic algorithm <math>V</math> such that for any input <math>x</mat ...have a randomized algorithm <math>A</math> running in expected polynomial time for any input such that for any input <math>x</math>, <math>A(x)=f(x)</math ...

*For all <math>i</math>, <math>|H_i|</math> is computable in poly-time. *For any <math>x\in V</math>, it can be determined in poly-time whether <math>x\in H_i</math>. ...

(3) The <math>\ell_2</math> mixing time of the random walk over <math>n</math> items with distribution <math>\{p^{( ...(v) = \frac{1}{\sqrt{n}}</math>, then show that <math>\ell_2</math> mixing time of <math>\{X_i\}_{i\geq 0}</math> is at least <math>\Omega\left(\frac{\log( ...

* '''Time period''': Over time, the demand for goods would tend to become more price elastic. For example, ...

Topics that I'm considering to cover at next time when I teach this class (perhaps): Feel free to send me an email at any time to tell what topics you would like this class to cover in future. ...

# Give a poly-time greedy algorithm for finding the weighted max <math>k</math>-cut. Prove tha ::Fill in the blank parenthesis. Give an analysis of the running time of the algorithm. And prove that the approximation ratio is 0.5. ...

# Give a poly-time greedy algorithm for finding the weighted max <math>k</math>-cut. Prove tha ::Fill in the blank parenthesis. Give an analysis of the running time of the algorithm. And prove that the approximation ratio is 0.5. ...

...ted KMP algorithm inspired by automaton theory runs in <math>O(n+m)</math> time. ...in, uses the idea of fingerprinting and also runs in <math>O(n + m)</math> time. ...

[[File:Sine waves different frequencies.svg|thumb|250px|As time elapses—here moving left to right on the [[horizontal]] axis—the five [[Sin ...]'''Frequency''' is how often an event repeats itself over a set amount of time. ...

...hat its note value (how long it lasts) does not count as part of the total time value of the [[Bar (music)|measure]]. ...a in small print. This usually means it must be played by taking half the time value of the next note (for example: an appoggiatura in front of a quaver ( ...

== Mixing Time == ...ain to approach the stationary distribution. To formally define the mixing time, we need a notion of the distance between two probability distributions. ...

...of time, and so that is one way to think of calculus—studying functions of time. There are two different types of calculus. '''Differential calculus''' div ...land and [[Gottfried Leibniz]] in Germany figured out calculus at the same time, working separately from each other. Newton wanted to have a new way to pre ...