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...hain from an arbitrary state, run the Markov chain for a sufficiently long time, and return the current state. ...iently long time <math>T</math>, and return the current independent set at time <math>T</math>. ...

...ether a certain NP complete problem could be solved in quadratic or linear time.<ref>Juris Hartmanis 1989, [http://ecommons.library.cornell.edu/bitstream/1 ...to figure out if the answer is right or wrong, but it may take a very long time for the computer to actually come up with "1, 2, 3, 4, 5" on its own. For s ...

and the distribution at time <math>t</math> when the initial distribution is <math>q</math>, is given by .../math>. Therefore, we have the following corollary which bounds the mixing time by graph expansion. ...

= Mixing Time= The '''mixing time''' of a Markov chain gives the rate at which a Markov chain converges to th ...

...e <math>n</math> is the number of vertices, so the algorithm terminates in time <math>O(n^2)</math>. We leave this as an exercise. 1-\Pr[\mbox{failed every time}] &= 1-\Pr[{RandomContract}\mbox{ fails}]^{n(n-1)/2} \\ ...

* '''Time''': 2015年10月10日 |bgcolor="#A7C1F2" align="center"|'''Time''' ...

...arbitrary]] basis into a friendly basis. Like from our original set, each time we use the process on a new vector, it is guaranteed to be mutually friendl ...

这个结果还有个缺陷，不是最坏时间复杂度O(1)而是amortized time complexity，平摊时间复杂度是O(1)。原因在于FKS的hash function的分配并不平均。 ...还是计算的效率都远远落后与[DHKP97]提出的那个已在在现实中大量应用hash function。因此现实中人们宁愿忍受糟糕的worst-case time complexity，也仍旧使用随机性不够好却可以高效计算的[DHKP97]的hash function。 ...

:We design an algorithm with '''''guaranteed''''' worst-case running time, which approximates the optimum within a '''''guaranteed''''' approximation ...re particularly interested in the approximation algorithms running in poly-time of the input size, for the '''NP-hard''' optimization problems. ...

Now we use the idea of electrical network to analyze the cover time of random walk. Consider an undirected graph <math>G=(V,E)</math>, we const Armed with this theorem, we can now give a better estimation of the cover time of random walk. Let <math>T</math> be a spanning tree of <math>G</math>, an ...

...lem, and then give an FPTAS for the problem based on the pseudo-polynomial time algorithm. ...

...lication algorithm (in theory) is <math>O(n^{2.376})</math>, and so is the time complexity of this method. ...domized algorithm, due to Freivalds, that runs in only <math>O(n^2)</math> time: ...

...er a [[domain]] or determining the response of the system over a period of time, the [[independent variable]]s are modulated, while the parameters are held ...m being considered; parameters are dimensionless, or have the dimension of time or its reciprocal." John D. Trimmer, 1950, Response of Physical Systems (Ne ...

...riable <math>X</math> (think that <math>X</math> is a cost such as running time of a randomized algorithm). We call this a '''tail bound''', or a '''tail i ...ed algorithm for a decision problem <math>f</math>, whose expected running time is within <math>T(n)</math> on any input of size <math>n</math>. We transfo ...

...uss|Gauss]] in his etude of [[hypergeometric series]] (1813) for the first time rigorously investigated under which conditions a series converged to a limi ...Bolzano]] (''Der binomische Lehrsatz'', Prague 1816, little noticed at the time) and by [[Karl Weierstraß]] in the 1870s. ...

...feel that you are not contributing enough to your group, then try to spend time thinking about the problems alone before working with your group. If you en ...ccomodate late submission requests ONLY IF you made such requests ahead of time. ...

...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. ...

...#4D72BE" align="center" style="width: 21%"|<font size=3, color=white>'''时间 Time'''</font> |align="center"|Entropic independence and tight mixing time of random walks ...

...mbush]] or military surprise, a military strategy to strike the enemy at a time or place or in a manner for which they are unprepared ...

...e is named after [[Richard Hamming]] who developed it in the 1940s. At the time, Hamming worked with machines that had [[relay]]s and used [[punched card]] ...