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== Online Algorithms and Competitive Ratio== For online algorithms, a notion similar to the approximation ratio, the '''competitive ratio''' w ...

We present our algorithms in the original set cover setting (instead of the hitting set version). ...</math> is also the best approximation ratio achievable by polynomial time algorithms, assuming that '''NP'''<math>neq</math>'''P'''. ...

...ters of random walks are closely related to the performances of randomized algorithms based on random walks: ...

[[Category:Algorithms]] ...

...ly speaking). We need to introduce some general concepts for approximation algorithms. ...>. Apparently, this is a more natural way to relax the FPTAS to randomized algorithms as it mimics the way of generalizing class '''P''' to '''BPP''' for decisio ...

* Dowling, W. and Gallier, J. (1984), "Linear-time algorithms for testing the satisfiability of propositional Horn formulae". ''[[Journal ...

...''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis'', by Michael Mitzenmacher, Eli Upfal; Cambridge Universi ...y] and other [https://peteroupc.github.io/bernoulli.html Bernoulli factory algorithms] ...

...The argument uses an important principle for the probabilistic analysis of algorithms: the principle of deferred decisions. ...ortant idea called '''random walks'''. There is a huge class of randomized algorithms for random sampling based on this principle. ...

...''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis'', by Michael Mitzenmacher, Eli Upfal; Cambridge Universi ...y] and other [https://peteroupc.github.io/bernoulli.html Bernoulli factory algorithms] ...

;Oblivious routing algorithms ...ven more oblivious than this standard definition.) Compared to the routing algorithms which are adaptive to the path that the packet traversed, oblivious routing ...

;Oblivious routing algorithms ...ven more oblivious than this standard definition.) Compared to the routing algorithms which are adaptive to the path that the packet traversed, oblivious routing ...

...ions <math>f:\{0,1\}^*\rightarrow\mathbb{N}</math> computable by poly-time algorithms. The classes '''FP''' and '''#P''' are the analogs of '''P''' and '''NP''' For deterministic algorithms, there are negative news for this problem. ...

...nd for the number of rounds required in the worst case by such distributed algorithms. This suggests us to define such a computational model for local distributed algorithms: any <math>t</math>-round local algorithm is described by a function ...

...nd for the number of rounds required in the worst case by such distributed algorithms. This suggests us to define such a computational model for local distributed algorithms: any <math>t</math>-round local algorithm is described by a function ...

...s a very simple scheme for boosting the accuracy of Monte Carlo randomized algorithms with two-sided errors. ...

...raphs] have found extensive applications in computer science, in designing algorithms, [http://en.wikipedia.org/wiki/Error_correcting_code error correcting codes ...te. Studies of these two problems revolutionized the area of approximation algorithms. ...

...ps://people.csail.mit.edu/jsolomon/share/book/numerical_book.pdf Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics. Justin Solom ...

The Feistel construction is also used in cryptographic algorithms other than block ciphers. For example, the [[Optimal Asymmetric Encryption ...

;Oblivious routing algorithms ...ven more oblivious than this standard definition.) Compared to the routing algorithms which are adaptive to the path that the packet traversed, oblivious routing ...

...is a structure shared by a class of optimization problems for which greedy algorithms work. ...