# chebyshev

Published articles for chebyshev.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Load Balancing and the Power of Hashing

DevFeed: [Load Balancing and the Power of Hashing](<https://devfeed.tech/articles/load-balancing-and-the-power-of-hashing-40393.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/12/28/load-balancing-and-the-power-of-hashing/>)

Published: 2015-12-28T09:00:31Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [function](<https://devfeed.tech/topics/function.md>), [Load Balancing](<https://devfeed.tech/topics/load-balancing.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [math](<https://devfeed.tech/topics/math.md>)

Tags: [abstraction](<https://devfeed.tech/tags/abstraction.md>), [algorithm](<https://devfeed.tech/tags/algorithm.md>), [algorithms](<https://devfeed.tech/tags/algorithms.md>), [chebyshev](<https://devfeed.tech/tags/chebyshev.md>), [hashing](<https://devfeed.tech/tags/hashing.md>), [load-balancing](<https://devfeed.tech/tags/load-balancing.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [software](<https://devfeed.tech/tags/software.md>)

### AI overview

This article explains why hashing is useful when processing data too large for a single machine. It introduces hash functions and families of hash functions, then applies their properties to efficient resource allocation through load balancing.

### Source excerpt

Here's a bit of folklore I often hear (and retell) that's somewhere between a joke and deep wisdom: if you're doing a software interview that involves some algorithms problem that seems hard, your best bet is to use hash tables. More succinctly put: Google loves hash tables. As someone with a passion for math and theoretical CS, it's kind of silly and reductionist. But if you actually work with terabytes of data that can't fit on a single machine, it also makes sense.

## Probabilistic Bounds -- A Primer

DevFeed: [Probabilistic Bounds -- A Primer](<https://devfeed.tech/articles/probabilistic-bounds-a-primer-40312.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/04/15/probabilistic-bounds-a-primer/>)

Published: 2013-04-15T11:14:32Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [math](<https://devfeed.tech/topics/math.md>), [Learning](<https://devfeed.tech/topics/learning.md>), [Streaming](<https://devfeed.tech/topics/streaming.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [algorithms](<https://devfeed.tech/tags/algorithms.md>), [chebyshev](<https://devfeed.tech/tags/chebyshev.md>), [chernoff](<https://devfeed.tech/tags/chernoff.md>), [chernoff-bound](<https://devfeed.tech/tags/chernoff-bound.md>), [inequality](<https://devfeed.tech/tags/inequality.md>), [learning-theory](<https://devfeed.tech/tags/learning-theory.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [markov](<https://devfeed.tech/tags/markov.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [probabilistic](<https://devfeed.tech/tags/probabilistic.md>), [probabilistic-method](<https://devfeed.tech/tags/probabilistic-method.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [random-variables](<https://devfeed.tech/tags/random-variables.md>), [streaming](<https://devfeed.tech/tags/streaming.md>), [streaming-algorithms](<https://devfeed.tech/tags/streaming-algorithms.md>), [variance](<https://devfeed.tech/tags/variance.md>)

### AI overview

This tutorial introduces probabilistic bounds used in algorithm analysis, machine learning theory, randomized algorithms, and streaming algorithms. It focuses on the Chernoff bound and presents simpler bounds from Markov's and Chebyshev's inequalities, including short proofs.

### Source excerpt

Probabilistic arguments are a key tool for the analysis of algorithms in machine learning theory and probability theory. They also assume a prominent role in the analysis of randomized and streaming algorithms, where one imposes a restriction on the amount of storage space an algorithm is allowed to use for its computations (usually sublinear in the size of the input). While a whole host of probabilistic arguments are used, one theorem in particular (or family of theorems) is ubiquitous: the Chernoff bound.