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blog.computationalcomplexity.org | ||
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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yufeizhao.wordpress.com
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| | | | | This post is adapted from my new expository survey Extremal regular graphs: independent sets and graph homomorphisms. The earliest result in extremal graph theory is usually credited to Mantel, who proved, in 1907, that a graph on $latex {n}$ vertices with no triangles contains at most $latex {n^2/4}$ edges, where the maximum is achieved for... | |
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lucatrevisan.wordpress.com
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| | | | | The spectral norm of the infinite $latex {d}&fg=000000$-regular tree is $latex {2 \sqrt {d-1}}&fg=000000$. We will see what this means and how to prove it. When talking about the expansion of random graphs, abobut the construction of Ramanujan expanders, as well as about sparsifiers, community detection, and several other problems, the number $latex {2 \sqrt{d-1}}&fg=000000$... | |
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www.aidancooper.co.uk
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| | | In this article, we will explore how Shapley values work - not using cryptic formulae, but by way of code and simplified explanations. | ||
