Optimal resource allocation in networks gives rise to some of the most fundamental problems at the intersection of algorithms, stochastic processes, and learning.
We know that for matrices A and B, AB is not the same as BA in general. But suppose B is a polynomial in A, like B = A^2 - 3A + I (note I = A^0). Then AB is indeed the same as BA.
Tiling of a surface is acted upon by its automorphism group. The tilings with single vertex orbit, the transitive tilings, are well studied since antiquity.
Raghavendra's famous result from 2008 fully characterizes the inapproximability of every maximum constraint satisfaction problem (Max-CSP). However, the result inherently loses perfect completeness.
"Paper: Yuchen Zhang, John C Duchi, Michael I Jordan, Martin J Wainwright, Information-theoretic lower bounds for distributed statistical estimation with communication constraints"
Paper: Nachum Dershowitz and Yuri Gurevich, "A Natural Axiomatization of Computability and Proof of Church's Thesis" https://doi.org/10.2178/bsl/1231081370