Wikipedia:Reference desk/Archives/Mathematics/2016 April 20

= April 20 =

Miminum Flow Problem
Hi, I know that maximum flow problem is in $$P$$. But what about the minimum flow problem? Is it in $$P$$ too? Is it $$NP-complete$$? 213.8.204.61 (talk) 10:28, 20 April 2016 (UTC)
 * Isn't the minimum flow zero? -- SGBailey (talk) 16:07, 20 April 2016 (UTC)
 * For minimum flow problems, maximum flow problem is expanded so that in addition to a capacity defined for each edge, there is also a nonnegative lower bound of flow defined for each edge, and if a least one such lower bound is positive, then the minimum flow will not be zero.
 * Algorithms for minimum flows (Computer Science Journal of Moldova, vol.9, no.3(27), 2001) gives such a definition and claims to "present a generic preflow algorithm and several implementations of it, that solve the minimum flow problem in O(n2m) time." -- ToE 21:24, 20 April 2016 (UTC)
 * I was asked to implement a reduction of this to standard max flow. Since I was told it was possible (and eventually found out how), the problem at hand clearly is in P.--Jasper Deng (talk) 07:37, 24 April 2016 (UTC)
 * Thank you!! 213.8.204.72 (talk) 17:38, 25 April 2016 (UTC)

Octavan primes
I just noticed a Wikipedia article called Quartan prime, which means a prime number of the form a^4 + b^4. How many octavan primes are known?? (You should be able to guess what I mean easily here!) (Note: n has to be a power of 2 for a^n + b^n to be prime.) Georgia guy (talk) 17:12, 20 April 2016 (UTC)


 * Some are shown at https://oeis.org/A006686. —Wavelength (talk) 17:22, 20 April 2016 (UTC)