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I wonder if it isn't possible to do this for other greedy algorithms, or algorithms which are trying to find optimal solutions through heuristics.
Earlier quoted context omitted.
I've been out of school for a while, what does m^(1+o(1)) mean? Isn't any constant trivially in "o(1)"? So m^1000 is in this class? Or are they using it informally to mean "a very small number"?
The o(1) here represents a decreasing function in m, such as 1/m. (Note: This is little o, not big o.) Therefore, for any k > 1: m^(1+o(1)) grows more slowly than m^k but faster than m
So basically they took a greedy algorithm that used a combinatorial approach and transformed it to use a calculus approach by inspiring from a related problem of "electrical flow through a network". I wonder if it isn't possible to do this for other greedy algorithms, or algorithms which are trying to find optimal solutions through heuristics.
Not a comment in regard to this article in particular, but I love Quanta Magazine. Just the right amount of detail for a non-scientist and consistently fascinating subject matter.
Earlier quoted context omitted.
I'd agree with you ~1 year ago but I think a lot of their articles now tend to water-down lots of complex subjects in rigorous math papers. Still remains one of my favorite websites.
i think they have to water it down so much because hardly anyone would understand the math, even people who consider themselves good at math or have degrees in STEM..it's just so advanced even relative to that .
As someone who loves math but who only knows a little, I find the articles manage to convey the broad ideas quite well. What it is, why it matters. I could stand more detail, but I guess many others couldn't.
So basically they took a greedy algorithm that used a combinatorial approach and transformed it to use a calculus approach by inspiring from a related problem of "electrical flow through a network". I wonder if it isn't possible to do this for other greedy algorithms, or algorithms which are trying to find optimal solutions through heuristics.
It looks like this solution works for a specific group of problems. So it won't be applicable to all problems that use greedy (or other) heuristics.
Update your leetcode answers folks.