What good books are there on the subject of P = NP, NP-completeness and the like?
I have Fortnow's "The Golden Ticket" and Garey & Johnson's "Computers and Intractability"
How else can I get into the subject and slowly creep towards the forefront of research? Who is actively researching it? What literature/publications can I read to bring me up to speed?
I've been a profesional software engineer for 16 years and still don't know that P = NP is all about.
Is okay though, an computer assemblyman doesn't have to know how the components he's assembling work.
Angel Sanders
It's a CS problem, not an engineering problem. Shit is mostly a concern for mathematicians anyways, but the repercussions of a proof are, as always, in the mechanism we'd find to get here and how powerful that math could be to other uses.
Jeremiah Reed
The Nature of Computation Moore
Lucas Evans
OP is a fast reader.
>I've been a profesional software engineer for 16 years and still don't know that P = NP is all about.
Try to make an algorithm that finds the shortest tour among a few cities (without visiting a city twice). No matter how good you are it will take kinda long.
No try to sort an array: Wow, that was much faster, wasn't it?
Hudson Cooper
But why?
Carson Ramirez
>I've been a profesional software engineer for 16 years and still don't know that P = NP is all about. >professional yeah, nope. pajeet level at best.
Oliver Gray
Thank you user.
Andrew Bennett
what exactly is P and NP? i understand they are sets of problem types but can someone explain what it means to solve a problem "in polynomial time"? or what a question and answer may look like?
Lucas Peterson
they are complexity classes.
>but can someone explain what it means to solve a problem "in polynomial time"? you don't know what polynomial means ? did you ever attend a school ?
Oliver Ortiz
>what it means to solve a problem "in polynomial time"? In a number of operations that has polynomial complexity (i.e.: that converges to a polynomial function when the size of the input grows).
Kevin Harris
i know what polynomial functions look like, but i mean what is the metric? does time translate to literal seconds or is it processor cycles or math operations or what?
Easton Ortiz
are you literally retarded or something ?
Dominic Miller
i was hoping for some user who was smarter than me to break it down and make teach me something.
i'm ignorant on the subject. do you feel better now?
Noah Brooks
Usually it's count of a certain operation, and even more usually comparision.
We're talking algorithms here so an entire instruction set model doesn't make much sense.
Ian Myers
no, but i feel sorry for you. are you american ?
anyway, you said you know what a polynomial function looks like. just imagine that thats how the runtime grows with the size of the input set. now look up an exponential function e.g.
Cameron Reed
The Bible.
Andrew Bell
Thanks! Great read!
Ian Hernandez
Say you want to search an array for an element. Best case scenario is it's the first element in the array. Happy dayz Worst case scenario is the element isn't even in the array. Thus you've made N comparisons where N is the number of elements in the array, and haven't found the thing you were looking for. So the average case is N/2.
Jacob Richardson
Now suppose you want to see if any element from one array is present in another. If the first array has M elements and the second array has N elements, then the worst case scenario will be M * N comparisons. See how this differs from the first algorithm? The running time increases depending on the algorithm. Now you have an idea of what time complexity is.