Algorithm for creating a school timetable

I’ve been wondering if there are known solutions for algorithm of creating a school timetable. Basically, it’s about optimizing “hour-dispersion” (both in teachers and classes case) for given class-subject-teacher associations. We can assume that we have sets of classes, lesson subjects and teachers associated with each other at the input and that timetable should fit … Read more

What are the differences between NP, NP-Complete and NP-Hard?

What are the differences between NP, NP-Complete and NP-Hard? I am aware of many resources all over the web. I’d like to read your explanations, and the reason is they might be different from what’s out there, or there is something that I’m not aware of. Answer I assume that you are looking for intuitive … Read more

How to the NP hard of a problem that search for a subset of points with maximum scores?

Suppose in a plane, there is a set of points, whose distance to (0,0) is always 1: [(0,1),(1,0),(0.707,0.707),(0.707,−0.707),…] Each point is assigned with a weight (possible negative): [w(0,1)=1,w(1,0)=2,w(0.707,0.707)=−1,w(0.707,−0.707)=−2,…] Suppose the standard deviation of the points are defined as the top answer here: Find a subset of points S such that SUM(w)×STD is maximized. My … Read more

CircuitSAT to 1-in-3SAT

This question follows Unique 3SAT to Unique 1-in-3SAT Consider an AND gate such that (A ∧ B) = C. It can be trivially expressed in 3SAT with 4 clauses and no extra variables. (A∨B∨¯C)∧(A∨¯B∨¯C)∧(¯A∨B∨¯C)∧(¯A∨¯B∨C) | A | B | C | |—|—|—| | 0 | 0 | 0 | | 0 | 0 | 1 … Read more

How to Show Subset Sum ≤p\le_p 3-Partition

Given a set of integers S (positive and negative, may contain duplicates) can S be divided into three disjoint subsets that all sum to the same value? Prove this problem is NP-complete. Is it possible to show directly that Subset Sum ≤p 3-Partition, or would I have to do Subset Sum ≤p Partition ≤p 3-Partition? … Read more

Would P=BPP\mathsf{P=BPP} imply dIP=IP\mathsf{dIP=IP} and if not then why?

Complexity class IP includes all problems that can be solved using an interactive proof system where the verifier is a probabilistic polynomial time machine, and the prover is a machine of an unbounded power. It is known to be equal to PSPACE. Making the verifier a deterministic machine would make a complexity class dIP which … Read more