This is a problem I've had on my mind for a long time. Being the son of a teacher and a programmer, it occurred to me early on... but I still haven't found a solution for it. So this is the problem. One needs to create a time schedule for a school, using some constraints. These are generally divided in two categories: Sanity Checks ...
I studied TSP in college in the context of NP Completeness. I have never actually had a situation where it would apply to a practical problem. A little bit of research shows that it has been used to pick the cheapest path to move a drill around, that is making holes in circuit boards. That is pretty much all I could find. Are you ...
Given an array of items, each of which has a value and cost, what's the best algorithm determine the items required to reach a minimum value at the minimum cost? eg: Item: Value -> Cost ------------------- A 20 -> 11 B 7 -> 5 C 1 -> 2 MinValue = 30 naive solution: A + B + C + C + C. Value: 30, Cost 22 best option: A...
What's the best way to describe the algorithmic complexity of collusion detection for a ten-million-player online poker site? Assume (I don't think these assumptions make much difference so feel free to ignore them, but just to clarify): That the site has 10,000,000 registered users. That these players have played a total of 5 billion...
Here's a problem that I seem to be running into working with an accounting system. I have a set of transactions, but their sum does not equal the amount that the accounting department thinks that it should. They are not questioning the math, just the transactions being included :p Is there an algorithm that would help me determine whic...
I have a digraph which is strongly connected (i.e. there is a path from i to j and j to i for each pair of nodes (i, j) in the graph G). I wish to find a strongly connected graph out of this graph such that the sum of all edges is the least. To put it differently, I need to get rid of edges in such a way that after removing them, the g...
I need to write a program (a project for university) that solves (approx) an NP-hard problem. It is a variation of Linear ordering problems. In general, I will have very large inputs (as Graphs) and will try to find the best solution (based on a function that will 'rate' each solution) Will there be a difference if I write this in C-sty...
I'm faced with a 3 dimensional bin packing problem and am currently conducting some preliminary research as to which algorithms/heuristics are currently yielding the best results. Since the problem is NP hard I do not expect to find the optimal solution in every case, but I was wondering: 1) what are the best exact solvers? Branch and...
Sorry the question title isn't very clear, this is a challenging question to ask without providing a more concrete example. Consider the following scenario: I have a number of friends whose birthdays are coming up on dates (d1..dn), and I've managed to come up with a number of gifts I'd like to purchase them of cost (c1..cn). Unfortunat...
Recently I read a seminar work which says: The matching algorithm [for general graphs] can be extended to the weighted case, which appears to be one of the "hardest" combinatorial optimization problems that can be solved in polynomial time. Immediately the following question came to my mind: Do you know other "P-hard" pro...
What is the best book for a student learning about concepts such as NP-hard, NP-complete and P=?NP? I've already got the CLR but it doesn't really cover these particular topics as thoroughly. ...
I would like to find an open source example of a code for deterministic annealing. It can be in almost any language: C, C++, MatLab/Octave, Fortran. I have already found a MatLab code for simulated annealing, so MatLab would be best. Here is a paper that describes the algorithm. Deterministic annealing is an optimization technique ...
Is there some language that is NP-complete but for which we know some "quick" algorithm? I don't mean like the ones for knapsack where we can do well on average, I mean that even in the worst case the runtime is something like 2^n^epsilon, where the result holds for any epsilon>0 and so we can allow it to get arbitrarily close to 0. ...
I ran into the following algorithmic problem while experimenting with classification algorithms. Elements are classified into a polyhierarchy, what I understand to be a poset with a single root. I have to solve the following problem, which looks a lot like the set cover problem. I uploaded my Latex-ed problem description here. Devising...