Questions tagged [optimization]

Questions about problems that entail selecting the best element from some set of available alternatives, and methods to solve them.

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Is unconstrained quadratic programming NP-hard?

I could not find the answer on the Internet. The case of quadratic programming with constraints is already solved on this forum, see Transforming SAT to Quadratic Programming in polynomial time. But ...
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Minimum amount of rectangles to create a 2-dimensional matrix

From this codegolf question. Consider an $r$ by $c$ matrix of nonnegative integers, called $M$. You also have a zero matrix of the same dimensions, called $N$. A "move" consists of replacing a ...
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Given we restrict the time and memory allowed what bounds can we place on a halting decider?

If a program is given as much memory and as much time to execute as it wants, then the halting problem is undecidable, and by Rice's theroem all non-trivial, semantic properties of programs like that ...
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Minimal hitting set with respect to set inclusion from a book “Parameterized Complexity Theory”

In the first chapter of "Parameterized Complexity Theory" by Flum and Grohe, an example is presented to find a hitting set of minimal cardinality. In Fig. 1.3, the author says a black colored leaf ...
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Can an optimization algorithm be “universal”?

I am wondering if a Bayesian Optimization framework (e.g. Google's Vizier) can be used in lieu of a traditional solver like Gurobi or CPLEX. In trying to answer this question, I realized that I don'...
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A variant of coin change problem

Consider a cashier machine that takes payments in coins. We feed the machine coins one by one until the value is more than the amount we should have paid. Then the machine returns the extra amount in ...
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Question about complexity of TSP Optimization problem

Is this statement true? Optimization TSP problems are known to be NP-hard, as we do not have a minimum cost to compare against, and in order to verify a solution is optimal, we need to iterate ...
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Find all local minima in a big 2d array

Assume we have a big 2d array. All its elements are either zeros or natural numbers. A local minimum is an element that is less than all its 8 neighbors. Is there an effective algorithm to find all ...
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For what applications of the traveling salesman problem, does visiting each city at most once truely matter?

Traditionally, the traveling salesman problem has you visit a city at least once and at most once. However, if you were an actual traveling salesman, you would want the least cost route to visit each ...
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Modification of dynamic programming for a knapsack problem

We have the following recursive function for the dynamic programming problem for a knapsack problem: \begin{align} V(i,w)=&max[ V(i-1,w), v_i +V(i-1,w-w_i)], \quad 1\leq i \leq n, 0\leq w \leq W \...
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