# 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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### Efficient algorithm to find minimum steps to cover all the given points in infinite 2D grid?

Problem statement: You are in an infinite 2D grid where you can move in any of the 8 directions : ...
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### An algorithm for a minimization problem, How to minimize the wasted length of combination of multiple items with different length and number

Suppose there is an unlimited number of pipes, each has length $x$ meters. There is a list of requirements of pipes with shorter length than $x$. The number of these items are also given. For example ...
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### Minimal number of unions of sets such that no union has more than N elements

I have some sets, and can combine them by taking their union. I can take unions of the unions, too. I want to take unions until the total number of sets is as small as possible, with one caveat: that ...
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### Improve algorithmic complexity

We have an array of N size. We have to perform Q queries on it, in which each Query contains and Index I for which we do: ...
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### Optimal Selection of Non-Overlapping Jobs

I'm trying to find what the family of problem is - as well as an approach - for the following: I have a set of tasks T = [t1, ..., tn] to do, each of which has a corresponding reward ri. Each task ...
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### Variant of assignment problem

This is something like assignment problem, we have 2 group of people, first contains $n$ person and second contains $m$ person. we have a matrix $C$ which is an $n \times m$ matrix and our goal is to ...
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### What is the difference in SMO algorithm for SVM and SMO for one class?

Please let know if this is not the correct forum to ask this question. If not can anyone please tell where can I ask this question? I am trying to understand the difference between the paper : https:/...
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### What is the best hash functions for millions of String keys?

I have a situation where there are a million Keys of type String and I want to use the Symbol table to store the key and the value. The problem that the retrieval process is too slow and I want to ...
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### Scheduling algorithm for a student's study times given assignments, expected time, due dates, and class times

I would like to create an algorithm that advises a student when they should work on certain assignments given the expected time each assignment will take, and the due date of each assignment. Say that ...
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### simple question about epsilon and estimation turing machines

i am getting really confused by it. i got to a point i had to calculate the lim when $n \rightarrow \infty$ for an optimization problem, and i got to the point that i had to calculate a fairly simple ...
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### Encoding set of At-Most-One constraints as a MAX-SAT problem

Assume a set of variable $V$ = $\{v_1,...,v_m\}$. Given total $n$ at-most-one (AMO) constraints (at most one element in a given set is true) set [of the below form], over the variable set $V$,  AMO \...
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### Can someone help me understand the time and space complexity?

Can anyone help me understand the time and space complexity here? I know zip() is O(1) and sorted() is O(n). The loop has the ...
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### How to use XML format of graphs in Graph neural network?

I have manually labeled directed graphs that I need a GNN to train on and then predict when given a new directed graph, what the labels for the vertexes in the graph should be. My graphs are in the ...
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### How to do supervised learning without knowing the target

I'm working on an optimization algorithm that I think could be considered machine learning, but I'm not sure. Basically I have a model that I want to optimize by adjusting its parameters. I don't ...
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### Inexact cover, or cover with gaps

Dancing Links: wikipedia article, research paper is an implementation of algorithm X for exact cover problem. In the Knuth's research papaer, linked above it is shown how Polymino problem (that is ...
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### Integer Linear programming formulation if then condition

I want to create constraints such that I can implement the following condition: Let A be an integer variable >= 0 with an upper bound of 12 I want to introduce the following variable B also an ...
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### Are most metaheuristic algorithms different metaphors for the same method?

Most times I encounter this random metaphors for metaheuristic optimization they seem like a modified genetic algorithm to me. What do you think? Is there a way to remove the analogies/metaphors to ...
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### Trying to design an algorithm for finding a number in a range

I'm trying to design an algorithm that finds a number in a given range. The only signal we get for a given guess is: "Is our guess less than the magic number?" I'm trying to: Optimize the ...
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### Method for combining derivative free optimization results of different data inputs

I am working on an algorithm that has multiple fixed parameters. The algorithm analyzes time series data and spits out a number. The fixed parameters need to be such that this number is as small as ...
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### Probability of Attaining the/a Global Optimum

Suppose for a given optimization problem, $A$, the size of the search space $S$ is |$S$|. If the fitness landscape defined by $A$ is unimodal, then there is clearly only one global optimum. Given that ...
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### Min number of register without spilling

The program below uses six temporary variables a, b, c, d, e, f. a = 1 b = 10 c = 20 d = a+b e = c+d f = c+e b = c+e e = b+f d = 5+e return d+f Assuming that all ...
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### SVMs - Fat (Margin) Boundary: Why is $\max\frac1{||\theta||}=\min \frac{ ||\theta||^2}{2}$?

I am trying to understand SVMs in depth watching lectures from MIT. The professor to reduces the classification problem into an optimization problem. To do that, he first defines the decision and ...
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### Efficient algorithm to compute the diameter of a convex set?

Is there a polynomial algorithm that can compute the diameter (the distance between the furthest points) of a convex set? It is possible to do it efficiently for a set of points, but imagine that the ...
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### How can TSP be an NP-optimization problem, when a feasible solution $s$ must be polynomial bounded in the instance size $|I|$?

How can TSP be an NP-optimization problem ? The definition of an NP-optimization problem $\Pi$ states that for each instance $I \in \Pi$ , the set of feasible solutions $S_\Pi(I)$ is non-empty and ...
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### Has it been proven that the optimization TSP is (or is not) polynomial-time verifiable if P ≠ NP?

The optimization version of TSP asks for the length of the shortest tour. Unlike the decision version of TSP, there's no obvious way to verify a proposed solution of the optimization problem in ...
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### Is there an optimization algorithm that could help match the maximum number clients to servers with constraints?

How do you go about solving the following problem that tries to match the greatest number of clients with servers with constraints? I'm trying to identify an algorithm or simulation that could help me ...
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### Measure divergence in Particle Swarm Optimization

I'd like to monitor divergence/diversity in my swarm during the particle swarm optimization algorithm to measure when the swarm search space is converging. This would be used as one metric to be ...
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### Must an optimization problem with a greedy algorithm belong to P?

If it is known that for some optimization problem there is a greedy algorithm that solves it and the solution includes sorting of input at the preliminary stage, is it necessarily true that the ...