# 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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### Optimize stacking time series by offsetting start times (feels like a backpack problem?)

Given a time-series of data collected from a single running process that takes 8 hours to complete: Minute GB of Disk Space Used 0 0 1 8 2 15 3 22 ...Etc. It is sampled every minute, for 8 ...
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### Optimal clustering with optimal number of clusters as well as max and min cluster size constraints

I need to cluster $N$ data points. I don't know the number of clusters to be formed. It needs to be found optimally. Also, there is maximum and minimum cluster size constraints, where $C_{\max}$ is ...
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### Polynomial time optimization problems belong to which complexity class?

I know that $\mathsf{P}$ class is only defined for decision problems. Therefore, a problem like "Does there exist an $(s,t)$ path of length $k$ in the graph $G$?" is in $\mathsf{P}$. One can ...
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### What does a recursive min s,t-cut optimize?

Consider the following algorithm sketch: Given an edge-weighted directed acyclic graph $G = (V, E, w : E \to \mathbb{N})$, adjoin a temporary source $s$ and sink $t$ to get $G' = (V', E', w')$. $G'$ ...
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### Minimum Vertex Cover of 2 vertex disjoint odd cycles that have edges between them

Consider the graph $G$, which is comprised of 2 vertex disjoint odd cycles ($C_1$, $C_2$) where $|C_1|$ and $|C_2| \geq 5$. $G$ is sub-cubic and connected, with edges in between the cycles. Because $G$...
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### Reduction from TSP to ATSP does not imply constant factor approximation algorithm

As I understand there is a constant factor approximation algorithm (e.g Christofides algorithm) for the symmetric TSP problem. This is however not the case for the asymmetric TSP problem (I am ...
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### Multi-Objective Implicit Hitting Set for Multi-Objective MaxSAT

MaxSAT is a problem related to SAT where there is a finite collection of hard and soft clauses which share boolean variables. The hard clauses must be satisfied while the soft clauses have a weight. ...
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### How to check whether a lattice polytope embeds into another lattice polytope?

Suppose I have two polytopes $P\subset \mathbb R^m$ and $Q\subset \mathbb R^n$ with vertices with integral coordinates. How do I check whether $P$ is embeddable into $Q$? More precisely, "...
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### Which branch of computer science uses mathematical optimization the most?

I am beginning with my masters degree in mathematics and I will specialize in optimization theory. My minor is computer science and wanted to know which branch of computer science fits my ...
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### Find the k length path that maximize a node associate metric

Let's say I have : a Graph g v vertices. Each vertex is associated to a cost c. A special vertex called the starter vertex or vs. I want to find the path p of length 10 (for example), that start ...
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### If P = NP, do these NP-complete problems reduce to these specific easier versions?

I am trying to understand reductions and NP-completeness from Algorithms by Dasgupta et al. Chapter 8 has the table below and I am wondering: if $P = NP$ does each of the problems on the left reduce ...
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### SSA Copy Folding

When can we fold copies in SSA? We are clearly allowed to fold a copy such as a0 = call foo() b0 = a0 But what about a program such as ...
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### Coordinate descent for Lasso, Question about algorithm

I'm not sure why the algorithm computes $c_k$ with $\sum_{j \neq k} w_j x_{i, j}$. Why does one need to ignore the $k^{th}$ feature here? I'm not sure how this is derived. Is this the result of taking ...
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### How are randomized restarts in local search 4 times likely to give bad local minima?

I am reading section 9.3.3 Dealing with local optima in Algorithms by Dasgupta et al. and the authors mention that in randomized restarts, it is four times likely to end up with a bad solution. They, ...
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### 2-Dimensional interval scheduling problem

I have a problem that is similar to the conventional interval scheduling algorithm but it is two dimensional, so I have another metric to take into account. My dataset format: Cars with the start and ...
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### 0/1 Knapsack problem with minimal cost

so i have this problem where: I have to accomplish a challenge A with n quests. Each quest gives me: p points and needs t time to be done. The object is to complete the challenge A that needs M ...
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### Online approximation algorithm for median?

Is there a well-known or (relatively) easily-implementable streaming algorithm for approximating the median of the last, say, $k$ elements of a stream $c_1,c_2,c_3,\dots$? The scenario is: I have a ...
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### Exit quickly from a maze with a local view of the maze

How to efficiently exit from a maze where you know the initial position of the player (1,1), the exit (49,49)? You don't know the maze configuration but you know where your player is, and which ...
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### Is the Jacobian matrix calculation process correctly on this energy function?

When I implemented the paper Dynamic Fusion published in 2015 CVPR, I came into the trouble with how to solve the energy function: E(W_t, V, D_t, \mathcal{E}) = \text{Data}(W_t, V, D_t) + λ\text{Reg}...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### How do I assign homes to hospitals based on locality? (clustering, kmeans?)

I have a large set of $(X)$ hospitals and $(Y)$ homes, where $(Y)$ is much larger than $(X)$, and their respective coordinates. Each hospital can handle any home within a 50 mile radius, and up to 10,...
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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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### Bin packing when items can be broken

In the bin packing problem, there are some $m$ items of size less than $1$, and they have to be packed into as few as possible bins of size $1$. The problem is NP-hard, but if we are allowed to break ...
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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 ...
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### Partitioning list into two parts of almost equal sum

I was given this problem in class, and I have no idea how to solve it. The problem is: "Given a list of positive integers, divide the numbers into 2 groups such that the difference between the ...
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### Equally optimal nodes during minimax with alpha-beta pruning

Alpha-beta pruning is an optimization for minimax that reduces the number of nodes visited without changing the final result. However, both minimax and alpha-beta only return the optimal node value (...
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### Computing a fractional matching of maximum product in a bipartite graph

Given a bipartite graph $(X\cup Y, E)$ with edge weights, it is easy to find a matching in which the product of weights is maximum: replace each edge weight with its logarithm, and find a matching in ...
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### Which data structure can be used to determine most experienced person in a shift?

Problem Statement: There are $n$ hours in a day and you have $w$ workers. For each worker $i$ you will be given $x_i$ (work experience), $s_i$ (shift start time) and $e_i$ (shift end time) on a ...
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### How to remove an ordering requirement from a board game simulation?

The Problem: I'm trying to simulate part of the game tantrix which is a board game played with hexagonal tiles. Each tile has 3 lines of different colors that each start at one side of the hexagon ...
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### Maximum-coverage minimum-overlap intersection of sets

I'm having troubles finding information on how to solve/optimize a problem I'm currently facing, which probably means I'm either approaching it poorly and/or I don't know what to search for. The ...
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### What is a good approach to deciding which jobs (from a list of HPC jobs) should be ran locally vs. on the cloud given time & cost constraints?

Cloud computing has transformed the landscape of compute operations. Of course, there are still many labs/businesses with local, large-scale compute clusters. For those businesses who keep the ...
Problem The enemy army has taken $n$ of our cities. In each city $i$ the enemy has placed $e_i$ soldiers. We have $n$ teams, each team $j$ with $d_j$ soldiers. If we place more soldiers in a city ...