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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20
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1answer
2k views

How to pack polygons inside another polygon?

I have ordered a few leather sheets from which I would like to build juggling balls by sewing edges together. I'm using the Platonic solids for the shape of the balls. I can scan the leather sheets ...
8
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0answers
609 views

Chained operations on sequences with two operators

Given a binary expresion tree, with addition and multiplication operations, how can we optimize it's evaluation? Can we learn from matrix chain multiplication? A generalization of matrix chain ...
9
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1answer
187 views

Fixed-length decision-tree-like feature selection to minimize average search performance

I have a complex query $Q$ used to search a dataset $S$ to find $H_\text{exact} = \{s \in S \mid \text{where $Q(s)$ is True}\}$. Each query takes on average time $t$ so the overall time in the linear ...
0
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1answer
2k views

Integer LP formulation and the existence of a solution

A film producer is seeking actors and investors for his new movie. There are $n$ available actors; actor $i$ charges $s_i$ dollars. For funding, there are $m$ available investors. Investor $j$ will ...
1
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0answers
120 views

Is it possible to analyse computation?

Take a Turing machine, with a terminating program, convert it to some representation of the machine which captures, in a lossless manner, its state as it performs the computation. So you have a ...
6
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1answer
163 views

Can all packing/covering problems be rephrased as set packing/covering problems?

Can all packing problems be rephrased as set packing problems? Can all covering problems be rephrased as set covering problems? In other words, I was wondering if set packing/covering problems are ...
5
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3answers
2k views

Min cost max flow in bipartite run time

I have a bipartite graph with $|E|=O(|V|^2)$, a super-source and a super-sink. I am looking for the min-cost max-flow (the max-flow of all possible max-flows that has the minimum cost). For the sake ...
6
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2answers
951 views

A variant of the Assignment Problem

In my variant of the assignment problem I have a set $A$ of agents and a set (of possibly different cardinality) $T$ of tasks. Each agent needs to be assigned exactly $n$ or $n+1$ tasks, and each task ...
4
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1answer
171 views

Time - Complexity Convex Optimization and Eigen Decomposition

Say I had the choice of choosing one out of the following two optimization problems which I could use to solve my problem. Which choice is the fastest? How much of a trade-off would it be? Is the ...
3
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0answers
46 views

A variant of the assignment problem (?) [duplicate]

Possible Duplicate: A variant of the Assignment Problem (Not a comp.scientist, but have the basic research. Please excuse me if I've overlooked anything obvious.) In my variant of the problem I ...
4
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1answer
184 views

Formulating a linear program s.t. only extreme point solutions are found

If there are many solutions to a linear program s.t. the objective function is minimized/maximized (= optimal solutions are on an edge of the polytope), how can I force an LP solver to find only an ...
2
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1answer
92 views

What is a good resource to learn about oriented matroids in the context of digraphs and optimization?

I am interested in oriented matroids in the context of directed graphs and optimization. Unfortunately, I know very little of the topic. Is there a book, article or a resource that serves as a good ...
1
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0answers
70 views

How to reduce MaxUNSAT to MaxSAT in a (almost) direct way?

In question How to reduce MaxUNSAT to MaxSAT? I was asking, how to reduce the MaxUNSAT problem to MaxSAT. With help of the given answer I could give a polynomial reduction : $MaxUNSAT \leq ...
2
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1answer
203 views

How to reduce MaxUNSAT to MaxSAT?

Is it possible to reduce MaxUNSAT to MaxSAT in a polynomial way ? When considering the MaxSAT problem, one often considers also the MinUNSAT problem, which is ...
3
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2answers
240 views

Recommended Reading for non-CS undergraduate student doing a research Project on Travelling Salesman Problem

I am an undergraduate student in Industrial Engineering. I have taken the topic of Travelling Salesman Problem as a Research Project for my final year. More specifically, I am focusing on Convex Hulls ...
6
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0answers
709 views

Minimum vertex-weight directed spanning tree where the weight function depends on the tree

Given a directed graph $G=(V,E)$ and a node $r\in V$, I need to grow a tree $T$ rooted at $r$ that has a minimum weight and spans all reachable nodes in $G$. The weight function assigns a non-...
8
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2answers
1k views

Known facets of the Travelling Salesman Problem polytope

For the branch-and-cut method, it is essential to know many facets of the polytopes generated by the problem. However, it is currently one of the hardest problems to actually calculate all facets of ...
1
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1answer
50 views

Produce decision version of the problem

An optimisation problem requires minimising some function $f(x)$, where $x$ is a vector of integers. What is the corresponding decision version of the problem?
15
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4answers
6k views

Given a set of sets, find the smallest set(s) containing at least one element from each set

Given a set $\mathbf{S}$ of sets, I’d like to find a set $M$ such that every set $S$ in $\mathbf{S}$ contains at least one element of $M$. I’d also like $M$ to contain as few elements as possible ...
11
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0answers
709 views

Fast algorithm for max-convolution with concave functions?

I'm interested in a discrete max-convolution problem, which is to compute $$r(c) = \max_{x | x \ge 0, \sum_k x_k = c} \left[ \sum_{k=1} f_k(x_k) \right] $$ for all values $c=0, \ldots, C$, where $x=(...
5
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1answer
3k views

Optimization problem vs decision problem - reduction

Assume we have an optimization problem with function $f$ to maximize. Then, the corresponding decision problem 'Does there exist a solution with $f\ge k$ for a given $k$?' can easily be reduced to ...
4
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3answers
949 views

Assign m agents to N points by minimizing the total distance

Suppose we have $N$ fixed points (set $S$ with $|S|=N$) on the plane and $m$ agents with fixed, known initial positions ($m<N$) outside $S$. We should transfer the agents so that in our final ...
11
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2answers
1k views

Minimize the maximum component of a sum of vectors

I'd like to learn something about this optimization problem: For given non-negative whole numbers $a_{i,j,k}$, find a function $f$ minimizing the expression $$\max_k \sum_i a_{i,f(i),k}$$ An example ...
8
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2answers
7k views

Algorithm to find optimal currency denominations

Mark lives in a tiny country populated by people who tend to over-think things. One day, the king of the country decides to redesign the country's currency to make giving change more efficient. The ...
2
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2answers
3k views

Function Maximization in Java

I have a bivariate function like $ f(x,y) = \frac{1}{x^3 \sqrt{\pi}}. e^{\frac{2-x}{x^2}} . y^3 . e^{3.y \over 3-y} $ and I want to find its global maximum over a range of $ x \in [0, 200] \text{, ...
23
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2answers
2k views

Collectively pay the bill problem

There are $n$ people at a table. The $i$th person has to pay $p_i$ dollars. Some people don't have the right bills to pay exactly $p_i$, so they come up with the following algorithm. First, ...
8
votes
2answers
571 views

Minimizing the total variation of a sequence of discrete choices

My setup is something like this: I have a sequence of sets of integers $C_i (1\leq i\leq n)$, with $|C_i|$ relatively small - on the order of four or five items for all $i$. I want to choose a ...
2
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2answers
1k views

How to use dynamic programming to solve this?

Here is the question: suppose we are given x cents, the amount we want to pay, and a 6-tuple (p, n, d, q, l, t) that represents respectively the number of pennies, nickels, dimes, quarters, loonies ...
2
votes
1answer
201 views

Neighbourhood in local search metaheuristic

I cannot seem to find an answer to this question with Google, so I am going to ask here: is it required for a good neighbourhood function that it in principle (i. e. by recursively considering all ...
3
votes
1answer
466 views

Efficient bandwidth algorithm

Recently I sort of stumbled on a problem of finding an efficient topology given a weighted directed graph. Consider the following scenario: Node 1 is connected to 2,3,4 at 50 Mbps. Node 1 has 100 ...
1
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0answers
50 views

How to use greedy algorithm to solve this? [duplicate]

Possible Duplicate: How to use greedy algorithm to solve this? You are given $n$ integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ ...
6
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2answers
5k views

How to find spanning tree of a graph that minimizes the maximum edge weight?

Suppose we have a graph G. How can we find a spanning tree that minimizes the maximum weight of all the edges in the tree? I am convinced that by simply finding an MST of G would suffice, but I am ...
5
votes
1answer
1k views

Weighted subset sum problem

Given an integer sequence $\{ a_1, a_2, \ldots, a_N \}$ that has length $N$ and a fixed integer $M\leq N$, the problem is to find a subset $A =\{i_1, \dots, i_M\} \subseteq [N]$ with $1 \leq i_1 \lt ...
20
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4answers
1k views

How to use a greedy algorithm to find the non-decreasing sequence closest to the given one?

You are given n integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirement that the $b_i$'s form a non-...
4
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1answer
126 views

Need help understanding this optimization problem on graphs

Has anyone seen this problem before? It's suppose to be NP-complete. We are given vertices $V_1,\dots ,V_n$ and possible parent sets for each vertex. Each parent set has an associated cost. Let $O$ ...
7
votes
1answer
361 views

In s-t directed graph, how to find many small cuts?

Solving the maximum flow problem yields one qualified minimal cut. But I want several (maybe hundreds) small cuts as candidates. The cuts don't have to be minimum cuts, as long as they are small (in ...
6
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2answers
120 views

Optimizing a join where each table has a selection

Consider the following query: ...
2
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0answers
1k views

Golden Section, Fibonacci and Dichotomic Searches

I wonder if somebody could quickly and briefly outline some of the similarities and differences between the line search methods Golden Section Search, Fibonacci Search and Dichotomic Search. I know ...
8
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0answers
180 views

Optimizing order of graph reduction to minimize memory usage

Having extracted the data-flow in some rather large programs as directed, acyclic graphs, I'd now like to optimize the order of evaluation to minimze the maximum amount of memory used. That is, given ...
10
votes
2answers
328 views

How do I classify my emulator input optimization problem, and with which algorithm should I approach it?

Due to the nature of the question, I have to include lots of background information (because my question is: how do I narrow this down?) That said, it can be summarized (to the best of my knowledge) ...
3
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0answers
375 views

Cyclic coordinate method: how does it differ from Hook & Jeeves and Rosenbrock?

I have trouble understanding the cyclic coordinate method. How does it differ with the Hook and Jeeves method and the Rosenbrock method? From a past exam text: Describe the cyclic coordinate ...
8
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3answers
581 views

What is the name of this logistic variant of TSP?

I have a logistic problem that can be seen as a variant of $\text{TSP}$. It is so natural, I'm sure it has been studied in Operations research or something similar. Here's one way of looking at the ...
11
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1answer
955 views

Distribute objects in a cube so that they have maximum distance between each other

I'm trying to use a color camera to track multiple objects in space. Each object will have a different color and in order to be able to distinguish well between each objects I'm trying to make sure ...
1
vote
2answers
223 views

Complexity of an optimisation problem in 3D

I have a collection $P \subseteq \mathbb{R}^3$ of $N$ particles and there is a function $f : P^2 \to \mathbb{R}$. I want to find which configuration of the system minimizes the value of $f$. Can ...
5
votes
1answer
944 views

Optimizing a strictly monotone function

I am looking for algorithms to optimize a strictly monotonic function $f$ such that $f(x) < y$ $f : [a,b] \longrightarrow [c,d] \qquad \text{where } [a,b] \subset {\mathbb N}, [c,d] \subset {\...
10
votes
2answers
249 views

Ordering elements so that some elements don't come between others

Given an integer $n$ and set of triplets of distinct integers $$S \subseteq \{(i, j, k) \mid 1\le i,j,k \le n, i \neq j, j \neq k, i \neq k\},$$ find an algorithm which either finds a permutation $\pi$...
11
votes
1answer
554 views

A continuous optimization problem that reduces to TSP

Suppose I am given a finite set of points $p_1,p_2,..p_n$ in the plane, and asked to draw a twice-differentiable curve $C(P)$ through the $p_i$'s, such that its perimeter is as small as possible. ...
7
votes
1answer
1k views

How to implement the details of shotgun hill climbing to make it effective?

I am currently working on a solution to a problem for which (after a bit of research) the use of a hill climbing, and more specificly a shotgun (or random-restart) hill climbing algorithmic idea seems ...
9
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2answers
11k views

Branch and Bound explanation

I have a test about the branch and bound algorithm. I understand theoretically how this algorithm works but I couldn't find examples that illustrates how this algorithm can be implemented practically. ...
26
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2answers
8k views

Optimization version of decision problems

It is known that each optimization/search problem has an equivalent decision problem. For example the shortest path problem optimization/search version: Given an undirected unweighted graph $G ...