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

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1answer
12 views

What is the optimal strategy for filtering a large collection of items with multiple filter functions?

I have a large collection of items, and a list of independent filters (boolean functions). I want to find the collection of items that pass all of my filters as quickly as possible. This must involve ...
5
votes
1answer
68 views

Find set of points with maximum distance inside given intervals?

Let $A$ be a set of $n$ closed intervals, $I_i$, with both extremes positive integers. Is there an efficient algorithm to find a set of $n$ points $P_i$, with $P_i \in I_i$, such that the minimum ...
5
votes
3answers
174 views

How to choose the maximum number of nodes (with constraints) from a graph

Consider a connected undirected acyclic graph $G$ with $n$ nodes and $n-1$ edges. The nodes have non-negative integer weights less than $n$. A positive integer $x$ is given and you want to choose at ...
13
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2answers
171 views
+150

How many cookies in the cookie box? — Tiling stars

With holiday season coming up I decided to make some cinnamon stars. That was fun (and the result tasty), but my inner nerd cringed when I put the first tray of stars in the box and they would not fit ...
-2
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0answers
32 views

Assigning cars to maximise profit

Dynamic Programming- The Car Rental Agency has four cars available at the Central Headquarter. There are requests from three marketing outlets for one car apiece. Based on customer satisfaction, ...
0
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2answers
43 views

Genetic Algorithm Minimum Population Size

Is there a minimum limit to a pool (population) size when using the genetic algorithm to solve an optimization problem? For example a population of size 2.
0
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2answers
48 views

find the optimal combination [closed]

Suppose I have these values with weights -- $$ x_1 = 2\\ x_2 = 4\\ x_3 = 5\\ $$ There is no negative or $0$ value. I need to find $2$ element subset with maximum value computed from a function ...
1
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0answers
23 views

How should I choose the neighborhood structure for simulated annealing for my problem?

There are $n$ students and $m$ courses. Each student $i$ wants to attend a subset $C_i \subseteq \{1,\ldots,m\}$ of the courses. There are $k$ time slots on a weekly schedule. The goal is to select a ...
0
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0answers
13 views

Prove a characterisation of the minimum directed cycle mean cost

Let $\mathcal G = (\mathcal V, \mathcal A)$ be directed graph with associated edge costs $c_{i,j}$ that has at least one directed cycle. Define the directed cycle mean cost to be $\frac {\{\text {sum ...
3
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1answer
78 views

Given an optimal solution to the LP, show how it can be used to construct a directed cycle with minimal directed cycle mean cost

Let $\mathcal G = (\mathcal V, \mathcal A)$ be directed graph with associated edge costs $c_{i,j}$ that has at least one directed cycle. Define the directed cycle mean cost to be $\frac {\{\text {sum ...
1
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0answers
33 views

Set of points partitioned into max subsets of size N with no intersecting edges

Question Given a set of X kd (k-dimensional) points, find the maximum number of closed subsets of these points such that no subsets (each forming a convex hull) overlap or intersect, that each subset ...
3
votes
2answers
42 views

Find a MST such that it's mostly red (original graph's edges are colored red and blue)

Consider the following problem: Given a simple, strongly-connected, weighted graph G=(V,E), of which every edge is colored either red or blue (in addition to having a numeric weight). Find an ...
1
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1answer
85 views

Minimize sum of squared error

I have an array of real numbers, I want to partition them into k sets. In each set, I calculate the sum of squared error. Then, I add up all the sum of squared error for all the set. I want to ...
0
votes
0answers
23 views

How can I solve this constrained assignment problem?

The assignment problem is defined as follows: There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on ...
8
votes
0answers
49 views

Minimal cumulative set sum [migrated]

Consider this problem: Given a list of finite sets, find an ordering $s_1, s_2, s_3, \ldots$ that minimizes $|s_1| + |s_1 \cup s_2| + |s_1 \cup s_2 \cup s_3| + \ldots$. Are there known algorithms ...
1
vote
1answer
55 views

Formulate the Marriage Problem into a Maximum-flow problem (Graph theory)

Suppose I have $M=\{1,\ldots, n\}$ men and $W = \{1, \ldots, n\}$ women and $B =\{1, \ldots, m\}$ brokers, such that each broker knows a subset of $M \times W$ and for each pair in this subset a ...
1
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0answers
8 views

The most efficient way of finding/storing neighbourhood info during octree creation

Currently I have a program which at some point creates an octree and AFTER the creation loops through all the nodes, for every node (O(n2/2)) and thus finds the neighbours, by a brute-force box-box ...
1
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0answers
16 views

Introduction to Linear Optimization: Driving the artificial variables out of the basis (case: no entries in the $j$-row are nonzero)

Reading the book Introduction to Linear Optimization by Bertsimas and Tsiklisis, I've come across the following subject: Driving the artificial variables out of the basis. The description is as ...
1
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0answers
24 views

Separate points inside set

I have a set of points corresponding to pictures on map. Because location precision is not very important, I want to separate the points inside the set to maximize the summed up distance between the ...
1
vote
1answer
23 views

Why would this Semidefinite Program be Dual Infeasible?

My semidefinite program amounts to two constraints, $L_1 = 0$ and $L_2 = 0$ where $L_i$ are linear functions of my variables $x_{ij}$ with the additional constraint that the $x_{ij}$ matrix is ...
2
votes
1answer
27 views

How can the max-flow and min-cut problems, if dual to one another, both have unbounded optimal value?

The max-flow min-cut theorem states that the value of the maximum flow is equal to the minimum cut capacity. It is possible that the max-flow and min-cut is equal to $\infty$. However, reading ...
5
votes
1answer
340 views

What is the formal name for this algorithmic problem?

I'm doing some work on a problem and I'm finding it difficult to research it with out the actual name of the problem, since the problem I'm working on gives it it's own abstraction. The problem is ...
3
votes
1answer
48 views

What is the Certificate for Set Cover?

Consider the set cover problem: given a collection of sets ${\cal U}$ whose elements come from $\{1, \ldots, m\}$ find the smallest number of sets in ${\cal U}$ whose union is all of $\{1, \ldots, ...
2
votes
1answer
171 views

Is Differential Evolution a genetic algorithm?

I am trying to classify the Differential Evolution algorithm according to the framework in the book: Introduction to Evolutionary Computing The authors classify the field of evolutionary ...
2
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1answer
50 views

Is ecological bin packing NP-hard?

The ACM Contest Problem 102 (HTML or PDF) can be paraphrased as: Given 3 bins each containing possibly different number of bottles of 3 colors, move the bottles so that there is one color per bin, ...
0
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0answers
14 views

Is current hardware adequate for neural networks ? Are there more adequate hardware?

If you have a large neural network and you use more than 10 cores, it will be limited by the fact each core will need to read/write data that it can't access fast enough. I've read about some samsung ...
4
votes
1answer
161 views

Fixed size set to contain the maximum number of given sets

I asked this question in SO here I have about 1000 sets of size <=5 containing numbers 1 to 100. {1}, {4}, {1,3}, {3,5,6}, {4,5,6,7}, {5,25,42,67,100} ... ...
2
votes
1answer
36 views

What algorithm is suitable for very small scale, time dependent optimization?

I have a time-dependent (dynamic) optimization problem: $$ f_t : [0;1]^2 \mapsto \mathbb{R}^+; t \in [1, \dots, n] $$ $f_t$ is to be maximized. That is for each $t$ I would like to find a relatively ...
1
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0answers
13 views

State of art quadratic knacksack algorithms

What is the current status to quadratic knacksack problem? Say, how many variables can the state of art solver handle? Thank you.
-1
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1answer
75 views

how to improve solution generated by greedy method for 0-1 knapsack? [closed]

I am working on 0-1 knapsack using greedy method, I have some problem in it. It's already proved that solution generated by greedy method for 0-1 knapsack is may or may not be optimal. If solution ...
4
votes
1answer
20 views

How to order objects to minimize non-adjacency cost

I have an array of $N$ objects, each appearing exactly once. I also have a list of $M$ pairs of the objects. Each pair has a "non-adjacency cost" that must be paid if the two objects are not adjacent ...
-2
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1answer
48 views

Dynamic Programming Approach

when we are trying to solve a problem with dynamic programming. we have to follow some general steps characterize the solution structure Recursively define optimal solution compute the value from ...
4
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2answers
65 views

Largest N squares that fit in a rectangle

I was working on a project and I needed to display N squares inside a rectangle area and I want them to be as large as possible, no rotations. More formally: Problem: Given N equal-sized squares and ...
-1
votes
1answer
16 views

What algorithms solve the minimun multidimensional multidemand 0-1 knapsack problem?

I've found an heuristic algorithm[scatter search] that solves the common version of MDMKP(MultiDemand Multidimensional Knapsack Problem)[the one that maximizes] but what about the minimize version? is ...
1
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0answers
20 views

Given a set of sets and a storage area, find an order that minimizes the sum of the differences between each set and the storage area

This problem is based on an order picking problem with a forward area. The problem description is as follows. We have a warehouse with a set of items $I$ and a forward area $F$ of size $k$. Each ...
3
votes
1answer
54 views

Maximum minimal set coverage

Suppose we are given a universal set $U$ and a family of subsets of $U$, denoted by $F$ (elements in $F$ are subsets of $U$). We assume that all elements in $F$ can cover $U$, i.e., $U\subseteq ...
2
votes
0answers
65 views

Job scheduling problem in O(n log n)

There are $n \leq 10^6$ kinds of cake layers, and for each kind we have a machine capable of baking it in one unit of time and nothing more. Now, a cake is a sequence of layers, more specificly a ...
1
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1answer
42 views

Assuming finite optimal cost of a specific LP, find an optimal solution directly

Minimize $\sum^n_{i=1} c_i x_i$ subject to $\sum^n_{i=1} a_i x_i = b$ (a single constraint), $x_i \ge 0$. Derive a simple test for feasibility of this problem Assuming the optimal cost is ...
4
votes
3answers
168 views

Cutting equal sticks from different sticks

You have $n$ sticks of arbitrary lengths, not necessarily integral. By cutting some sticks, you want to get $k<n$ sticks such that: All $k$ sticks have the same length; All $k$ sticks are at ...
0
votes
1answer
113 views

Algorithm for finding best combination of elements

Say I have a very large, arbitrary number of variables, each of which I can assign to be type A, B, or C. The types come with expenses: Type A's are the least expensive, and C's are the most ...
3
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0answers
61 views

What is this discrete/combinatorial optimization problem?

There exist very rich literature on discrete optimization problems such as variants of knapsack problem, traveling salesman problem, orienteering problem, tourist trip design problem and etc. ...
2
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0answers
61 views

Optimal vehicle routing on map

Currently I am developing a piece of software that solves the vehicle routing problem. The task is the following: I have several vehicles along the town I have lots of destination points along the ...
4
votes
1answer
125 views

Maximum sum subset of an array with an extra condition

We are given numbers $n \leq 200$, $k \leq 10$ and an array of $3n$ positive integers not greater than $10^6$. Find the maximum possible sum of a subset of elements of this array, such that in every ...
0
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0answers
51 views

A Fast Algorithm to Approximately Solve a Modified Version of The Thomson Problem

The problem I'm trying to solve is the same as the Thomson Problem except that the objective isn't to minimize $$ U(N) = \sum_{i < j} \frac{1}{r_{ij}}, $$ given $r_{ij} = |\mathbf{r_i} - ...
3
votes
0answers
55 views

Efficient update to rational flow network?

Once we've computed the max flow in a flow network with integral capacities, we can change one of its edges' capacity by a unit and recompute a maxflow in linear time using BFS. Is there something ...
11
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2answers
309 views

Algorithm to distribute items “evenly”

I'm searching for an algorithm to distribute values from a list so that the resulting list is as "balanced" or "evenly distributed" as possible (in quotes because I'm not sure these are the best ways ...
0
votes
1answer
93 views

NP-hardness proof, what is wrong with it?

My question is the following: If we have a problem divided into two versions, weighted and unweighted. Can we prove that the unweighted problem is NP-hard from the fact that the weighted problem is ...
0
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0answers
37 views

What is the global function we are trying to Optimise with Clustering Algorithms?

I am doing some reading (and implementation) of some Clustering Algorithms. First I started with the well known K-Mean algorithm and implemented it directly from a paper. Got a kind of decent ...
3
votes
0answers
61 views

What kind of scheduling problem is this?

I'm working on a problem and would like to do some research on similar problems to help refine my approach. Can anyone help me identify what kind of problem this is or, at least, what kind of ...
4
votes
0answers
67 views

Rate Pooling Optimization Algorythim

I have thousands of wireless LTE hotspots. Each month I need to assign each hotspot a rate plan. Each hotspot uses some amount of data in a month (represented in megabytes). Each rate plan has some ...