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
34 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
5 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 ...
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0answers
13 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
20 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
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1answer
22 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 ...
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0answers
16 views

A* search.How it works and its algorithms in artificial intelligence [on hold]

how does the A* search work with an illustration of a graph?
2
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1answer
21 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 ...
1
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0answers
13 views

Software to solve Semidefinite Programs [migrated]

I'm looking for software to solve a particular semidefinite program. The constraints are specified as a set of linear constraints on pairwise products of the components of some vector $(x^i)_i \in ...
5
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1answer
331 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
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1answer
44 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
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1answer
147 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
49 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, ...
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0answers
12 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
157 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
61 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
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1answer
18 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 ...
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1answer
44 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 ...
3
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2answers
57 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
13 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
51 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
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0answers
60 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
41 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
165 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
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1answer
106 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
60 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
59 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
120 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
50 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
49 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
270 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
88 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
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0answers
56 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
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0answers
65 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 ...
3
votes
1answer
56 views

Optimal way for grouping events

I am creating an event notification system. Each event has a user and a subject, such that, 'user did event to the subject'. Now while presenting these the events need to be grouped. All the events ...
4
votes
3answers
96 views

Most time-optimal parallel algorithms to calculate the determinant and inverse of a matrix

I am writing a numeric library to exploit GPU massive parallelism and one of the implemented primitives is a matrix class. Naturally I require a determinant and inverse function for this class and I ...
4
votes
1answer
56 views

Algorithm to find most nodes in distinct cycles

I am trying to design a program where people trade objects within a fixed set of objects. They offer a single product, and designate a set of products they are willing to accept for that product. ...
-1
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1answer
65 views

Board cutting problem

To cut a wooden board, a sawmill charges proportional to the length of the board. The cost of cutting a single board into many smaller boards will thus depend on the order of the cuts. As an example, ...
1
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0answers
72 views

Massively parallel unconstrained minimization; f is a black box

My objective function, f, is complicated and embodies several disparate constraints I want my simulation to optimize simultaneously. So I can't really even assume it's continuous; it is probably ...
3
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0answers
72 views

Formulating Integer Program for passing packages on a cycle

Can't seem to figure out the IP formulation for this. Question Suppose there are $n$ people connected in a circular fashion as demonstrated by the diagram. Individuals need to send packages to each ...
3
votes
2answers
99 views

Pick a subgraph that maximizes the total cost of min-spanning tree among all subgraphs of the same size

There is a complete graph $G$ with $n$ vertices and each edge has a distinct weight. Is there an efficient (not necessarily optimal) algorithm to select $k$ vertices from the graph $G$, such that the ...
3
votes
1answer
89 views

Variable Length Encoding of Integers

I was just researching Fibonacci encoding of integers. Numbers are encoded in binary and where no two consecutive bits are equal to 1 - other than to terminate the number. Now other schemes are ...
2
votes
1answer
48 views

Progressive discrete multifunction optimization

I have a set of functions $F$. The functions effectively take a set $S$ that is always a subset of a global set of all possible values $G$, where $|G|>1000$. (alternatively, they could take a ...
3
votes
1answer
47 views

Does FACTORING have optimal substructure or analog to it?

Is there any approach to FACTORING that can leverage optimal substructure allowing the problem to be decomposed into smaller subproblems? That is, perhaps being unnecessarily verbose, until an easily ...
0
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1answer
97 views

Looking for an algorithm to solve a specific Vehicle Routing Problem

I am trying to figure out a way to create routes for trucks to complete a list of orders(drops/stops), while minimizing distance traveled. There is only ever 1 company warehouse in the area. The ...
1
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0answers
45 views

Palstar algorithm Dynamic Programming getting the result [closed]

I recently started to read abour dynamic programming, and I am doing an exercise on it. The problem to solve: Given a String, find the least amount of palindromes it can be split into, and print out ...
1
vote
1answer
32 views

Text search by first order formula

I am searching for substrings that satisfy a given first order formula in a moderately sized text. The formula is made out of usual $\wedge, \neg, \exists$ and predicates ...