A problem in combinatorial optimization. Given a set of items with both weight and value, determine the number of each item to include in a collection so that the total weight is at most a given limit and the value of the collection is maximized.

learn more… | top users | synonyms

2
votes
1answer
33 views

Why is Ibarra Kim for 0/1 knapsack an fully polynomial time approximation scheme (FPTAS)?

According to one of my CS lectures, there is an fully polynomial time approximation scheme for the 0/1 Knapsack problem. A first version was developed by Ibarra and Kim, but there are several improved ...
4
votes
0answers
64 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 ...
0
votes
1answer
61 views

Dynamic Programming Solution to 0,1 KnapSack Problem

I am trying to understand the DP solution to the basic knapsack problem.However even after reading through a variety of tutorials ,its still beyond my comprehension.I am taking an algorithmics course ...
1
vote
2answers
129 views

Correctness proof of greedy algorithm for 0-1 knapsack problem

We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an ...
1
vote
0answers
67 views

Integer knapsack problem with bounded weights

Is there any literature about the complexity of the integer knapsack problem with bounded weights? To make it clear, I want an optimal solution to the following problem: $\max \sum_{i=1}^k c_i \cdot ...
0
votes
0answers
65 views

Is this problem a knapsack problem?

I have the following problem. Maximize $\sum\limits_{m=1}^M\sum\limits_{n=1}^N x_{mn}$ subject to: $\sum\limits_{\substack{m^\prime=1\\ m^\prime \neq m}}^M\sum\limits_{\substack{n^\prime=1\\ ...
2
votes
0answers
30 views

Adversarial bin packing

An adversary gives you a set of items whose total size is $x$ (he gets to choose how $x$ is distributed. e.g. there may be $k-1$ items of size $\frac{x}{k}$ and 2 items of size $\frac{x}{2k}$). The ...
2
votes
1answer
485 views

Variant of the knapsack problem

How would you approach the knapsack problem in a dynamic programming situation if you now have to limit the number of item in the knapsack by a constant $p$ ? This is the same problem (max weight of ...
2
votes
1answer
1k views

Confusion related to time complexity of dynamic programming algorithm for knapsack problem

I have this confusion related to the time complexity of the algorithm solving the knapsack problem using dynamic programming I didn't get how the time complexity of the algorithm came out to be ...
1
vote
3answers
607 views

Find non-overlapping scheduled jobs with maximum cost

Given a set of n jobs with [start time, end time, cost] find a subset so that no 2 jobs overlap and the cost is maximum. Now I'm not sure if a greedy algorithm will do the trick. That is, sort by ...
-6
votes
1answer
211 views

Maximizing profit

Problem: Given 11 numbers {N1,N2,N3,N4,N5,N6,N7,N8,N9,N10,N11} where N1:amount of profit from product A N2:amount of profit from Product B N3:amount of ...
3
votes
0answers
210 views

Dynamic Knapsack Problem - Algorithms and References

I don't know the right name for this problem, or if there is a name, but it is inspired by my initial interpretation of the title of this question (my question is very different, so the link may be ...
0
votes
1answer
266 views

Knapsack problem with multiple constraints

I am unsure if I have even identified the problem correctly, but reading up on knapsack problem seems the closest to what I am trying to solve: A cook has $k$ ingredients of $p$ quantities. Given ...
3
votes
2answers
226 views

Algorithm to pack any small boxes into a big box

I have a container with a certain dimension. A number of small boxes that may be different in size is to be packed into the container. How to arrange the small boxes such that the container contains ...
2
votes
0answers
311 views

Relations between the knapsack problem, the bin packing problem, and the set packing problem?

I wonder what relations are between the knapsack problem, the bin packing problem and the set packing problem? From their mathematical formulations, I don't see the first two belong to the third one ...
3
votes
1answer
185 views

Adjacent house , dynamic programming problem

I have to be honest this is a homework problem, but I just need to discuss this with some one. The problem is there is a row of n houses, with different profit e.g profit1 for house 1, it can be ...
3
votes
0answers
149 views

Reduction from knapsack problem to Integer relation that equals one

My question is related to the Integer Relation Detection Problem which can be formulated as: $\qquad a_1x_1 + a_2x_2 + \cdots + a_nx_n = 0$ Where $\forall i. a_i\in\mathbb{Z} \land a_i<c \land ...
15
votes
0answers
264 views

Subset sum problem with many divisibility conditions

Let $S$ be a set of natural numbers. We consider $S$ under the divisibility partial order, i.e. $s_1 \leq s_2 \iff s_1 \mid s_2$. Let $\qquad \displaystyle \alpha(S) = \max \{|V| \mid V\subseteq S, ...
1
vote
2answers
156 views

From FACTOR To KNAPSACK

If there were an algorithm that factored in polynomial time by means of examining each possible factor of a complex number efficiently, could one not also use this algorithm to solve unbounded ...
7
votes
2answers
1k views

Algorithms for two and three dimensional Knapsack

I know that the 2D and 3D Knapsack problems are NPC, but is there any way to solve them in reasonable time if the instances are not very complicated? Would dynamic programming work? By 2D (3D) ...