# Questions tagged [optimization]

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

1,410 questions
Filter by
Sorted by
Tagged with
285 views

### Bin packing problem or not?

Suppose I have $N$ bins and $M$ items as depicted in the figure below (3 bins and 3 items): Suppose that every bin has unit capacity and the weights of the items depend on the bins used. I want to ...
126 views

169 views

### Which potential function does this algorithm minimize or maximize?

Considering two sets $A, B$ containing some $p$-dimensional points $x \in \mathbb{R}^p$. Let $d_x^S = \min_{x' \in S \setminus \{x\}} \lVert \mathbf{x} - \mathbf{x'} \rVert$ denote the Euclidean ...
264 views

### NTP: synchronisation of time between two machines for ICMP timestamping

Some guy on the internet recommends using the same ntp server when it is required to troubleshoot asymmetric routes through ICMP, and it's somewhat important to have synchronised time between the two ...
121 views

### Scheduling optimization problem in theta(n)

I've been told it is possible to find a solution to this optimization problem in $\Theta(n)$ but I still don't know how I could do it. I did find easily a solution in $n\lg (n)$ though. I only need to ...
2k views

### Maximum subset intersection problem

Given N finite subsets of the finite universe set E, it is necessary to find the intersection which contains maxumum number of subsets. Let call this problem MSI (Maximum Subset Intersetion). Firstly ...
39 views

### Does it make sense to examine the dual of a feasbility problem?

Consider a standard feasibility problem. The goal is to examine the state of feasible solutions for $Ax=b$ to find an $x$ that satisfies some property. Does the dual of this problem tell us anything ...
2k views

117 views

### Algorithm to maximize function of subsets

Let's say I have a finite set S with, say, 1000 elements, and a function f on some subset of S. Suppose that f has no useful mathematical properties. What algorithm is most relevant in finding the ...
2k views

### Find disjoint contiguous sub-arrays in better than $\mathcal O(n^2)$

Given an array of integers. Find two disjoint contiguous sub-arrays such that the absolute difference between the sum of two sub-array is maximum. The sub-arrays should not overlap and it can not be ...
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, ...
301 views

### Is this NP-hard: min-weight n-clique in a complete n-partite graph

I have a complete $n$-partite graph, where each partite set has $n$ vertices (yes it's also $n$), so the graph has $n^2$ vertices in total. My problem is to find a minimum weight $n$-clique in the ...
98 views

### Multicommodity circulation formulation

On the circulation problem page on wikipedia, the multicommodity circulation problem formulation seems to be insufficient, since we can just set all but one flow to $0$, and reduce it to a circulation ...