Algorithm: Removing as few elements as possible from a set in order to enforce no subsets.

Posted by phimuemue on Stack Overflow See other posts from Stack Overflow or by phimuemue
Published on 2010-05-19T11:59:05Z Indexed on 2010/05/19 12:20 UTC
Read the original article Hit count: 171

Filed under:

algorithm

|

subset

Hello, I got a problem which I do not know how to solve:

I have a set of sets A = {A_1, A_2, ..., A_n} and I have a set B.

The target now is to remove as few elements as possible from B (creating B'), such that, after removing the elements for all 1 <= i <= n, A_i is not a subset of B'.

For example, if we have A_1 = {1,2}, A_2 = {1,3,4}, A_3={2,5}, and B={1,2,3,4,5}, we could e.g. remove 1 and 2 from B (that would yield B'={3,4,5}, which is not a superset of one of the A_i).

Does anybody know an algorithm for determining the (minimal number of) elements to be removed?

© Stack Overflow or respective owner

Related posts about algorithm

Jpeg Algorithm vs BMP Algorithm?

as seen on Super User - Search for 'Super User'
I'm just wonder, what the differences are between creating a BMP file algorithm and JPG file algorithm ? If you know the others images' format algorithm, please post them. Thanks. >>> More
word disambiguation algorithm (Lesk algorithm)

as seen on Stack Overflow - Search for 'Stack Overflow'
Hii.. Can anybody help me to find an algorithm in Java code to find synonyms of a search word based on the context and I want to implement the algorithm with WordNet database. For example, "I am running a Java program". From the context, I want to find the synonyms for the word "running", but the… >>> More
Search algorithm (with a sort algorithm already implemented)

as seen on Stack Overflow - Search for 'Stack Overflow'
Hello, Im doing a Java application and Im facing some doubts in which concerns performance. I have a PriorityQueue which guarantees me the element removed is the one with greater priority. That PriorityQueue has instances of class Event (which implements Comparable interface). Each Event is associated… >>> More
Is there any algorithm for finding LINES by PIXEL COLORS on picture?

as seen on Stack Overflow - Search for 'Stack Overflow'
So I have Image like this I want to get something like this (I hevent drawn all lines I want but I hope you can get my idea) I need algorithm for finding all straight lines on it by just reading colors of pixels. No hard math, no Haar, no Hough. Some algorithm which would be based on points… >>> More
collsion issues with quadtree [on hold]

as seen on Game Development - Search for 'Game Development'
So i implemented a Quad tree in Java for my 2D game and everything works fine except for when i run my collision detection algorithm, which checks if a object has hit another object and which side it hit.My problem is 80% of the time the collision algorithm works but sometimes the objects just go… >>> More

Related posts about subset

The subsets-sum problem and the solvability of NP-complete problems

as seen on Stack Overflow - Search for 'Stack Overflow'
I was reading about the subset-sums problem when I came up with what appears to be a general-purpose algorithm for solving it: (defun subset-contains-sum (set sum) (let ((subsets) (new-subset) (new-sum)) (dolist (element set) (dolist (subset-sum subsets) (setf… >>> More
Sitewide 301 Redirect with a subset of different redirects

as seen on Stack Overflow - Search for 'Stack Overflow'
I am trying to make a sitewide 301 redirect for a site with around 400 pages but also have a subset of about 10 individual pages that don't follow the sitewide redirect and should point somewhere else. Any ideas how to format such redirect rules so the sitewide redirect doesnt conflict with the… >>> More
Django Admin: Detect if a subset of an object fields has changed and which of them

as seen on Stack Overflow - Search for 'Stack Overflow'
I need to detect when some of the fields of certain model have changed in the admin, to later send notifications depending on which fields changed and previous/current values of those fields. I tried using a ModelForm and overriding the save() method, but the form's self.cleaned_data and seld.instance… >>> More
Subset a data.frame by list and apply function on each part, by rows

as seen on Stack Overflow - Search for 'Stack Overflow'
This may seem as a typical plyr problem, but I have something different in mind. Here's the function that I want to optimize (skip the for loop). # dummy data set.seed(1985) lst <- list(a=1:10, b=11:15, c=16:20) m <- matrix(round(runif(200, 1, 7)), 10) m <- as.data.frame(m) dfsub <-… >>> More
Is information a subset of data?

as seen on Stack Overflow - Search for 'Stack Overflow'
I apologize as I don't know whether this is more of a math question that belongs on mathoverflow or if it's a computer science question that belongs here. That said, I believe I understand the fundamental difference between data, information, and knowledge. My understanding is that information… >>> More