Questions tagged [disjoint-sets]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
0answers
12 views

Algorithm to check if a family contains two disjoint sets

Let $\mathcal F_1$ and $\mathcal F_2$ be a families of subsets of $\{1,\dots, m\}$. Such that $|\mathcal F_1| = n_1$ and $|\mathcal F_2| = n_2$. I would like to check if there is $f_1\in \mathcal F_1$...
1
vote
1answer
56 views

Check if two graphs are edge-disjoint

Two undirected graphs $G$ and $H$ on the vertices $1,2,\ldots,n$ are disjoint if the intersection of their edge sets is empty. Assume both $G$ and $H$ are represented by adjacency matrices. ...
0
votes
0answers
39 views

Augment the tree data structure for disjoint sets to implement the PRINT operation

Consider the following new operation for disjoint sets PRINT(x): print every element in S_x the set containing x One Approach that I found but couldn't figure out completely : In addition to tree we ...
0
votes
1answer
31 views

walk / traverse a disjoint set that has union rank and path compression

I'm studying CLRS section 21.3, which introduces a union rank + path-compressed implementation of disjoint set. The implementations of MAKE-SET, UNION, LINK, and FIND-SET on p 571 of the book all work ...
1
vote
1answer
17 views

Definition of Disjointness for binary strings

Basically, most of the definition for disjointness are such that $DISJ(A, B) = 1$ if $A \cap B = \emptyset $ and $DISJ(A, B) = 0$ for other case. My confusion is how is $0$'s influence in here. For ...
3
votes
0answers
35 views

What's the best non-amortized disjoint set?

In practice, the amortized O(α(n)) data structure is good for every case. But if I want to be pedantic and require each operation to be under a certain time complexity, what's the currently known best ...
1
vote
1answer
97 views

Difficulty in few steps in proof of "Amortized cost of $\text{Find-Set}$ operation is $\Theta(\alpha(n))$"assuming union by rank, path compression

I was reading the section of data structures for disjoint sets from the text Introduction to Algorithms by Cormen et. al .I faced difficulty in understanding few steps in the proof of the lemma as ...
2
votes
1answer
1k views

Runtime difference bewteen Union by Rank and Union by Size for union-find

I was studying Union Find, and according to Wikipedia, there are 2 types of union: union by rank and Union by size. My question is, what is the runtime difference between the two (if any)? Intuitively,...
1
vote
1answer
91 views

Amortized analysis for disjoint sets' find-set(x) function (from CLRS)

I start off by apologizing for the fact that I don't really know how to use latex/markdown. My question, however, is directly from the Introduction To Algorithms book by Cormen et al. The topic ...