0

Disjoint sets problem

Let A and B be two sets , are they disjoint ?

Question

Prove that any algorithm for solving disjoint sets takes at least O(nlog n).

The idea I thought about is to prove that sorting can be reduced to disjoint set problem.

How do I do that ?

advocateofnone
  • 2,527
  • 3
  • 17
  • 39
Zaid Alyafeai
  • 155
  • 1
  • 13

1 Answers1

1

I don't really understand your question exactly , there are some pretty fast linear sorting algorithms that take O(n) like radix bucket and counting sorts which maybe suitable depending on the nature of your input .

Your question was if you can reduce IN POLYNOMIAL TIME sorting to disjoint sets,and even in taht case this could very possibly not solve your problem because if you can reduce sorting to disjoint sets in polynomial time it would mean that disjoint sets is atleast as hard as sorting which means that an algorithm solving disjoint sets might take longer than the algorithm for solving sorting .

Gherbi Hicham
  • 2,416
  • 4
  • 26
  • 41
  • What is meant by sorting is element-comparison based algorithms. Of course , disjoint sets problem is at leas as hard as sorting. – Zaid Alyafeai Feb 13 '15 at 21:04