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4
votes
2answers
62 views

Generation of random binary trees

Given n, I want to randomly generate a binary tree (unlabelled) that has n end nodes. Could someone kindly provide a reference containing an algorithm for doing that? I attempted to do as follows: ...
6
votes
4answers
230 views

What is a good algorithm for generating random DFAs?

I am generating random DFAs to test a DFA reduction algorithm on them. The algorithm that I'm using right now is as follows: for each state $q$, for each symbol in the alphabet $c$, add $\delta (q, ...
2
votes
1answer
52 views

Mean number of edges between two equal partitions

For a random undirected graph with $n$ nodes, where each node has $k$ incident edges ($nk/2$ edges in total), the vertex set is partitioned into two sets each having $n/2$ nodes. What is the ...
3
votes
1answer
186 views

What is the probability of friendship conditioned on the number of mutual friends

Let Alice and Bob be two users chosen uniformly at random from a social network (e.g. Facebook). What is the probability that they are friends assuming that they share $k$ mutual friends? I am ...
9
votes
1answer
294 views

Number of clique in random graphs

There is a family of random graphs $G(n, p)$ with $n$ nodes (due to Gilbert). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_k$ be the number of cliques of ...