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12 votes
0 answers
530 views

Finding the diameter of an unknown tree: Is BFS optimal?

I'm interested on the following nice problem that is somewhat standard in CS, but I was surprised on the lack of references on the optimal algorithm to this problem. Ana and Banana plays the ...
Curious's user avatar
  • 63
7 votes
1 answer
222 views

Bound on queries to a tree with unusual probabilities

Consider a tree $\mathcal{T}(r) = (V,E)$ rooted at $r \in V$. Let $\kappa_r: V \longrightarrow [0,1]$ such that $\sum_{v \in V} \kappa_r(v)^2 = 1$. Furthermore, for any given vertex $v \neq r$, $\...
Michael Jarret's user avatar
4 votes
1 answer
672 views

Algorithm to generate free unlabelled trees uniformly at random

I am implementing an algorithm to generate free unlabelled trees uniformly at random (uar). For this I found this paper by Herbert S. Wilf (The uniform selection of trees. 1981. In Journal of ...
Lluís Alemany-Puig's user avatar
2 votes
1 answer
181 views

What is the relation between size of maximum clique and branchwidth?

Let $bw(G)$ be the branchwidth of graph $G$ and $\omega(G)$ be the size of maximum clique in $G$. I think the following inequality holds: $$ \omega(G)\leq bw(G) $$ Intuition: Assume (in reverse of ...
Omid Ebrahimi's user avatar
2 votes
0 answers
110 views

Does there exist a linear-time algorithm to find a basis of the null space of the adjacency matrix of a tree?

I am working on a decomposition of trees based on the null space of the adjacency matrix of the tree. Most algorithm on trees are really fast. The decomposition could give some algorithms to find ...
Daniel Alejandro Jaume's user avatar
1 vote
1 answer
220 views

Construct a rooted plane tree with nodes labelled

A rooted tree is a tree with a distinguished root node. When a rooted tree is embedded in a plane, a cyclic ordering is induced on the subtrees of the root. Such trees are called rooted plane trees. ...
Xin Zhang's user avatar
  • 1,190
1 vote
0 answers
52 views

How can we hang the weighted trees so that vertices nearer to root (based on distances, not hop count) lie in upper levels?

I have a set of edge weighted trees, each tree rooted at some vertex. Consider these trees are hung from the roots and vertices are arranged in some levels. I wish to design an algorithm (...
Hemraj Raikwar's user avatar
1 vote
0 answers
82 views

Treewidth problem equivalence

Say we are solving a tree decomposition problem, e.g. given a graph $G = (V, E)$ we try to find a chordal graph $H$ such that $V(H) = V(G)$, $E(G) \in E(H)$ and the maximal clique in $H$ is minimal ...
qbit-'s user avatar
  • 71
0 votes
1 answer
181 views

Bound on queries to a tree with unusual probabilties -- follow-up

This question follows up on Bound on queries to a tree with unusual probabilities, where @fedja was able to disprove my conjecture under only constraints (1-4) below. I restate the relevant facts here ...
Michael Jarret's user avatar