All Questions
9 questions
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 ...
- 63
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 (...
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.
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- 1,190
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 ...
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 ...
- 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 ...
- 209
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 $v \neq r$, $\...
- 209
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 ...
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 ...
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