1
vote
2answers
170 views

Prove that if all edge-costs are different, then there is only one cheapest tree.

Prove that if all edge-costs are different, then there is only one cheapest tree (minimum spanning tree). (Use contradiction and make sure to keep track of the costs of the different trees involved.) ...
1
vote
2answers
54 views

When trees are the answer: what is the question?

For which optimization problems are (abstract) trees the best solution? E.g. binary search trees are somehow optimal data structures for quick search. But why for example do botanic trees grow as ...
2
votes
2answers
46 views

Finding an Isolated Maximum subset of tree

Given an Oriented Tree T(V,E) with n nodes, each node have an non-negative number (the numbers are not related to nodes order). A subgroup Z of V called an Isolated if it doesn't include two nodes ...
0
votes
0answers
17 views

Which cut-off for collapsing this tree?

I have a Newick tree that is built by comparing similarity (euclidean distance) of Position Weight Matrices (PWMs or PSSMs) of DNA regulatory motifs that are ~5-9 bp long sequences. An interactive ...
2
votes
1answer
2k views

Show that Minimum Spanning Tree is unique

Show that MST is unique in case the edge weights are pairwise different $(w(e)\neq w(f) \text{ for } e\neq f)$. I thought that the proof can be done for example by contradiction, saying that we ...
0
votes
0answers
49 views

An MST-like problem with vertex selection

Consider a planar pointset in a rectangle, where every point has a color (an integer label). We need to select one point of every color, so as to minimize the cost of a planar MST of selected points ...