Find Node Operation in Kadelmia: why does it pick elements from bucket instead of looking through the entire routing table?

Question

The first step of the find node operation is as follows (as described in the paper):

The lookup initiator starts by picking α nodes from its closest non-empty k-bucket (or, if that bucket has fewer than α entries, it just takes the α closest nodes it knows of).

Why does it pick the elements directly from the bucket, as opposed to looking for k closest elements across all elements in all buckets? I believe the latter is what happens in step 2 of the algorithm, and can be seen in the visualization here.

Answer 1

I guess this is simply under the assumption that α ≤ k. Under that condition you will get the k closest nodes automatically from the closest bucket, or if the bucket contains fewer than α nodes the bracketed condition will apply

(or, if that bucket has fewer than α entries, it just takes the α closest nodes it knows of)

Also note that you're looking at the pre-proceedings version of the paper, which does not contain the full kademlia description. You can find the full paper here.