I'm now learning Kademlia network by reading the classical paper Kademlia: A Peer-to-peer Information System Based on the XOR Metric. I want to understand the complexity of its operation but still cannot figure it out.

In the

*3 Sketch of proof*section, the paper gives two definitions:

1.

**Depth of a node (h)**: 160 − i, where i is the smallest index of a non-empty bucket

2.

**Node y’s bucket height in node x**: the index of the bucket into which x would insert y minus the index of x’s

**least significant empty bucket**.

And three conclusions:

1. With overwhelming probability the height of a any given node will be within a constant of log n for a system with n nodes.

2. The bucket height of the closest node to an ID in the kth-closest node will likely be within a constant of

**log k**.

3. If none of this node’s h

**most significant k-buckets**is empty, the lookup procedure will find a node half as close (or rather whose distance is one bit shorter) in each step, and thus turn up the node in

**h − log k**steps.

So my questions are:

1. What is "

**least significant empty bucket**" and "

**most significant k-buckets**"?

2. How to explain the

**depth**and

**bucket height**in visual way?

3. How to understand the second and third conclusions, say, why

**log k**and

**h - log k**?

Thanks.