Question

Consider the following simplified BitTorrent scenario. There is a swarm of 128peers and, during the time in question, no peers join or leave the swarm. It takes a peer 1 unit of time to upload or download a piece, during which time it can only do one or the other. Initially, one peer has the whole file and the others have nothing. If the swarm’s target file consists of only 1 piece, what is the minimum time necessary for all the peers to obtain the file? Ignore all but upload/ download time.

Answer 1

Solution

Each and every peer will have the file after n time units

That means there is a swarm of 128 peers

Convert into 2 power

128=2 ⁷

So

All the peers will have the file after 7 time units

During each time unit, each and every peer with the piece can transmit it to one peer without that piece

so number of peers with the piece doubles with each time unit

2 ⁰ =1 at a time 0 unit

2 ¹=2 at a time 1 unit

2 ²=4 at a time 2 unit

2 ³=8 at a time 3 unit

2 ⁴= 16 at a time 4 unit

2 ⁵=32 at a time 5 unit

2 ⁶=64 at a time 6 unit

up to

2 ⁷=128 at a time 7 unit

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all the best