Minor Project Presentation
Optimal File Distribution in Peer-to-Peer Networks
Group Members –
Abhishek Sinha (2010CS10205)Ashwin Kumar (2010CS10211)Apoorv Garg (2009CS50235)
Supervisor –
Prof. Naveen Garg
The Model
Given a peer to peer network with a source server containing a file of F chunks, determine the minimum makespan for the distribution of file to all other nodes in the network.
1/24/20142 Optimal File Distribution in Peer to Peer Networks
Heterogeneous Symmetric Capacities
Symmetric u/l and d/l capacities, powers of 2
Greedy Strategy
Arrange peers in decreasing order of capacities.
Always serve the next k peers, using full upload capacity.
Claim
TGREEDY ≤ TOPT + F , where F is the file size.
1/24/20143 Optimal File Distribution in Peer to Peer Networks
Proof
Consider T0 , time when some peer’s upload capacity gets wasted.
Assume for contradiction, Topt < T0 .
Let k0 be the minimum index peer which is incomplete.
k = k0 – 1 has just finished download at T0 .
Consider the time T1 = T0 - 1/bk .
1/24/20144 Optimal File Distribution in Peer to Peer Networks
GREEDY Stays Behind
Upload in GREEDY (T1 to T0) Upload in OPT (T1 to T0)
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1/24/20145 Optimal File Distribution in Peer to Peer Networks
Proof
This means that .
At T1 , minimum index peer which is incomplete is ≤ k.
Thus, we proceed by induction.
This implies a contraction. Fraction of file in Greedy ≥ Optimal in initial stages.
Thus, TOPT ≥ T0 . But TGREEDY ≤ T0 + F .
Hence, TGREEDY ≤ TOPT + F , as claimed.
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1/24/20146 Optimal File Distribution in Peer to Peer Networks
Norms other than L∞
L1
Applied the same greedy approach.
Worst factor found = 8/7.
Example: 4 2 2 1 1, (G = 4, OPT = 3.5).
Tried to bound within 2 factor, but the same proof technique did not work.
L2 and higher
Makespan has contribution from all peers.
Could not bound the number of peers that finish after T0 .
1/24/20147 Optimal File Distribution in Peer to Peer Networks
Heterogeneous Asymmetric Capacities
Special Cases
Highest upload capacity peer also has Highest download capacity: Same proof works in this case.
ui = r * ci , where r = 1,{2,1/2}: Same as above.
General Case
Heuristic #1: Serve using full upload capacity to set of peers with max upload capacity.
Bad Example: Server’s u/l cap = 32.
Set1 { 8 peers with u/l cap = 8, d/l = 4 }
Set2 { 4 peers with u/l cap = 8, d/l = 8 }
Set3 { 8 peers with u/l cap = 8, d/l = 8 }
1/24/20148 Optimal File Distribution in Peer to Peer Networks
Heterogeneous Asymmetric Capacities
The heuristic would choose set1 with total upload capacity = 64 (set2 has upload cap 32).
At T = 1/4, total upload capacity = 32 + 64.
Now let’s choose set2 instead of set1.
At T = 1/8, total upload capacity = 32 + 32.
At T = 1/4, total upload capacity = 32 + 32 + 64.
Heuristic is bad.
1/24/20149 Optimal File Distribution in Peer to Peer Networks
Heterogeneous Asymmetric Capacities
General Case
Heuristic #2: Serve in decreasing order of product of upload and download capacities.
Bad Example.
Consider the case where the server has capacity 128 and all the other peers have d/l capacities as 128 and u/l capacities as 64.
For greedy, server ends up serving all.
Optimal would have been to allow the other peers to serve at 64.
The greedy has a makespan of (n/128) whereas the optimal’smakespan would be logarithmic in n.
1/24/201410 Optimal File Distribution in Peer to Peer Networks
References
Optimal File Distribution in Peer-to-Peer Networks: Kai-Simon Goetzmann, Tobias Harks, Max Klimm, and Konstantin Miller - In Proc. of the 22nd International Symposium on Algorithms and Computation (ISAAC), Yokohama, Japan, December 2011
1/24/201411 Optimal File Distribution in Peer to Peer Networks
THANK YOU
Any Questions?
