The document proposes piece-picking algorithms for peer-to-peer live streaming and video-on-demand based on the knapsack problem. The piece-picking problem is closely related to the knapsack problem and existing knapsack algorithms can be analyzed and improved to meet requirements. Various knapsack-based algorithms are evaluated for complexity, dependency on network conditions, and applicability to different settings. The goal is to find the optimal tradeoff between smooth playback and highest possible video quality by selecting the best pieces to download from peers.

1. Contact1
InstituteofInformationTechnology(ITEC),ResearchGroupMultimediaCommunication(MMC),KlagenfurtUniversity,Austria
2
eLearningDepartment,ComputerandAutomationResearchInstituteoftheHungarianAcademyofSciences,Hungary
E-Mail1
firstname.lastname@itec.uni-klu.ac.at,2
sztibor@sztaki.hu/szobonya@sztaki.hu
Piece Utility and the Knapsack Problem
Piece-Picking Algorithms
Requirements:
 Bittorrent-based Peer-to-Peer system (Next-Share)
 For live streaming and video-on-demand
(rarest-first not suitable)
 Supporting layered content
 We need an algorithm that finds the best trade-off
between smooth playback and displaying the best
possible quality.
Approach:
The Piece-Picking problem is closely related to the
Knapsack problem.
 Analyze existing algorithms for solving the Knapsack
problem and try to improve them taking the requirements
of a Peer-to-Peer system into account.
Piece-Picking in Peer-to-Peer Networks
Evaluation
Network conditions change every 24 timeslots (60 sec.)
Algor. Complexity DC Applicability
Baseline O(m⋅n) not nec. For simple settings
DP O(S⋅m⋅n(2)
) dep. Higher comlexity
version suitable
MMKP O(m2
⋅ (n-1)2
⋅z) yes Includes also peer
selection
Greedy O(m⋅n⋅log(
max(m,n)))
no Suitable if utility is
well defined
DC: Dependency Check DP: Dynamic Programming
MMKP: Multiple-Choice Multidimensional Knapsack Problem
m: number of timeslots S: max. download bandwidth
n: number of layers z: number of neighbours
Utility Calculation
   jj jkliklijijkl prprwp ' 1' )(
 
 zl ijklijk wpwp ' ' )1(1
j
ijk
ijk
c
u
wu 

)( kj
ijkj
ijk
tt
wpd
u


 Sxc ijkj 
 1,0ijkx
kijijk xx 1
jkiijk xx 1
(1)
(2)
(3)
(4)
  ijkijk xu (5)
(6)
(7)
(8)
(9)
The Knapsack Problem
Maximize
Subject to
ti: the ith timeslot
tk: the kth decision point
lj: the jth layer of the stream
nl: the lth neighbour peer
pij: a piece at timeslot ti and layer lj
dj: the distortion reduction importance
prijkl: the probability that a piece will be
downloaded in time
wpijkl: the weighted probability that a
piece will be downloaded in time
from neighbour nl
wpijk: the weighted probability that a
piece will be downloaded in time
uijk: the utility of a piece
: the urgency weighting
cj: the required bandwidth for a piece
wuijk: the weighted utility of the piece
xijk:if piece pij is selected for download
Knapsack Problem-based Piece-Picking Algorithms for
Layered Content in Peer-to-Peer Networks
Michael Eberhard1
, Tibor Szkaliczki2
, Hermann Hellwagner1
, László Szobonya2
, Christian Timmerer1