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u 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
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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