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Contact 1 Institute of Information Technology (ITEC), Research Group Multimedia Communication (MMC), Klagenfurt University, Austria 2 eLearning Department, Computer and Automation Research Institute of the Hungarian Academy of Sciences, Hungary E-Mail 1 [email protected], 2 [email protected]/[email protected] 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(m 2 ⋅ (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 j j jkl i kl ij ijkl pr pr wp ' 1 ' ) ( z l ijkl ijk wp wp ' ' ) 1 ( 1 j ijk ijk c u wu ) ( k j ijk j ijk t t wp d u S x c ijk j 1 , 0 ijk x k ij ijk x x 1 jk i ijk x x 1 (1) (2) (3) (4) ijk ijk x u (5) (6) (7) (8) (9) The Knapsack Problem Maximize Subject to t i : the ith timeslot t k : the kth decision point l j : the jth layer of the stream n l : the lth neighbour peer p ij : a piece at timeslot t i and layer l j d j : the distortion reduction importance pr ijkl : the probability that a piece will be downloaded in time wp ijkl : the weighted probability that a piece will be downloaded in time from neighbour n l wp ijk : the weighted probability that a piece will be downloaded in time u ijk : the utility of a piece : the urgency weighting c j : the required bandwidth for a piece wu ijk : the weighted utility of the piece x ijk :if piece p ij is selected for download Knapsack Problem-based Piece-Picking Algorithms for Layered Content in Peer-to-Peer Networks Michael Eberhard 1 , Tibor Szkaliczki 2 , Hermann Hellwagner 1 , László Szobonya 2 , Christian Timmerer 1
