Knapsack problem based piece-picking algorithms for layered content in peer-to-peer networks

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Knapsack problem based piece-picking algorithms for layered content in peer-to-peer networks

  1. 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

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