Packing resizable items with application to video delivery over wireless networks

Sivan Albagli-Kim, Leah Epstein, Hadas Shachnai, Tami Tamir

Research output: Contribution to journalArticlepeer-review


Motivated by fundamental optimization problems in video delivery over wireless networks, we consider the following problem of packing resizable items (PRI). Given is a bin of capacity B>0, and a set I of items. Each item j∈I has a size sj>0. A packed item must stay in the bin for a fixed common time interval. To accommodate additional items in the bin, each item j can be compressed to a given size pj∈[0, sj) for at most a fraction qj∈[0, 1) of the packing interval, during one continuous sub-interval. The goal is to pack in the bin, for the given time interval, a subset of items of maximum cardinality. PRI is a generalization of the well-known Knapsack problem, and it is strongly NP-hard already for highly restricted instances.Our main result is an approximation algorithm that packs, for any instance I of PRI, at least 23OPT(I)-2 items, where OPT(I) is the number of items packed in an optimal solution. Our algorithm yields a better performance ratio for instances in which the maximum compression time of an item is qmax∈(0,12). For subclasses of instances arising in realistic scenarios, we give an algorithm that packs at least OPT(I). - 2 items. Finally, we show that a non-trivial subclass of instances admits an asymptotic fully polynomial time approximation scheme (AFPTAS).

Original languageEnglish
Pages (from-to)91-105
Number of pages15
JournalTheoretical Computer Science
Issue numberC
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2013 Elsevier B.V.


  • Approximation algorithms
  • Packing
  • Variable quality-of-service

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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