Lower Bounds on the Performance of Online Algorithms for Relaxed Packing Problems

János Balogh, György Dósa, Leah Epstein, Łukasz Jeż

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level objective in both problems is to pack arriving items of sizes at most 1 into bins of capacity 1 as efficiently as possible, but the exact formalizations differ. In the appointment scheduling problem, every item has to be assigned to a position, which can be seen as a time interval during a workday of length 1. That is, items are not assigned to bins, but only once all the items are processed, the optimal number of bins subject to chosen positions is determined, and this is the cost of the online algorithm. On the other hand, in the removable knapsack problem there is a fixed number of bins, and the goal of packing items, which consists in choosing a particular bin for every packed item (and nothing else), is to pack as valuable a subset as possible. In this last problem it is possible to reject items, that is, deliberately not pack them, as well as to remove packed items at any later point in time, which adds flexibility to the problem.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings
EditorsCristina Bazgan, Henning Fernau
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783031066771
StatePublished - 2022
Event33rd International Workshop on Combinatorial Algorithms, IWOCA 2022 - Trier, Germany
Duration: 7 Jun 20229 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13270 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference33rd International Workshop on Combinatorial Algorithms, IWOCA 2022

Bibliographical note

Publisher Copyright:
© 2022, Springer Nature Switzerland AG.


  • Bin packing
  • Competitive ratio
  • Online algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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