An Optimal Algorithm for Online Multiple Knapsack

An Optimal Algorithm for Online Multiple Knapsack

Abstract

In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of n bins (knapsacks) of equal size. The gain of an algorithm is equal to the sum of sizes of accepted items and the goal is to maximize the total gain. So far, for this natural problem, the best solution was the 0.5-competitive algorithm FirstFit (the result holds for any n ≥ 2). We present the first algorithm that beats this ratio, achieving the competitive ratio of 1/(1 + ln(2)) − O(1/n) ≈ 0.5906 − O(1/n). Our algorithm is deterministic and optimal up to lower-order terms, as the upper bound of 1/(1 + ln(2)) for randomized solutions was given previously by Cygan et al. [TOCS 2016].

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Authors
  • Bienkowski, Marcin
  • Pacut, Maciej
  • Piecuch, Krzysztof
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
The 47th International Colloquium on Automata, Languages and Programming (ICALP 2020)
Divisions
Communication Technologies
Subjects
Theoretische Informatik
Event Location
Saarbrucken
Event Type
Conference
Event Dates
July 8-11 2020
Date
8 July 2020
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