Online Submodular Maximization: Beating 1/2 Made Simple

Niv Buchbinder, Moran Feldman, Yuval Filmus, Mohit Garg

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


The problem of Submodular Welfare Maximization (SWM) captures an important subclass of combinatorial auctions and has been studied extensively from both computational and economic perspectives. In particular, it has been studied in a natural online setting in which items arrive one-by-one and should be allocated irrevocably upon arrival. In this setting, it is well known that the greedy algorithm achieves a competitive ratio of, and recently Kapralov et al. [22] showed that this ratio is optimal for the problem. Surprisingly, despite this impossibility result, Korula et al. [25] were able to show that the same algorithm is 0.5052-competitive when the items arrive in a uniformly random order, but unfortunately, their proof is very long and involved. In this work, we present an (arguably) much simpler analysis that provides a slightly better guarantee of 0.5096-competitiveness for the greedy algorithm in the random-arrival model. Moreover, this analysis applies also to a generalization of online SWM in which the sets defining a (simple) partition matroid arrive online in a uniformly random order, and we would like to maximize a monotone submodular function subject to this matroid. Furthermore, for this more general problem, we prove an upper bound of 0.576 on the competitive ratio of the greedy algorithm, ruling out the possibility that the competitiveness of this natural algorithm matches the optimal offline approximation ratio of.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 20th International Conference, IPCO 2019, Proceedings
EditorsAndrea Lodi, Viswanath Nagarajan
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783030179526
StatePublished - 2019
Event20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019 - Ann Arbor, United States
Duration: 22 May 201924 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11480 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019
Country/TerritoryUnited States
CityAnn Arbor

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.


  • Greedy algorithms
  • Online auctions
  • Submodular optimization


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