A constant factor approximation algorithm for reordering buffer management

Noa Avigdor-Elgrabli*, Yuval Rabani

*Corresponding author for this work

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

12 Scopus citations

Abstract

In the reordering buffer management problem (RBM) a sequence of n colored items enters a buffer with limited capacity k. When the buffer is full, one item is removed to the output sequence, making room for the next input item. This step is repeated until the input sequence is exhausted and the buffer is empty. The objective is to find a sequence of removals that minimizes the total number of color changes in the output sequence. The problem formalizes numerous applications in computer and production systems, and is known to be NP-hard. We give the first constant factor approximation guarantee for RBM. Our algorithm is based on an intricate "rounding" of the solution to an LP relaxation for RBM, so it also establishes a constant upper bound on the integrality gap of this relaxation. Our results improve upon the best previous bound of O(√log k) of Adamaszek et al. (STOC 2011) that used different methods and gave an online algorithm. Our constant factor approximation beats the super-constant lower bounds on the competitive ratio given by Adamaszek et al. This is the first demonstration of a polynomial time offline algorithm for RBM that is provably better than any online algorithm.

Original languageAmerican English
Title of host publicationProceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
PublisherAssociation for Computing Machinery
Pages973-984
Number of pages12
ISBN (Print)9781611972511
DOIs
StatePublished - 2013
Event24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 - New Orleans, LA, United States
Duration: 6 Jan 20138 Jan 2013

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
Country/TerritoryUnited States
CityNew Orleans, LA
Period6/01/138/01/13

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