The (h,k)-server problem on bounded-depth trees.

N. Bansal, M. Elias, L. Jez, G. Koumoutsos

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

6 Citations (Scopus)
72 Downloads (Pure)

Abstract

We study the k-server problem in the resource augmentation setting i.e., when the performance of the online algorithm with k servers is compared to the offline optimal solution with H ≤ k servers. The problem is very poorly understood beyond uniform metrics. For this special case, the classic k-server algorithms are roughly (1 + 1/∊)-competitive when k = (1 + ∊)h, for any ∊ > 0. Surprisingly however, no o(h)- competitive algorithm is known even for HSTs of depth 2 and even when k/h is arbitrarily large. We obtain several new results for the problem. First we show that the known k-server algorithms do not work even on very simple metrics. In particular, the Double Coverage algorithm has competitive ratio O(h) irrespective of the value of k, even for depth-2 HSTs. Similarly the Work Function Algorithm, that is believed to be optimal for all metric spaces when k = h, has competitive ratio O(h) on depth-3 HSTs even if k = 2h. Our main result is a new algorithm that is O(1)-competitive for constant depth trees, whenever k = (1 + ∊)h for any ∊ > 0. Finally, we give a general lower bound that any deterministic online algorithm has competitive ratio at least 2.4 even for depth-2 HSTs and when k/h is arbitrarily large. This gives a surprising qualitative separation between uniform metrics and depth-2 HSTs for the (h, k)-server problem, and gives the strongest known lower bound for the problem on general metrics.
Original languageEnglish
Title of host publicationProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 16-19 January 2017, Barcelona, Spain
EditorsPhilip N. Klein
Place of Publications.l.
PublisherSociety for Industrial and Applied Mathematics (SIAM)
Pages1022-1037
Number of pages16
ISBN (Electronic)978-1-61197-478-2
DOIs
Publication statusPublished - 2017
Event28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) - Barcelona, Spain
Duration: 16 Jan 201719 Jan 2017
Conference number: 28

Conference

Conference28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)
Abbreviated titleSODA 2017
Country/TerritorySpain
CityBarcelona
Period16/01/1719/01/17

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