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 language | English |
---|---|
Title of host publication | Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 16-19 January 2017, Barcelona, Spain |
Editors | Philip N. Klein |
Place of Publication | s.l. |
Publisher | Society for Industrial and Applied Mathematics (SIAM) |
Pages | 1022-1037 |
Number of pages | 16 |
ISBN (Electronic) | 978-1-61197-478-2 |
DOIs | |
Publication status | Published - 2017 |
Event | 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) - Barcelona, Spain Duration: 16 Jan 2017 → 19 Jan 2017 Conference number: 28 |
Conference
Conference | 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) |
---|---|
Abbreviated title | SODA 2017 |
Country/Territory | Spain |
City | Barcelona |
Period | 16/01/17 → 19/01/17 |