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

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

Content Provider	ACM Digital Library
Author	Eliáš, Marek Bansal, Nikhil Koumoutsos, Grigorios Jeż, Łukasz
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/ϵ)-competitive when k = (1 + ϵ)h, for any ϵ > 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 Ω(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 Ω(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 + ϵ)h for any ϵ > 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.
Starting Page	1022
Ending Page	1037
Page Count	16
File Format	PDF
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-01-16
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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