Managing Multiple Mobile Resources
We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC 6 (3), 14:1–14:17 2019 ) to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers...
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| Vydané v: | Theory of computing systems Ročník 65; číslo 6; s. 943 - 984 |
|---|---|
| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.08.2021
Springer Nature B.V |
| Predmet: | |
| ISSN: | 1432-4350, 1433-0490 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC
6
(3), 14:1–14:17
2019
) to a model where
k
identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers can be adapted by a limited distance
m
s
per round for each server. The costs are measured similarly to the classical Page Migration problem: i.e., answering a request induces costs proportional to the distance to the nearest server, and moving a server induces costs proportional to the distance multiplied with a weight
D
. We show that, in our model, no online algorithm can have a constant competitive ratio: i.e., one which is independent of the input length
n
, even if an augmented moving distance of (1 +
δ
)
m
s
is allowed for the online algorithm. Therefore we investigate a restriction of the power of the adversary dictating the sequence of requests: We demand
locality of requests
: i.e., that consecutive requests come from points in the Euclidean space with distance bounded by some constant
m
c
. We show constant lower bounds on the competitiveness in this setting (independent of
n
, but dependent on
k
,
m
s
and
m
c
). On the positive side, we present a deterministic online algorithm with bounded competitiveness when an augmented moving distance and locality of requests is assumed. Our algorithm simulates any given algorithm for the classical
k
-Page Migration problem as guidance for its servers and extends it by a greedy move of one server in every round. The resulting competitive ratio is polynomial in the number of servers
k
, the ratio between
m
c
and
m
s
, the inverse of the augmentation factor 1/
δ
and the competitive ratio of the simulated
k
-Page Migration algorithm. We also show how to directly adapt the Double Coverage algorithm (Chrobak et al. SIAM J. Discrete Math.
4
(2), 172–181
11
) for the
k
-Server problem to receive an algorithm with improved competitiveness on the line. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1432-4350 1433-0490 |
| DOI: | 10.1007/s00224-020-10023-8 |