A Constant Factor Approximation Algorithm for the Storage Allocation Problem
We study the storage allocation problem ( SAP ) which is a variant of the unsplittable flow problem on paths ( UFPP ). A SAP instance consists of a path P = ( V , E ) and a set J of tasks. Each edge e ∈ E has a capacity c e and each task j ∈ J is associated with a path I j in P , a demand d j and a...
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| Vydáno v: | Algorithmica Ročník 77; číslo 4; s. 1105 - 1127 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.04.2017
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We study the storage allocation problem (
SAP
) which is a variant of the unsplittable flow problem on paths (
UFPP
). A
SAP
instance consists of a path
P
=
(
V
,
E
)
and a set
J
of tasks. Each edge
e
∈
E
has a capacity
c
e
and each task
j
∈
J
is associated with a path
I
j
in
P
, a demand
d
j
and a weight
w
j
. The goal is to find a maximum weight subset
S
⊆
J
of tasks and a height function
h
:
S
→
R
+
such that (i)
h
(
j
)
+
d
j
≤
c
e
, for every
e
∈
I
j
; and (ii) if
j
,
i
∈
S
such that
I
j
∩
I
i
≠
∅
and
h
(
j
)
≥
h
(
i
)
, then
h
(
j
)
≥
h
(
i
)
+
d
i
.
SAP
can be seen as a rectangle packing problem in which rectangles can be moved vertically, but not horizontally. We present a polynomial time
(
9
+
ε
)
-approximation algorithm for
SAP
. Our algorithm is based on a variation of the framework for approximating
UFPP
by Bonsma et al. [FOCS 2011] and on a
(
4
+
ε
)
-approximation algorithm for
δ
-small
SAP
instances (in which
d
j
≤
δ
·
c
e
, for every
e
∈
I
j
, for a sufficiently small constant
δ
>
0
). In our algorithm for
δ
-small instances, tasks are packed carefully in strips in a
UFPP
manner, and then a
(
1
+
ε
)
factor is incurred by a reduction from
SAP
to
UFPP
in strips. The strips are stacked to form a
SAP
solution. Finally, we provide a
(
10
+
ε
)
-approximation algorithm for
SAP
on ring networks. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-016-0137-8 |