O(f) Bi-criteria Approximation for Capacitated Covering with Hard Capacities
We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = ( V , E ) with a maximum edge size f . Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available mult...
Uloženo v:
| Vydáno v: | Algorithmica Ročník 81; číslo 5; s. 1800 - 1817 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
15.05.2019
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph
G
=
(
V
,
E
)
with a maximum edge size
f
. Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available multiplicity. The objective is to find a minimum-weight vertex multiset such that the demands of the edges can be covered by the capacities of the vertices and the multiplicity of each vertex does not exceed its available multiplicity. In this paper we present an
O
(
f
) bi-criteria approximation for VC-HC that gives a trade-off on the number of augmented multiplicity and the cost of the resulting cover. In particular, we show that, by augmenting the available multiplicity by a factor of
k
≥
2
, a cover with a cost ratio of
1
+
1
k
-
1
(
f
-
1
)
to the optimal cover for the original instance can be obtained. This improves over the previously best known guarantee, which has a cost ratio of
f
2
via augmenting the available multiplicity by a factor of
f
. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-018-0506-6 |