Improved algorithms for finding length-bounded two vertex-disjoint paths in a planar graph and minmax k vertex-disjoint paths in a directed acyclic graph
This paper is composed of two parts. In the first part, an improved algorithm is presented for the problem of finding length-bounded two vertex-disjoint paths in an undirected planar graph. The presented algorithm requires O ( n 3 b min ) time and O ( n 2 b min ) space, where b min is the smaller of...
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| Vydáno v: | Journal of computer and system sciences Ročník 76; číslo 8; s. 697 - 708 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
01.12.2010
|
| Témata: | |
| ISSN: | 0022-0000, 1090-2724 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | This paper is composed of two parts. In the first part, an improved algorithm is presented for the problem of finding length-bounded two vertex-disjoint paths in an undirected planar graph. The presented algorithm requires
O
(
n
3
b
min
)
time and
O
(
n
2
b
min
)
space, where
b
min
is the smaller of the two given length bounds. In the second part of this paper, we consider the minmax
k vertex-disjoint paths problem on a directed acyclic graph, where
k
⩾
2
is a constant. An improved algorithm and a faster approximation scheme are presented. The presented algorithm requires
O
(
n
k
+
1
M
k
−
1
)
time and
O
(
n
k
M
k
−
1
)
space, and the presented approximation scheme requires
O
(
(
1
/
ϵ
)
k
−
1
n
2
k
log
k
−
1
M
)
time and
O
(
(
1
/
ϵ
)
k
−
1
n
2
k
−
1
log
k
−
1
M
)
space, where
ϵ is the given approximation parameter and
M is the length of the longest path in an optimal solution. |
|---|---|
| ISSN: | 0022-0000 1090-2724 |
| DOI: | 10.1016/j.jcss.2010.01.013 |