The subdivision-constrained routing requests problem
We are given a digraph D =( V , A ; w ), a length (delay) function w : A → R + , a positive integer d and a set of k requests, where s i ∈ V is called as the i th source node, t i ∈ V is called the i th sink node and B i is called as the i th length constraint. For a given positive integer d , the s...
Uložené v:
| Vydané v: | Journal of combinatorial optimization Ročník 27; číslo 1; s. 152 - 163 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Boston
Springer US
01.01.2014
|
| Predmet: | |
| ISSN: | 1382-6905, 1573-2886 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | We are given a digraph
D
=(
V
,
A
;
w
), a length (delay) function
w
:
A
→
R
+
, a positive integer
d
and a set
of
k
requests, where
s
i
∈
V
is called as the
i
th source node,
t
i
∈
V
is called the
i
th sink node and
B
i
is called as the
i
th length constraint. For a given positive integer
d
, the subdivision-constrained routing requests problem (SCRR, for short) is to find a directed subgraph
D
′=(
V
′,
A
′) of
D
, satisfying the two constraints: (1) Each request (
s
i
,
t
i
;
B
i
) has a path
P
i
from
s
i
to
t
i
in
D
′ with length
no more than
B
i
; (2) Insert some nodes uniformly on each arc
e
∈
A
′ to ensure that each new arc has length no more than
d
. The objective is to minimize the total number of the nodes inserted on the arcs in
A
′.
We obtain the following three main results: (1) The SCRR problem is at least as hard as the set cover problem even if each request has the same source
s
,
i.e.
,
s
i
=
s
for each
i
=1,2,…,
k
; (2) For each request (
s
,
t
;
B
), we design a dynamic programming algorithm to find a path from
s
to
t
with length no more than
B
such that the number of the nodes inserted on such a path is minimized, and as a corollary, we present a
k
-approximation algorithm to solve the SCRR problem for any
k
requests; (3) We finally present an optimal algorithm for the case where
contains all possible requests (
s
i
,
t
i
) in
V
×
V
and
B
i
is equal to the length of the shortest path in
D
from
s
i
to
t
i
. To the best of our knowledge, this is the first time that the dynamic programming algorithm within polynomial time in (2) is designed for a weighted optimization problem while previous optimal algorithms run in pseudo-polynomial time. |
|---|---|
| ISSN: | 1382-6905 1573-2886 |
| DOI: | 10.1007/s10878-012-9497-4 |