On the adaptivity gap of stochastic orienteering
The input to the stochastic orienteering problem (Gupta et al. in SODA, pp 1522–1538, 2012 ) consists of a budget B and metric ( V , d ) where each vertex v ∈ V has a job with a deterministic reward and a random processing time (drawn from a known distribution). The processing times are independe...
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| Vydané v: | Mathematical programming Ročník 154; číslo 1-2; s. 145 - 172 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2015
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0025-5610, 1436-4646 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | The input to the
stochastic orienteering
problem (Gupta et al. in SODA, pp 1522–1538,
2012
) consists of a budget
B
and metric (
V
,
d
) where each vertex
v
∈
V
has a job with a deterministic reward and a
random
processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a non-anticipatory policy (originating from a given root vertex) to run jobs at different vertices, that maximizes expected reward, subject to the total distance traveled plus processing times being at most
B
. An
adaptive
policy can choose the next vertex to visit based on observed random instantiations. Whereas, a
non-adaptive
policy is just given by a fixed ordering of vertices. The
adaptivity gap
is the worst-case ratio of the optimal adaptive and non-adaptive rewards. We prove an
Ω
(
log
log
B
)
1
/
2
lower bound on the adaptivity gap of stochastic orienteering. This provides a negative answer to the
O
(1)-adaptivity gap conjectured by Gupta et al. (
2012
), and comes close to the
O
(
log
log
B
)
upper bound. This result holds even on a line metric. We also show an
O
(
log
log
B
)
upper bound on the adaptivity gap for the
correlated
stochastic orienteering problem, where the reward of each job is random and possibly correlated to its processing time. Using this, we obtain an improved quasi-polynomial time
min
{
log
n
,
log
B
}
·
O
~
(
log
2
log
B
)
-approximation algorithm for correlated stochastic orienteering. |
|---|---|
| Bibliografia: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-015-0927-9 |