On efficient distributed construction of near optimal routing schemes
Given a distributed network represented by a weighted undirected graph G = ( V , E ) on n vertices, and a parameter k , we devise a randomized distributed algorithm that whp computes a routing scheme in O ( n 1 / 2 + 1 / k + D ) · n o ( 1 ) rounds, where D is the hop-diameter of the network. Moreove...
Gespeichert in:
| Veröffentlicht in: | Distributed computing Jg. 31; H. 2; S. 119 - 137 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2018
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0178-2770, 1432-0452 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Given a distributed network represented by a weighted undirected graph
G
=
(
V
,
E
)
on
n
vertices, and a parameter
k
, we devise a randomized distributed algorithm that whp computes a routing scheme in
O
(
n
1
/
2
+
1
/
k
+
D
)
·
n
o
(
1
)
rounds, where
D
is the hop-diameter of the network. Moreover, for odd
k
, the running time of our algorithm is
O
(
n
1
/
2
+
1
/
(
2
k
)
+
D
)
·
n
o
(
1
)
. Our running time nearly matches the lower bound of
Ω
~
(
n
1
/
2
+
D
)
rounds (which holds for any scheme with polynomial stretch). The routing tables are of size
O
~
(
n
1
/
k
)
, the labels are of size
O
(
k
log
2
n
)
, and every packet is routed on a path suffering stretch at most
4
k
-
5
+
o
(
1
)
. Our construction nearly matches the state-of-the-art for routing schemes built in a centralized sequential manner. The previous best algorithms for building routing tables in a distributed small messages model were by Lenzen and Patt-Shamir (In: Symposium on theory of computing conference, STOC’13, Palo Alto, CA, USA,
2013
) and Lenzen and Patt-Shamir (In: Proceedings of the 2015 ACM symposium on principles of distributed computing, PODC 2015, Donostia-San Sebastián, Spain,
2015
). The former has similar properties but suffers from substantially larger routing tables of size
O
(
n
1
/
2
+
1
/
k
)
, while the latter has sub-optimal running time of
O
~
(
min
{
(
n
D
)
1
/
2
·
n
1
/
k
,
n
2
/
3
+
2
/
(
3
k
)
+
D
}
)
. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-2770 1432-0452 |
| DOI: | 10.1007/s00446-017-0304-4 |