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research
On Efficient Distributed Construction of Near Optimal Routing Schemes
Authors
Michael Elkin
Ofer Neiman
Publication date
20 November 2016
Publisher
Doi
Cite
View
on
arXiv
Abstract
Given a distributed network represented by a weighted undirected graph
G
=
(
V
,
E
)
G=(V,E)
G
=
(
V
,
E
)
on
n
n
n
vertices, and a parameter
k
k
k
, we devise a distributed algorithm that computes a routing scheme in
(
n
1
/
2
+
1
/
k
+
D
)
β
n
o
(
1
)
(n^{1/2+1/k}+D)\cdot n^{o(1)}
(
n
1/2
+
1/
k
+
D
)
β
n
o
(
1
)
rounds, where
D
D
D
is the hop-diameter of the network. The running time matches the lower bound of
Ξ©
~
(
n
1
/
2
+
D
)
\tilde{\Omega}(n^{1/2}+D)
Ξ©
~
(
n
1/2
+
D
)
rounds (which holds for any scheme with polynomial stretch), up to lower order terms. The routing tables are of size
O
~
(
n
1
/
k
)
\tilde{O}(n^{1/k})
O
~
(
n
1/
k
)
, the labels are of size
O
(
k
log
β‘
2
n
)
O(k\log^2n)
O
(
k
lo
g
2
n
)
, and every packet is routed on a path suffering stretch at most
4
k
β
5
+
o
(
1
)
4k-5+o(1)
4
k
β
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 \cite[STOC 2013]{LP13} and \cite[PODC 2015]{LP15}. The former has similar properties but suffers from substantially larger routing tables of size
O
(
n
1
/
2
+
1
/
k
)
O(n^{1/2+1/k})
O
(
n
1/2
+
1/
k
)
, while the latter has sub-optimal running time of
O
~
(
min
β‘
{
(
n
D
)
1
/
2
β
n
1
/
k
,
n
2
/
3
+
2
/
(
3
k
)
+
D
}
)
\tilde{O}(\min\{(nD)^{1/2}\cdot n^{1/k},n^{2/3+2/(3k)}+D\})
O
~
(
min
{(
n
D
)
1/2
β
n
1/
k
,
n
2/3
+
2/
(
3
k
)
+
D
})
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info:doi/10.1145%2F2933057.293...
Last time updated on 16/02/2019