Affiliation:
1. The University of Sydney
Abstract
Driven by applications in graph analytics, the problem of efficiently computing all
k
-edge connected components (
k
-ECCs) of a graph
G
for
a user-given k
has been extensively and well studied. It is known that the
k
-ECCs of
G
for
all possible values
of
k
form a hierarchical structure. In this paper, we study the problem of efficiently constructing the hierarchy tree for
G
which compactly encodes the
k
-ECCs for all possible
k
values in space linear to the number of vertices
n.
All existing approaches construct the hierarchy tree in
O
(δ(
G
) × T
KECC
(
G
)
) time, where δ(
G
) is the degeneracy of
G
and T
KECC
(
G
)
is the time complexity of computing all
k
-ECCs of
G
for a specific
k
value. To improve the time complexity, we propose a divide-and-conquer approach running in
O
((log δ(
G
)) × T
KECC
(
G
)
) time, which is optimal up to a logarithmic factor. However, a straightforward implementation of our algorithm would result in a space complexity of
O
((
m
+
n
) log δ(
G
)). As main memory also becomes a scarce resource when processing large-scale graphs, we further propose techniques to optimize the space complexity to 2
m
+
O
(
n
log δ(
G
)), where
m
is the number of edges in
G.
Extensive experiments on large real graphs and synthetic graphs demonstrate that our approach outperforms the state-of-the-art approaches by up to 28 times in terms of running time, and by up to 8 times in terms of main memory usage. As a by-product, we also improve the space complexity of computing all
k
-ECCs for a specific
k
to 2
m
+
O
(
n
).
Publisher
Association for Computing Machinery (ACM)
Subject
General Earth and Planetary Sciences,Water Science and Technology,Geography, Planning and Development
Reference36 articles.
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