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research
A linear time algorithm for a variant of the max cut problem in series parallel graphs
Authors
Brahim Chaourar
Publication date
1 January 2017
Publisher
Doi
Cite
View
on
arXiv
Abstract
Given a graph
G
=
(
V
,
E
)
G=(V, E)
G
=
(
V
,
E
)
, a connected sides cut
(
U
,
V
\
U
)
(U, V\backslash U)
(
U
,
V
\
U
)
or
δ
(
U
)
\delta (U)
δ
(
U
)
is the set of edges of E linking all vertices of U to all vertices of
V
\
U
V\backslash U
V
\
U
such that the induced subgraphs
G
[
U
]
G[U]
G
[
U
]
and
G
[
V
\
U
]
G[V\backslash U]
G
[
V
\
U
]
are connected. Given a positive weight function
w
w
w
defined on
E
E
E
, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut
Ω
\Omega
Ω
such that
w
(
Ω
)
w(\Omega)
w
(
Ω
)
is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.Comment: 6 page
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Last time updated on 07/04/2018