Affiliation:
1. Purdue Univ., West Lafayette, IN
Abstract
An algorithm is presented for generating a succinct encoding of all pairs shortest path information in a directed planar graph
G
with real-valued edge costs but no negative cycles. The algorithm runs in
O
(
pn
) time, where
n
is the number of vertices in
G
, and
p
is the minimum cardinality of a subset of the faces that cover all vertices, taken over all planar embeddings of
G
. The algorithm is based on a decomposition of the graph into
O
(
pn
) outerplanar subgraphs satisfying certain separator properties. Linear-time algorithms are presented for various subproblems including that of finding an appropriate embedding of
G
and a corresponding face-on-vertex covering of cardinality
O
(
p
), and of generating all pairs shortest path information in a directed outerplannar graph.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
47 articles.
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