Fast Parallel Algorithms for the Subgraph Homeomorphism & the Subgraph Isomorphism Problems for Classes of Planar Graphs
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Date
1988-04-06
Authors
Lingas, Andrzej
Proskurowski, Andrzej
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We consider the problems of subgraph homeomorphism with fixed pattern graph,
recognition, and subgraph isomorphism for some classes of planar graphs. Following
the results of Robertson and Seymour on forbidden minor characterization, we show
that the problems of fixed subgraph homeomorphism and recognition for any family
of planar graphs closed under minor taking are in NC (i.e., they can be solved by an
algorithm running in poly-log time using polynomial number of processors). We also
show that the related subgraph isomorphism problem for biconnected outerplanar
·graphs is in NC. This is the first example of a restriction of subgraph isomorphism
to a non-trivial graph family admitting an NC algorithm
Description
23 pages
Keywords
planar graph, input graph, recursive call, simple polygon, subgraph isomorphism