| Summary: | 碩士 === 國立臺灣科技大學 === 電機工程研究所 === 82 === In this thesis, we shall present several algorithms for
determining the maximum number of vertex connectivity, testing
k-vertex connectivity, determining the maximum number of vertex
disjoint s-t paths and finding k-vertex disjoint s-t paths
problems on a permutation graph, respectively. We first give
several O(n ** 2) time sequential algorithms for determining
the maximum number of vertex connectivity, testing k-vertex
connectivity and determining the maximum number of vertex
disjoint s-t paths problems, respectively. Then, an O(k n ** 2)
time algorithm for finding k-vertex disjoint s-t paths problem
on a permutation graph is also proposed. Moreover, we also
derive the corresponding parallel algorithms for these problems
from the proposed sequential algorithms. On the EREW PRAM model
, we first propose several O(log n) time optimal speed-up
parallel algorithms for determining the maximum number of
vertex connectivity, testing k-vertex connectivity and
determining the maximum number of vertex disjoint s-t paths
problems, all with O(n ** 2 / log n) processors, respectively.
Then, an O(n log n) parallel algorithm for finding k-vertex
disjoint s-t paths problem using O(n ** 2 / log n) processors
is also developed, where k is a fixed integer.
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