Abstract
We investigate some properties of minimal interval and circular arc representations and give several optimal parallel recognition and construction algorithms. We show that, among other things, given an s × t interval or circular arc representation matrix, deciding if the representation is minimal can be done in O(log s) time with O(st/log s) EREW PRAM processors, or in O(1) time with O(st) Common CRCW PRAM processors; constructing a minimum interval representation can be done in O(log(st)) time with O(st/ log(st)) EREW PRAM processors, or in O(log t/log log t) time with O(st log log t/log t) Common CRCW PRAM processors, or in O(1) time with O(st) BSR processors. KeywordsIntersection PointIntersection GraphLeft EndpointInterval RepresentationParallel Random Access MachineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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