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dc.contributor.authorLiang, Weifa
dc.contributor.authorMcKay, Brendan D.
dc.contributor.authorShen, Hong
dc.date.accessioned2019-05-10T04:08:49Z
dc.date.available2019-05-10T04:08:49Z
dc.date.issued1996
dc.identifier.issn00200190
dc.identifier.doi10.1016/0020-0190(96)00037-3
dc.identifier.urihttp://hdl.handle.net/10072/120754
dc.description.abstractWe consider the problem of dynamically maintaining a solution of all pairs shortest paths in a directed weighted graph G = (V, E) undergoing a sequence of edge insertions and/or the edge cost decreases, and present a simple data structure to support the above operations. The proposed algorithm for maintaining the data structure requires O(logn) time and O(n2) processors for each of the operations above. Furthermore, our algorithm is able to answer n2 queries concerning the lengths of all pairs shortest paths in O(1) time, and to find n shortest paths in O(logn) time. The same bounds for similar operations can be achieved for other problems such as dynamically maintaining all pairs longest paths in a directed acyclic graph (DAG), the topological order of a DAG, and the transitive closure of a directed graph. To the best of our knowledge, no partially dynamic NC algorithm using O(n2) processors for these problems is known yet, despite the existence of several efficient sequential algorithms. All known NC algorithms for these problems are based on matrix multiplication which requires M(n) processors at least. Currently the best result for M(n) is n2.376 (Coppersmith and Winograd, 1987). Unless otherwise specified, our computational model is a CREW PRAM in which concurrent read to the same memory cell is allowed, but concurrent write to the same memory cell is forbidden.
dc.description.peerreviewedYes
dc.languageEnglish
dc.publisherNorth-Holland
dc.publisher.placeNetherlands
dc.relation.ispartofpagefrom149
dc.relation.ispartofpageto155
dc.relation.ispartofjournalInformation Processing Letters
dc.relation.ispartofvolume58
dc.subject.fieldofresearchLandscape Ecology
dc.subject.fieldofresearchMathematical Sciences
dc.subject.fieldofresearchInformation and Computing Sciences
dc.subject.fieldofresearchEngineering
dc.subject.fieldofresearchcode050104
dc.subject.fieldofresearchcode01
dc.subject.fieldofresearchcode08
dc.subject.fieldofresearchcode09
dc.titleNC Algorithms for Dynamically Solving the all Pairs Shortest Paths Problem and Related Problems
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.hasfulltextNo Full Text
gro.griffith.authorShen, Hong


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