A Practical Way To Maintain A Transitive Reduction
نویسندگان
چکیده
Several authors have studied methods to construct the transitive reduction of a directed graph, but little work has been done on how to maintain it. We are motivated by a real-world application which uses a transitively reduced graph at its core and must maintain the transitive reduction over a sequence of graph operations. This paper presents an efficient method to maintain the transitive reduction of a possibly cyclic directed graph under the following operations: Vertex Addition: This involves adding a new vertex along with an application specified set of new edges. Edge Removal: This involves removing an arbitrary edge in a transitive reduction and possibly insertion of additional edges to preserve implicit transitivity relationships We present overviews of how to efficiently perform these operations without storing the original graph or its transitive closure, and we give proofs of correctness and the time complexities.
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