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A Dynamic Data Structure for Checking Hyperacyclicity

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Show simple item record Liang, Percy Srebro, Nati
dc.contributor.other Algorithms 2005-12-22T02:20:16Z 2005-12-22T02:20:16Z 2005-01-03
dc.identifier.other MIT-CSAIL-TR-2005-001
dc.identifier.other MIT-LCS-TR-977
dc.description.abstract We present a dynamic data structure that keeps track of an acyclic hypergraph (equivalently, a triangulated graph) and enables verifying that adding a candidate hyperedge (clique) will not break the acyclicity of the augmented hypergraph. This is a generalization of the use of Tarjan's Union-Find data structure for maintaining acyclicity when augmenting forests, and the amortized time per operation has a similar almost-constant dependence on the size of the hypergraph. Such a data structure is useful when augmenting acyclic hypergraphs, e.g.\~in order to greedily construct a high-weight acyclic hypergraph. In designing this data structure, we introduce a hierarchical decomposition of acyclic hypergraphs that aid in understanding {\em hyper-connectivity}, and introduce a novel concept of a {\em hypercycle} which is excluded from acyclic hypergraphs.
dc.format.extent 12 p.
dc.format.extent 17306554 bytes
dc.format.extent 656257 bytes
dc.format.mimetype application/postscript
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.relation.ispartofseries Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory
dc.title A Dynamic Data Structure for Checking Hyperacyclicity

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