Succinct Data Structures for Chordal Graphs
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Date
2019-04-10
Authors
Wu, Kaiyu
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time.
We study the problem of succinctly storing a static chordal graph to answer adjacency, degree, neighbourhood and shortest path queries. Let G be a chordal graph with n vertices. We design a data structure using the information theoretic minimal n^2/4 + o(n^2) bits of space to support the queries:
whether two vertices u,v are adjacent in time f(n) for any f(n) \in \omega(1).
the degree of a vertex in O(1) time.
the vertices adjacent to u in O(f(n)^2) time per neighbour
the length of the shortest path from u to v in O(n f(n)) time