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ICALP
2011
Springer

Compact Navigation and Distance Oracles for Graphs with Small Treewidth

13 years 1 months ago
Compact Navigation and Distance Oracles for Graphs with Small Treewidth
Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build space-efficient encodings (oracles) to perform various queries efficiently. We assume the word RAM model where the size of a word is Ω (log n) bits. The first oracle, we present, is the navigation oracle which facilitates primitive navigation operations of adjacency, neighborhood, and degree queries. By way of an enumerate argument, which is of independent interest, we show the space requirement of the oracle is optimal to within lower order terms for all treewidths. The oracle supports the mentioned queries all in constant worst-case time. The second oracle, we present, is an exact distance oracle which facilitates distance queries between any pair of vertices (i.e., an all-pair shortest-path oracle). The space requirement of the oracle is also optimal to within lower order terms. Moreover, the distanc...
Arash Farzan, Shahin Kamali
Added 29 Aug 2011
Updated 29 Aug 2011
Type Journal
Year 2011
Where ICALP
Authors Arash Farzan, Shahin Kamali
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