Efficient Vertex-Label Distance Oracles for Planar Graphs

Efficient Vertex-Label Distance Oracles for Planar Graphs We consider distance queries in vertex-labeled planar graphs. For any fixed 0 < πœ– ≤ 1/2 we show how to preprocess a directed planar graph with vertex labels and arc lengths into a data structure that answers queries of the following form. Given a vertex u and a label λ return a (1 + πœ–)-approximation of the distance from u to its closest vertex with label λ. For a directed planar graph with n vertices, such that the ratio of the largest to smallest arc length is bounded by N, the preprocessing time is O(πœ– − 2 n lg 3n lg(n N)), the data structure size is O(πœ– − 1 n lg n lg(n N)), and the query time is O(lg lg n lg lg(n N) + πœ– − 1). We also point out that a vertex label distance oracle for undirected planar graphs suggested in an earlier version of this paper is incorrect. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

Efficient Vertex-Label Distance Oracles for Planar Graphs

Loading next page...
 
/lp/springer_journal/efficient-vertex-label-distance-oracles-for-planar-graphs-09CIj6ITTV
Publisher
Springer US
Copyright
Copyright Β© 2017 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
D.O.I.
10.1007/s00224-017-9827-0
Publisher site
See Article on Publisher Site

Abstract

We consider distance queries in vertex-labeled planar graphs. For any fixed 0 < πœ– ≤ 1/2 we show how to preprocess a directed planar graph with vertex labels and arc lengths into a data structure that answers queries of the following form. Given a vertex u and a label λ return a (1 + πœ–)-approximation of the distance from u to its closest vertex with label λ. For a directed planar graph with n vertices, such that the ratio of the largest to smallest arc length is bounded by N, the preprocessing time is O(πœ– − 2 n lg 3n lg(n N)), the data structure size is O(πœ– − 1 n lg n lg(n N)), and the query time is O(lg lg n lg lg(n N) + πœ– − 1). We also point out that a vertex label distance oracle for undirected planar graphs suggested in an earlier version of this paper is incorrect.

Journal

Theory of Computing SystemsSpringer Journals

Published: Dec 12, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off