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DOI: 10.4230/LIPIcs.SOCG.2015.240
URN: urn:nbn:de:0030-drops-51132
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5113/
Bokal, Drago ; Cabello, Sergio ; Eppstein, David
Finding All Maximal Subsequences with Hereditary Properties
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Abstract
Consider a sequence s_1,...,s_n of points in the plane. We want to find all maximal subsequences with a given hereditary property P: find for all indices i the largest index j^*(i) such that s_i,...,s_{j^*(i)} has property P. We provide a general methodology that leads to the following specific results:- In O(n log^2 n) time we can find all maximal subsequences with diameter at most 1.
- In O(n log n loglog n) time we can find all maximal subsequences whose convex hull has area at most 1.
- In O(n) time we can find all maximal subsequences that define monotone paths in some (subpath-dependent) direction.
The same methodology works for graph planarity, as follows. Consider a sequence of edges e_1,...,e_n over a vertex set V. In O(n log n) time we can find, for all indices i, the largest index j^*(i) such that (V,{e_i,..., e_{j^*(i)}}) is planar.
BibTeX - Entry
@InProceedings{bokal_et_al:LIPIcs:2015:5113,
author = {Drago Bokal and Sergio Cabello and David Eppstein},
title = {{Finding All Maximal Subsequences with Hereditary Properties}},
booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)},
pages = {240--254},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-83-5},
ISSN = {1868-8969},
year = {2015},
volume = {34},
editor = {Lars Arge and J{\'a}nos Pach},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5113},
URN = {urn:nbn:de:0030-drops-51132},
doi = {10.4230/LIPIcs.SOCG.2015.240},
annote = {Keywords: convex hull, diameter, monotone path, sequence of points, trajectory}
}
| Keywords: | convex hull, diameter, monotone path, sequence of points, trajectory | |
| Seminar: | 31st International Symposium on Computational Geometry (SoCG 2015) | |
| Issue date: | 2015 | |
| Date of publication: | 12.06.2015 |
