Computing Largest Minimum Color-Spanning Intervals of Imprecise Points
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00585146" target="_blank" >RIV/67985807:_____/24:00585146 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-031-55598-5_6" target="_blank" >http://dx.doi.org/10.1007/978-3-031-55598-5_6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-55598-5_6" target="_blank" >10.1007/978-3-031-55598-5_6</a>
Alternative languages
Result language
angličtina
Original language name
Computing Largest Minimum Color-Spanning Intervals of Imprecise Points
Original language description
We study a geometric facility location problem under imprecision. Given n unit intervals in the real line, each with one of k colors, the goal is to place one point in each interval such that the resulting minimum color-spanning interval is as large as possible. A minimum color-spanning interval is an interval of minimum size that contains at least one point from a given interval of each color. We prove that if the input intervals are pairwise disjoint, the problem can be solved in O (n) time, even for intervals of arbitrary length. For overlapping intervals, the problem becomes much more difficult. Nevertheless, we show that it can be solved in O (n2 log n) time when k = 2, by exploiting several structural properties of candidate solutions, combined with a number of advanced algorithmic techniques. Interestingly, this shows a sharp contrast with the 2-dimensional version of the problem, recently shown to be NP hard.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
LATIN 2024: Theoretical Informatics. Proceedings, part I
ISBN
978-3-031-55597-8
ISSN
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e-ISSN
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Number of pages
16
Pages from-to
81-96
Publisher name
Springer
Place of publication
Cham
Event location
Puerto Varas
Event date
Mar 18, 2024
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001214186800006