Computing Largest Minimum Color-Spanning Intervals of Imprecise Points

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00375488" target="_blank" >RIV/68407700:21240/24:00375488 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/978-3-031-55598-5_6" target="_blank" >https://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>

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(n^2 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

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GX23-04949X" target="_blank" >GX23-04949X: Fundamental questions of discrete geometry</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

16th Latin American Theoretical Informatics Symposium (LATIN 2024)

ISBN

978-3-031-55598-5

ISSN

1611-3349

e-ISSN

1611-3349

Number of pages

16

Pages from-to

81-96

Publisher name

Springer, Cham

Place of publication

—

Event location

Puerto Varas

Event date

Mar 18, 2024

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001214186800006