Geometric planar networks on bichromatic collinear points

Sayan Bandyapadhyay; Aritra Banik; Sujoy Bhore; Martin Nöllenburg

doi:10.1016/j.tcs.2021.09.035

Geometric planar networks on bichromatic collinear points

Sayan Bandyapadhyay, Aritra Banik, Sujoy Bhore, Martin Nöllenburg

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study three classical graph problems – Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the Euclidean plane, and many of them are NP-hard. In this work, we consider these problems for collinear points. We show that almost all of these problems can be solved in linear time in this setting.

Original language	English
Pages (from-to)	124-136
Number of pages	13
Journal	Theoretical Computer Science
Volume	895
DOIs	https://doi.org/10.1016/j.tcs.2021.09.035
State	Published - 4 Dec 2021
Externally published	Yes

Keywords

Collinear points
Hamiltonian path
Minimum prefect matching
Minimum spanning tree
Red-blue points

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2021.09.035

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title = "Geometric planar networks on bichromatic collinear points",

abstract = "We study three classical graph problems – Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the Euclidean plane, and many of them are NP-hard. In this work, we consider these problems for collinear points. We show that almost all of these problems can be solved in linear time in this setting.",

keywords = "Collinear points, Hamiltonian path, Minimum prefect matching, Minimum spanning tree, Red-blue points",

author = "Sayan Bandyapadhyay and Aritra Banik and Sujoy Bhore and Martin N{\"o}llenburg",

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T1 - Geometric planar networks on bichromatic collinear points

AU - Bandyapadhyay, Sayan

AU - Banik, Aritra

AU - Bhore, Sujoy

AU - Nöllenburg, Martin

PY - 2021/12/4

Y1 - 2021/12/4

N2 - We study three classical graph problems – Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the Euclidean plane, and many of them are NP-hard. In this work, we consider these problems for collinear points. We show that almost all of these problems can be solved in linear time in this setting.

AB - We study three classical graph problems – Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the Euclidean plane, and many of them are NP-hard. In this work, we consider these problems for collinear points. We show that almost all of these problems can be solved in linear time in this setting.

KW - Collinear points

KW - Hamiltonian path

KW - Minimum prefect matching

KW - Minimum spanning tree

KW - Red-blue points

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DO - 10.1016/j.tcs.2021.09.035

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VL - 895

SP - 124

EP - 136

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Geometric planar networks on bichromatic collinear points

Abstract

Keywords

ASJC Scopus subject areas

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