Approximation ratio of the min-degree greedy algorithm for Maximum Independent Set on interval and chordal graphs

Steven Chaplick; Martin Frohn; Steven Kelk; Johann Lottermoser; Matúš Mihalák

doi:10.1016/j.dam.2024.09.009

Approximation ratio of the min-degree greedy algorithm for Maximum Independent Set on interval and chordal graphs

Steven Chaplick^*, Martin Frohn, Steven Kelk, Johann Lottermoser, Matúš Mihalák

^*Corresponding author for this work

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

Abstract

In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a (2/3)-approximation for the MAXIMUM INDEPENDENT SET problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a (1/2)-approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of [Formula presented] of the greedy algorithm for general graphs of maximum degree Δ.

Original language	English
Pages (from-to)	275-281
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	360
DOIs	https://doi.org/10.1016/j.dam.2024.09.009
Publication status	Published - 15 Jan 2025

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https://linkinghub.elsevier.com/retrieve/pii/S0166218X24003986

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Approximation Ratio of the Min-Degree Greedy Algorithm for Maximum Independent Set on Interval and Chordal Graphs
Chaplick, S., Frohn, M., Kelk, S., Lottermoser, J. & Mihalak, M., 16 Mar 2024, 2403.10868 ed., Cornell University - arXiv, (arXiv.org; No. 2403.10868).
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Cite this

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title = "Approximation ratio of the min-degree greedy algorithm for Maximum Independent Set on interval and chordal graphs",

abstract = "In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a (2/3)-approximation for the MAXIMUM INDEPENDENT SET problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a (1/2)-approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of [Formula presented] of the greedy algorithm for general graphs of maximum degree Δ.",

author = "Steven Chaplick and Martin Frohn and Steven Kelk and Johann Lottermoser and Mat{\'u}{\v s} Mihal{\'a}k",

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AU - Chaplick, Steven

AU - Frohn, Martin

AU - Kelk, Steven

AU - Lottermoser, Johann

AU - Mihalák, Matúš

PY - 2025/1/15

Y1 - 2025/1/15

N2 - In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a (2/3)-approximation for the MAXIMUM INDEPENDENT SET problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a (1/2)-approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of [Formula presented] of the greedy algorithm for general graphs of maximum degree Δ.

AB - In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a (2/3)-approximation for the MAXIMUM INDEPENDENT SET problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a (1/2)-approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of [Formula presented] of the greedy algorithm for general graphs of maximum degree Δ.

U2 - 10.1016/j.dam.2024.09.009

DO - 10.1016/j.dam.2024.09.009

M3 - Article

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VL - 360

SP - 275

EP - 281

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Approximation ratio of the min-degree greedy algorithm for Maximum Independent Set on interval and chordal graphs

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Approximation Ratio of the Min-Degree Greedy Algorithm for Maximum Independent Set on Interval and Chordal Graphs

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