Work

Approximation Algorithms for Polynomial-Expansion and Low-Density Graphs

Year: 2015

Type: preprint

Abstract: We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient $(1+\varepsilon)$-approximation algorithms for these graphs, for Independent Set, Set Cover, and Dominating Set problems, among others. We also prove corresponding hardness of approximation for some of these optimization problems, providing a characterization of their intractability in terms of density.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1501.00721

Authors: Har-Peled, Sariel, Quanrud, Kent

Institution: University of Illinois Urbana-Champaign

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: AF: Small: Towards better geometric algorithms: Summarizing, partitioning and shrinking data, AF: Small: Efficient Proximity and Similarity Search in Computational Geometry

OpenAlex ID: W4301066671

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