A generic framework for approximation analysis of greedy algorithms for star bicoloring

This paper presents a generic framework for the design and comparison of polynomial-time approximation algorithms for MINIMUM STAR BICOLORING. This generic framework is parameterized by algorithms which produce sequences of distance- 2 independent sets. As our main technical result we show that, whe...

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Bibliographic Details
Published inOptimization methods & software Vol. 36; no. 4; pp. 869 - 890
Main Authors Juedes, David W., Jones, Jeffrey S.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.07.2021
Taylor & Francis Ltd
Subjects
acyclic bicoloring
Algorithms
Approximation
approximation algorithms
automatic differentiation
Greedy algorithms
Jacobi matrix method
Jacobian matrix
Jacobians
Mathematical analysis
Matrix algebra
Parameterization
Polynomials
Star bicoloring
Upper bounds
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ISSN1055-6788
1029-4937
DOI10.1080/10556788.2019.1649671

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Summary:This paper presents a generic framework for the design and comparison of polynomial-time approximation algorithms for MINIMUM STAR BICOLORING. This generic framework is parameterized by algorithms which produce sequences of distance- 2 independent sets. As our main technical result we show that, when the parameterized algorithm produces sequences of distance- 2 independent sets that remove at least edges during each step, the generic framework produces a polynomial-time approximation algorithm for MINIMUM STAR BICOLORING that is always at least of optimal. Under the generic framework, we model two algorithms for MINIMUM STAR BICOLORING from the literature: Complete Direct Cover (CDC) [Hossain and Steihaug, Computing a sparse Jacobian matrix by rows and columns, Optim. Methods Softw. 10 (1998), pp. 33-48] and ASBC [Juedes and Jones, Coloring Jacobians revisited: A new algorithm for star and acyclic bicoloring, Optim. Methods Softw. 27(1-3) (2012), pp. 295-309]. We apply our main result to show approximation upper bounds of and , respectively, for these two algorithms. Our approximation upper bound for CDC is the first known approximation analysis for this algorithm. In addition to modelling CDC and ASBC, we use the generic framework to build and analyze three new approximation algorithms for MINIMUM STAR BICOLORING: MAX-NEIGHBORHOOD, MAX-RATIO , and LOCAL-SEARCH-k .
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2019.1649671