An Improved Randomized Approximation Algorithm for Maximum Triangle Packing

• Published in: Algorithmic Aspects in Information and Management Vol. 5034; pp. 97 - 108
• Main Authors: Chen, Zhi-Zhong, Tanahashi, Ruka, Wang, Lusheng
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2008; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Approximation Algorithm; Cycle Cover; Discrete Apply Mathematic; Path Component; Random Choice
• ISBN: 354068865X; 9783540688655
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-68880-8_11

This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm and claimed that it achieves an expected ratio of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{89}{169}(1 - \epsilon)$\end{document} for any constant ε> 0. However, their analysis was flawed. We present a new randomized polynomial-time approximation algorithm for the problem which achieves an expected ratio very close to their claimed expected ratio.