The Power of Local Optimization: Approximation Algorithms for Maximum-leaf Spanning Tree (1996)
| Venue: | In Proceedings, Thirtieth Annual Allerton Conference on Communication, Control and Computing |
| Citations: | 19 - 3 self |
BibTeX
@INPROCEEDINGS{Lu96thepower,
author = {Hsueh-i Lu and R. Ravi and R. Ravi},
title = {The Power of Local Optimization: Approximation Algorithms for Maximum-leaf Spanning Tree},
booktitle = {In Proceedings, Thirtieth Annual Allerton Conference on Communication, Control and Computing},
year = {1996},
pages = {533--542}
}
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Abstract
Given an undirected graph G, finding a spanning tree of G with maximum number of leaves is NP-complete. We use the simple technique of local optimization to provide the first approximation algorithms for this problem. Our algorithms run in polynomial time to produce locally optimal solutions. We prove that locally optimal solutions to this problem are globally nearoptimal. In particular, we prove that two such algorithms have performance ratios of 5 and 3. The latter algorithm employs more powerful local-improvement steps than the former and hence has higher running time. This may indicate an interesting trade-off between the performance ratios and the running times of the series of algorithms we describe. Keywords: Approximation algorithms, NP-complete problems, Performance ratio, Local optimization, Communication network design, Combinatorial algorithms. 1 Introduction Given an undirected graph G = (V; E), the Maximum Leaf Spanning Tree problem is to find a spanning tree of G with ...
