License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.46
URN: urn:nbn:de:0030-drops-115422
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11542/
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Chen, Yong ; Goebel, Randy ; Su, Bing ; Tong, Weitian ; Xu, Yao ; Zhang, An

A 21/16-Approximation for the Minimum 3-Path Partition Problem

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LIPIcs-ISAAC-2019-46.pdf (0.6 MB)

Abstract

The minimum k-path partition (Min-k-PP for short) problem targets to partition an input graph into the smallest number of paths, each of which has order at most k. We focus on the special case when k=3. Existing literature mainly concentrates on the exact algorithms for special graphs, such as trees. Because of the challenge of NP-hardness on general graphs, the approximability of the Min-3-PP problem attracts researchers' attention. The first approximation algorithm dates back about 10 years and achieves an approximation ratio of 3/2, which was recently improved to 13/9 and further to 4/3. We investigate the 3/2-approximation algorithm for the Min-3-PP problem and discover several interesting structural properties. Instead of studying the unweighted Min-3-PP problem directly, we design a novel weight schema for l-paths, l in {1, 2, 3}, and investigate the weighted version. A greedy local search algorithm is proposed to generate a heavy path partition. We show the achieved path partition has the least 1-paths, which is also the key ingredient for the algorithms with ratios 13/9 and 4/3. When switching back to the unweighted objective function, we prove the approximation ratio 21/16 via amortized analysis.

BibTeX - Entry

@InProceedings{chen_et_al:LIPIcs:2019:11542,
  author =	{Yong Chen and Randy Goebel and Bing Su and Weitian Tong and Yao Xu and An Zhang},
  title =	{{A 21/16-Approximation for the Minimum 3-Path Partition Problem}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11542},
  URN =		{urn:nbn:de:0030-drops-115422},
  doi =		{10.4230/LIPIcs.ISAAC.2019.46},
  annote =	{Keywords: 3-path partition, exact set cover, approximation algorithm, local search, amortized analysis}
}

Keywords: 3-path partition, exact set cover, approximation algorithm, local search, amortized analysis
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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