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DOI: 10.4230/LIPIcs.ICALP.2018.79
URN: urn:nbn:de:0030-drops-90830
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9083/
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Huang, Zhiyi ; Tang, Zhihao Gavin ; Wu, Xiaowei ; Zhang, Yuhao

Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

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LIPIcs-ICALP-2018-79.pdf (0.9 MB)


Abstract

We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of the offline vertex, but also on the arrival time of the online vertex. To our knowledge, this is the first competitive ratio strictly larger than 1-1/e for an online bipartite matching problem achieved under the randomized primal-dual framework. Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest offer at its arrival.

BibTeX - Entry

@InProceedings{huang_et_al:LIPIcs:2018:9083,
  author =	{Zhiyi Huang and Zhihao Gavin Tang and Xiaowei Wu and Yuhao Zhang},
  title =	{{Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9083},
  URN =		{urn:nbn:de:0030-drops-90830},
  doi =		{10.4230/LIPIcs.ICALP.2018.79},
  annote =	{Keywords: Vertex Weighted, Online Bipartite Matching, Randomized Primal-Dual}
}

Keywords: Vertex Weighted, Online Bipartite Matching, Randomized Primal-Dual
Seminar: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 29.06.2018


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