| Status | 已發表Published |
| Fully Online Matching II: Beating Ranking and Water-filling | |
Huang, Z. ; Tang, Z.; Wu, X.; Zhang, Y.
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| 2020-11-01 | |
| Source Publication | IEEE 61st Annual Symposium on Foundations of Computer Science
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| Abstract | Karp, Vazirani, and Vazirani (STOC 1990) initiated the study of online bipartite matching, which has held a central role in online algorithms ever since. Of particular importance are the Ranking algorithm for integral matching and the Water-filling algorithm for fractional matching. Most algorithms in the literature can be viewed as adaptations of these two in the corresponding models. Recently, Huang et al.~(STOC 2018, SODA 2019) introduced a more general model called fully online matching, which considers general graphs and allows all vertices to arrive online. They also generalized Ranking and Water-filling to fully online matching and gave some tight analysis: Ranking is Ω≈0.567-competitive on bipartite graphs where the Ω-constant satisfies Ω e^Ω=1, and Water-filling is 2−2–√≈0.585-competitive on general graphs. We propose fully online matching algorithms strictly better than Ranking and Water-filling. For integral matching on bipartite graphs, we build on the online primal dual analysis of Ranking and Water-filling to design a 0.569-competitive hybrid algorithm called Balanced Ranking. To our knowledge, it is the first integral algorithm in the online matching literature that successfully integrates ideas from Water-filling. For fractional matching on general graphs, we give a 0.592-competitive algorithm called Eager Water-filling, which may match a vertex on its arrival. By contrast, the original Water-filling algorithm always matches vertices at their deadlines. Our result for fractional matching further shows a separation between fully online matching and the general vertex arrival model by Wang and Wong (ICALP 2015), due to an upper bound of 0.5914 in the latter model by Buchbinder, Segev, and Tkach (ESA 2017). |
| Keyword | Fully Online Matching Ranking Water-filling |
| Language | 英語English |
| The Source to Article | PB_Publication |
| PUB ID | 55615 |
| Document Type | Conference paper |
| Collection | THE STATE KEY LABORATORY OF INTERNET OF THINGS FOR SMART CITY (UNIVERSITY OF MACAU) |
| Corresponding Author | Huang, Z.; Tang, Z.; Wu, X.; Zhang, Y. |
| Recommended Citation GB/T 7714 | Huang, Z.,Tang, Z.,Wu, X.,et al. Fully Online Matching II: Beating Ranking and Water-filling[C], 2020. |
| APA | Huang, Z.., Tang, Z.., Wu, X.., & Zhang, Y. (2020). Fully Online Matching II: Beating Ranking and Water-filling. IEEE 61st Annual Symposium on Foundations of Computer Science. |
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