# Uniform Page Migration Problem in Euclidean Space

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

## 3. Algorithm and Its Upper Bound Analysis

**Lemma 1.**

**Proof.**

**Theorem 1.**

**Proof.**

## 4. A Lower Bound for PQ

**Theorem 2.**

**Proof.**

## 5. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Bienkowski, M. Migrating and replicating data in networks. Comput. Sci.-Res. Dev.
**2012**, 27, 169–179. [Google Scholar] [CrossRef] - Black, D.L.; Sleator, D.D. Competitive Algorithms for Replication and Migration Problems; Technical Report CMU-CS-89-201; Carnegie Mellon University: Pittsburgh, PA, USA, 1989. [Google Scholar]
- Chrobak, M.; Larmore, L.L.; Reingold, N.; Westbrook, J. Page migration algorithms using work functions. J. Algorithms.
**1997**, 24, 124–157. [Google Scholar] [CrossRef] - Westbrook, J. Randomized algorithms for multiprocessor page migration. SIAM J. Comput.
**1994**, 23, 951–965. [Google Scholar] [CrossRef] - Matsubayashi, A. Uniform page migration on general networks. Int. J. Pure Appl. Math.
**2008**, 42, 161–168. [Google Scholar] - Meyer auf der Heide, F.; Vöcking, B.; Westermann, M. Provably Good and Practical Strategies for Non-Uniform Data Management in Networks. In Proceedings of the 7th Annual European Symposium on Algorithms (LNCS 1643), Prague, Czech Republic, 16–18 July 1999; Springer: New York, NY, USA; pp. 89–100.
- Maggs, B.M.; Meyer auf der Heide, F.; Vöcking, B.; Westermann, M. Exploiting Locality for Data Management in Systems of Limited Bandwidth. In Proceedings of the 38th Annual Symposium on Foundations of Computer Science, Miami Beach, FL, USA, 19–22 October 1997; pp. 284–293.
- Bartal, Y.; Charikar, M.; Indyk, P. On page migration and other relaxed task systems. Theor. Comput. Sci.
**2001**, 268, 43–66. [Google Scholar] [CrossRef] - Matsubayashi, A. A 3+Omega (1) Lower Bound for Page Migration. In Proceedings of the 2015 Third International Symposium on Computing and Networking, Sapporo, Japan, 8–11 December 2015; pp. 314–320.
- Matsubayashi, A. Asymptotically optimal online page migration on three points. Algorithmica
**2015**, 71, 1035–1064. [Google Scholar] [CrossRef] - Bartal, Y.; Fiat, A.; Rabani, Y. Competitive algorithms for distributed data management. J. Comput. Syst. Sci.
**1995**, 51, 341–358. [Google Scholar] [CrossRef] - Lund, C.; Reingold, N.; Westbrook, J.; Yan, D. Competitive on-line algorithms for distributed data management. SIAM J. Comput.
**1999**, 28, 1086–1111. [Google Scholar] [CrossRef]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Khorramian, A.; Matsubayashi, A. Uniform Page Migration Problem in Euclidean Space. *Algorithms* **2016**, *9*, 57.
https://doi.org/10.3390/a9030057

**AMA Style**

Khorramian A, Matsubayashi A. Uniform Page Migration Problem in Euclidean Space. *Algorithms*. 2016; 9(3):57.
https://doi.org/10.3390/a9030057

**Chicago/Turabian Style**

Khorramian, Amanj, and Akira Matsubayashi. 2016. "Uniform Page Migration Problem in Euclidean Space" *Algorithms* 9, no. 3: 57.
https://doi.org/10.3390/a9030057