This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Performance of B±Trees with Partial Expansions
June 1989 (vol. 1 no. 2)
pp. 248-257

The authors mathematically analyze the behavior of B/sup trees with partial expansions file structure under random insertions, focusing on the expected storage utilization and the expected cost of insertions. The model can be used for studying both the asymptotic and dynamic behavior. The accuracy of the model is confirmed by simulation. Disk space management is found to be more difficult than for standard B/sup trees. Two simple space-management schemes specifically designed for handling buckets of two different sizes are investigated. It is found that an overall storage utilization of 81% can be achieved in practice.

[1] M. Abramowitz and I. Stegun,Handbook of Mathematical Functions. New York: Dover, 1972.
[2] R. Baeza-Yates, "The expected behavior of B+-trees,"Acta Inform., vol. 26, pp. 439-471, 1989.
[3] R. Baeza-Yates, "A dynamic storage allocation algorithm and its application to B+-trees," inProc. XIII Latin Amer. Conf. Inform. Sci. (EXPODATA 87), vol. 2, Bogota, Colombia, 1987, pp. 1122-1132.
[4] A. Clausing, "Kantorovich-type inequalities,"Amer. Math. Monthly, vol. 89, no. 5, pp. 314-330, 1982.
[5] C. Comer, "The ubiquitousB-trees,"ACM Comput. Surveys, vol. 11, no. 2, pp. 121-136, June 1979.
[6] B. Eisenbarth, N. Ziviani, G. Gonnet, K. Mehlhorn, and D. Wood, "The theory of fringe analysis and its application to 2-3 trees and B-trees,"Inform. Contr., vol. 55, nos. 1-3, pp. 125-174, 1982.
[7] G. Frederickson, "Improving storage utilization in balanced trees," inProc. 17th Allerton Conf. Commun., Contr. Comput., Monticello, IL, 1979, pp. 255-264.
[8] P-Å. Larson, "Linear hashing with partial expansions," inProc. 6th Int. Conf. Very Large Data Bases, Montreal, Canada, 1980, pp. 224- 232.
[9] D. Lomet, "Partial expansions for file organizations with an index,"ACM Trans. Database Syst., vol. 12, no. 1, pp. 65-84, 1987.
[10] T. Nakamura and T. Mizoguchi, "An analysis of storage utilization factor in block split data structuring scheme," inProc. 4th Int. Conf. Very Large Data Bases, Berlin, 1978, pp. 489-495.
[11] A. Yao, "On random 2-3 trees,"Acta Inform., vol. 9, pp. 159-170, 1978.

Index Terms:
performance; mathematical analysis; asymptotic behaviour; disk space management; buckets handling; B/sup trees; partial expansions; behavior; file structure; random insertions; expected storage utilization; expected cost; insertions; dynamic behavior; simulation; space-management schemes; storage utilization; data structures
Citation:
R.A. Baeza-Yates, P.-A. Larson, "Performance of B±Trees with Partial Expansions," IEEE Transactions on Knowledge and Data Engineering, vol. 1, no. 2, pp. 248-257, June 1989, doi:10.1109/69.87964
Usage of this product signifies your acceptance of the Terms of Use.