This Article 
 Bibliographic References 
 Add to: 
Indexing Valid Time Databases via B+-Trees
November/December 1999 (vol. 11 no. 6)
pp. 929-947

Abstract—We present an approach, named MAP21, which uses standard $\rm B^+$-trees to provide efficient indexing of valid time ranges. The MAP21 approach is based on mapping one dimensional ranges to one dimensional points where the lexicographical order among the ranges is preserved. The proposed approach may employ more than one tree, each indexing a disjoint subset of the indexed data. When compared to the Time Index and the $\rm R^*$-tree we show that MAP21's performance is comparable to or better than those, depending on the type of query. In terms of storage, MAP21's structure was less than 10 percent larger than the $\rm R^*$-tree's and much smaller than the Time Index's. The main contribution of this paper though, is to show that standard $\rm B^+$-trees, available in virtually any DBMS, can be used to provide an efficient temporal index.

[1] R.T. Snodgrass and I. Ahn, "Temporal Databases," Computer, vol. 19, no. 9, pp. 35-42, Sept. 1986.
[2] C.S. Jensen, J. Clifford, R. Elmasri, S.K. Gadia, P. Hayes and S. Jajodia, eds., "A Glossary of Temporal Database Concepts," ACM SIGMOD Record, vol. 23, no. 1, pp. 52-64, Mar. 1994.
[3] E. McKenzie, “Bibliography: Temporal Databases,” ACM SIGMOD Record, vol. 15, no. 4, pp. 40-52, Dec. 1986.
[4] M.D. Soo, "Bibliography on Temporal Databases," ACM SIGMOD Record, vol. 20, no. 1, pp. 14-23, 1991.
[5] N. Kline, "An Update of the Temporal Database Bibliography," SIGMOD Record, vol. 22, no. 4, Dec. 1993.
[6] G. Özsoyovglu and R.T. Snodgrass, “Temporal and Real-Time Databases: A Survey,” IEEE Trans. Knowledge and Data Eng., vol. 7, no. 4, pp. 513–532, 1995.
[7] V.J. Tsotras and A. Kumar, “Temporal Database Bibliography Update,” ACM SIGMOD Record, vol. 25, no. 1, pp. 41-51, Mar. 1996.
[8] B. Salzberg and V.J. Tsotras, "A Comparison of Access Methods for Time-Evolving Data," ACM Computing Surveys, to appear; also available as Technical Report No. TR-18, TimeCenter, Aalborg Univ., 1997: .
[9] R. Elmasri, G.T.J. Wuu, and V. Kouramajian, “The Time Index and the Monotonic$\rm B^+$-Tree,” Temporal Databases: Theory, Design, and Implementation, A. Tansel et al., eds., chapter 18, pp. 433-456, Benjamin/Cummings, Redwood City, Calif., 1993.
[10] V. Kouramajian et al., “The Time Index+: An Incremental Access Structure for Temporal Databases,” Proc. Third Int'l Conf. Knowledge and Information Management, Gaithersburg, Md., pp. 296-303, Nov. 1994.
[11] H. Shen, B.C. Ooi, and H.J. Lu, "The tp-Index: A Dynamic and Efficient Indexing Mechanism for Temporal Databases," Proc. IEEE Conf. Data Eng., pp. 274-281, 1994.
[12] C.-H. Ang and K.-P. Tan, “The Interval B-Tree,” Information Processing Letters, vol. 53, no. 2, pp. 85-89, Jan. 1995.
[13] C.H. Goh et al., “Indexing Temporal Data Using Existing$\rm B^+$-Trees,” Data and Knowledge Eng., vol. 18, pp. 147-165, 1996.
[14] H. Gunadhi and A. Segev, "Efficient Indexing Methods for Temporal Relations," EEE Trans. Knowledge and Data Eng., vol. 5, pp. 496-509, 1993.
[15] V.J. Tsotras and N. Kangelaris, "The Snapshot Index: An I/O-Optimal Access Method for Timeslice Queries," Information Systems, vol. 20, no. 3, pp. 237-260, 1995.
[16] D. Lomet and B. Salzberg, “Transaction Time Databases,” Temporal Databases: Theory, Design, and Implementation, A. Tansel et al., eds., chapter 16, pp. 388-417, Benjamin/Cummings, Redwood City, Calif., 1993.
[17] T. Sellis, N. Roussopoulos, and C. Faloutsos, “The R+-Tree: A Dynamic Index for Multidimensional Objects,” Proc. 13th Int'l Conf. Very Large Data Bases (VLDB), 1987.
[18] C. Faloutsos and Y. Rong, "DOT: A Spatial Access Method Using Fractals," Proc. Seventh Int'l Conf. Data Eng., IEEE, 1991.
[19] J. Orenstein, “Spatial Query Processing in an Object-Oriented Database System,” Proc. Fifth ACM-SIGMOD Conf., pp. 326-336, 1986.
[20] A. Guttman, “R-Trees: A Dynamic Index Structure for Spatial Searching,” Proc. ACM SIGMOD Conf. Management of Data, 1984.
[21] N. Beckmann, H.-P. Kriegel, R. Schneider, and B. Seeger, “The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles,” Proc. ACM SIGMOD Conf. Management of Data, 1990.
[22] H. Samet, The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
[23] M.A. Nascimento, M.H. Dunham, and V. Kouramajian, “A Multiple Tree Mapping-Based Approach for Valid-Time Ranges Indexing,” J. Brazilian Computer Soc., vol. 2, no. 3, pp. 36-46, Apr. 1996.
[24] R. Elmasri and S.B. Navathe, Fundamentals of Database Systems, second ed., Benjamin/Cummings, 1994.
[25] T. Johnson and D. Shasha, “The Performance of Concurrent Data Structure Algorithms,” ACM Trans. Database Systems, vol. 18, no. 1, pp. 51-101, Mar. 1993.
[26] M.A. Nascimento and M.H. Dunham, “Indexing Valid Time Databases via$\rm B^+$-Trees—The MAP21 Approach,” Technical Report CSE-97-08, SEAS, Southern Methodist Univ., Dallas, 1997.
[27] J. Clifford, C.E. Dyreson, T. Isakowitz, C.S. Jensen, and R.T. Snodgrass, “On the Semantics of‘Now’in Databases,” ACM Trans. Database Systems, vol. 22, no. 2, pp. 171–214, 1997.
[28] M.A. Nascimento, “Efficient Indexing of Temporal Databases via$\rm B^+$-Trees,” PhD thesis, Southern Methodist Univ., Dallas, Aug. 1996.
[29] B. Seeger and P.-A. Larson, “Multi-Disk B-Trees,” Proc. 1991 ACM SIGMOD Int'l Conf. Management Data, Denver, pp. 436-445, June 1991.
[30] The TSQL2 Temporal Query Language. R.T. Snodgrass, ed., Kluwer Academic Publishers, 1995.
[31] M.D. Soo, N. Kline, and R.T. Snodgrass, “SQL-92 Combatibility Issues,” TSQL2 Temporal Query Language, R.T. Snodgrass, ed., chapter 26, pp. 501-504, Kluwer, Boston, 1995.
[32] M.H. Böhlen, R.T. Snodgrass, and M.D. Soo, “Coalescing in Temporal Databases,” Proc. Very Large Data Base Conf., pp. 180–191, 1996.
[33] A. Steiner, “TimeDB Home Page,” URL: publications2.html personal/steinerTimeDB.html, Dec. 1996.
[34] Oracle Corp., Oracle 7 Server—SQL Language Reference Manual, 1992.
[35] Y. Theodoridis and D. Papadias, “Range Queries Involving Spatial Relations: A Performance Analysis,” Proc. Second Int'l Conf. Spatial Information Theory, Semmering, Austria, pp. 537-552, Sept. 1995.
[36] I. Kamel and C. Faloutsos, "Parallel R-Trees," Proc. ACM SIGMOD Conf., pp. 195-204, 1992.
[37] V. Kouramajian, R. Elmasri, and A. Chaudhry, “Declustering Techniques for Parallelizing Temporal Access Structures,” Proc. 10th IEEE Int'l Conf. Data Eng., Houston, pp. 232-242, Feb. 1994.
[38] M.A. Nascimento and M.H. Dunham, “Using$\rm B^+$-Trees as a Practical Alternative to the Classical R-Tree,” Proc. 11th Brazilian Symp. Databases, Sao Carlos, Brazil, pp. 187-200, Oct. 1996.
[39] M.A. Nascimento and M.H. Dunham, “Using$\rm B^+$-Trees in a Two Disk-Single Processor Architecture to Efficiently Process Inclusion Spatial Queries,” extended abstract, Proc. Fifth ACM Int'l Workshop Advances in Geographical Information Systems, Las Vegas, Nev., pp. 5-8, Nov. 1997.
[40] A. Kumar, V.J. Tsotras, and C. Faloutsos, "Access Methods for Bitemporal Databases," Recent Advances in Temporal Databases, J. Clifford and A. Tuzhilin, eds., pp. 235-254. Springer-Verlag, 1995.
[41] M.A. Nascimento, M.H. Dunham, and R. Elmasri, “M-IVTT: An Index for Bitemporal Databases,” Proc. Seventh Int'l Conf. Databases and Expert Systems Applications, Zurich, Switzerland, pp. 779-790, Sept. 1996.
[42] J. Janninck, “Implementing Deletions in$\rm B^+$-Trees,” ACM SIGMOD Record, vol. 24, no. 1, pp. 6-8, Mar. 1995.

Index Terms:
Temporal databases, access structures, indexing, $\rm B^+$-trees, R-trees.
Mario A. Nascimento, Margaret H. Dunham, "Indexing Valid Time Databases via B+-Trees," IEEE Transactions on Knowledge and Data Engineering, vol. 11, no. 6, pp. 929-947, Nov.-Dec. 1999, doi:10.1109/69.824609
Usage of this product signifies your acceptance of the Terms of Use.