Cell-probe model

In computer science, the cell-probe model is a model of computation similar to the random-access machine, except that all operations are free except memory access. This model is useful for proving lower bounds of algorithms for data structure problems.

Overview

The cell-probe model is a minor modification of the random-access machine model, itself a minor modification of the counter machine model, in which computational cost is only assigned to accessing units of memory called cells.

In this model, computation is framed as a problem of querying a set of memory cells. The problem has two phases: the preprocessing phase and the query phase. The input to the first phase, the preprocessing phase, is a set of data from which to build some structure from memory cells. The input to the second phase, the query phase, is a query datum. The problem is to determine if the query datum was included in the original input data set. Operations are free except to access memory cells.

This model is useful in the analysis of data structures. In particular, the model clearly shows a minimum number of memory accesses to solve a problem in which there is stored data on which we would like to run some query. An example of such a problem is the dynamic partial sum problem.[1][2]

History

In Andrew Yao’s 1981 paper “Should Tables Be Sorted?”,[3] Yao described the cell-probe model and used it to give a minimum number of memory cell “probes” or accesses necessary to determine whether a given query datum exists within a table stored in memory.

References

1. ^ Jump up to:ab Pătraşcu, Mihai; Demaine, Erik D. (2006). “Logarithmic lower bounds in the cell-probe model”. SIAM Journal on Computing. 35 (4): 932–963. arXiv:cs/0502041. Bibcode:2005cs……..2041P. doi:10.1137/s0097539705447256.
2. ^ Jump up to:ab Pătraşcu, Mihai. “Lower Bounds for Dynamic Partial Sums” (PDF). Retrieved 9 April 2014.
3. ^Yao, Andrew Chi-Chih (July 1981). “Should Tables Be Sorted?”. J. ACM. 28 (3): 615–628. doi:10.1145/322261.322274.
4. ^ Jump up to:ab Chakrabarti, Amit; Regev, Oded (2004). “An optimal randomised cell probe lower bound for approximate nearest neighbour searching”. Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science: 473–482.
5. ^Zatloukal, Kevin (November 10, 2010). “Notes on “Logarithmic Lower Bounds in the Cell-Probe Model”” (PDF). Retrieved 9 April 2014.

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