The Bit Probe Complexity Measure Revisited

A static data structure problem consists of a set of data D, a set of queries Q and a function f with domain D × Q. Given a space bound b, a (good) solution to the problem is an encoding e: D → {0,1}b, so that for any y, f(x,y) can be determined (quickly) by probing e(x). The worst case number of probes needed is C b (f), the bit probe complexity of f. We study the properties of the complexity measure C b (·).

[1]  Leslie G. Valiant,et al.  Fast probabilistic algorithms for hamiltonian circuits and matchings , 1977, STOC '77.

[2]  Peter Frankl,et al.  Complexity classes in communication complexity theory , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[3]  Greg N. Frederickson,et al.  Data structures for on-line updating of minimum spanning trees , 1983, STOC.

[4]  H. Chernoff A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[5]  Leonard M. Adleman,et al.  Two theorems on random polynomial time , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[6]  Albert R. Meyer,et al.  The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.

[7]  Jeffrey Scott Vitter,et al.  A Complexity Theoretic Approach to Incremental Computation , 1993, STACS.

[8]  Peter Bro Miltersen On-Line Reevaluation of Functions , 1992 .

[9]  Peter Bro Miltersen,et al.  Complexity Models for Incremental Computation , 1994, Theor. Comput. Sci..

[10]  Andrew Chi-Chih Yao,et al.  Should Tables Be Sorted? , 1981, JACM.

[11]  Peter Elias,et al.  The Complexity of Some Simple Retrieval Problems , 1975, JACM.

[12]  Torben Hagerup,et al.  A Guided Tour of Chernoff Bounds , 1990, Inf. Process. Lett..

[13]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[14]  Kurt Mehlhorn,et al.  Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract) , 1982, STOC '82.

[15]  Greg N. Frederickson,et al.  Data Structures for On-Line Updating of Minimum Spanning Trees, with Applications , 1985, SIAM J. Comput..

[16]  Miklós Ajtai,et al.  A lower bound for finding predecessors in Yao's cell probe model , 1988, Comb..