Cell-Probe Proofs

Abstract

We study the nondeterministic cell-probe complexity of static data structures. We introduce cell-probe proofs (CPP), a proof system for the cell-probe model, which describes verification instead of computation in the cell-probe model. We present a combinatorial characterization of CPP. With this novel tool, we prove the following lower bounds for the nondeterministic cell-probe complexity of static data structures. –There exists a data structure problem with high nondeterministic cell-probe complexity. –For the exact nearest neighbor search (NNS) problem or the partial match problem in high dimensional Hamming space, for any data structure with Poly( n ) cells, each of which contains O ( n C ) bits where C < 1, the nondeterministic cell-probe complexity is at least Ω(log( d /log n )), where d is the dimension and n is the number of points in the data set. –For the polynomial evaluation problem of d -degree polynomial over finite field of size 2 k where d ≤ 2 k , for any data structure with s cells, each of which contains b bits, the nondeterministic cell-probe complexity is at least min (( k / b ( d − 1)), ( k −log( d −1)/log s )).