Cell-Probe Proofs

• Authors: Yitong Yin
• Venue: ACM Transactions on Computation Theory (TOCT)
• Year: 2010

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(nC) bits where C 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 2k where d ≤ 2k, 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)/logs)).