The Bit Probe Complexity Measure Revisited

Abstract

The bit probe complexity of a static data structure problem within a given size bound was defined by Elias and Flower. It is the number of bits one needs to probe in the data structure for worst case data and query with an optimal encoding of the data within the space bound. We make some furtber investigations into the properties of the bit probe complexity measure. We determine the complexity of the full problem, which is the problem where every possible query is allowed, within an additive constant. We show a trade off-between structure size and the number of bit probes for all problems. We show that the complexity of almost every problem, even with small query sets, equals that of the full problem. We show how communication complexity can be used to give small, but occasionally tight lower bounds for natural functions. We define the class of access feasible static structure problems and conjecture that not every polynomial time computable problem is access feasible. We show a link to dynamic problems by showing that if polynomial time computable functions without feasible static structures exist, then there are problems in P which can not be reevaluated efficiently on-line.