On the Cell Probe Complexity of Dynamic Membership

We study the dynamic membership problem, one of the most fundamental data structure problems, in the cell probe model with an arbitrary cell size. We consider a cell probe model equipped with a cache that consists of at least a constant number of cells; reading or writing the cache is free of charge. For nearly all common data structures, it is known that with sufficiently large cells together with the cache, we can significantly lower the amortized update cost to o(1). In this paper, we show that this is not the case for the dynamic membership problem. Specifically, for any deterministic membership data structure under a random input sequence, if the expected average query cost is no more than 1+ for some small constant , we prove that the expected amortized update cost must be at least (1), namely, it does not benefit from large block writes (and a cache). The space the structure uses is irrelevant to this lower bound. We also extend this lower bound to randomized membership structu...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: KE YI, QIN ZHANG
• Keywords: Cell Probe Model, Discrete Algorithms, Dynamic Membership Problem, Membership Data Structure, SODA 2010