SpaceSaving ^±

Abstract

In this paper, we propose the first deterministic algorithms to solve the frequency estimation and frequent item problems in the bounded-deletion model. We establish the space lower bound for solving the deterministic frequent items problem in the bounded-deletion model, and propose Lazy SpaceSaving ± and SpaceSaving ± algorithms with optimal space bound. We develop an efficient implementation of the SpaceSaving ± algorithm that minimizes the latency of update operations using novel data structures. The experimental evaluations testify that SpaceSaving ± has accurate frequency estimations and achieves very high recall and precision across different data distributions while using minimal space. Our experiments clearly demonstrate that, if allowed the same space, SpaceSaving± is more accurate than the state-of-the-art protocols with up to logU - 1/ logU of the items deleted, where U is the size of the input universe. Moreover, motivated by prior work, we propose Dyadic SpaceSaving ± , the first deterministic quantile approximation sketch in the bounded-deletion model.

Large very dense subgraphs in a stream of edges

“…The Spacesaving± [20] generalizes for the insertion and α-bounded deletion model. We will analyse it in some other work.…”

“…A. 4 The SpaceSaving algorithm ± [20] This algorithm introduced in [20] computes an approximation of the frequencies of the k most frequent items elements in a stream of insertions and deletions, with the bounded deletions hypothesis [14]. If D is the number of deletions and I the number of insertions, then D ≤ (1 − 1/α)I, for some constant α ≥ 1.…”

“…We combined two well known techniques: the Spacesaving algorithm [18,20] which deterministically selects the most frequent items approximately and the Minhash technique which approximates the low frequencies probabilistically. Our main results are:…”

“…If f decreases fast enough, we then only use space O(log 2 n • log log n). The analysis relies on the Spacesaving algorithm [18,20] and on sampling the stream.…”

“…In such a model, the number D of deletions is related to the number I of insertions: D ≤ (1 − 1/α)I, for some constant α ≥ 1.2 Our study of this model is deferred because the bounded deletions model is studied in[20] but the algorithm therein has some issues currently in the process of being corrected.…”