Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All-Distances Sketches, Revisited: HIP Estimators for Massive Graphs
  Analysis   Graph datasets with billions of edges, such as social and Web graphs, are
prevalent, and scalable computation is critical. All-distances sketches (ADS)
[Cohen 1997], are a powerful tool for scalable approximation of statistics.
  The sketch is a small size sample of the distance relation of a node which
emphasizes closer nodes. Sketches for all nodes are computed using a nearly
linear computation and estimators are applied to sketches of nodes to estimate
their properties.
  We provide, for the first time, a unified exposition of ADS algorithms and
applications. We present the Historic Inverse Probability (HIP) estimators
which are applied to the ADS of a node to estimate a large natural class of
statistics. For the important special cases of neighborhood cardinalities (the
number of nodes within some query distance) and closeness centralities, HIP
estimators have at most half the variance of previous estimators and we show
that this is essentially optimal. Moreover, HIP obtains a polynomial
improvement for more general statistics and the estimators are simple,
flexible, unbiased, and elegant.
  For approximate distinct counting on data streams, HIP outperforms the
original estimators for the HyperLogLog MinHash sketches (Flajolet et al.
2007), obtaining significantly improved estimation quality for this
state-of-the-art practical algorithm.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci