Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space- and Computationally-Efficient Set Reconciliation via Parity
  Bitmap Sketch (PBS)   Set reconciliation is a fundamental algorithmic problem that arises in many
networking, system, and database applications. In this problem, two large sets
A and B of objects (bitcoins, files, records, etc.) are stored respectively at
two different network-connected hosts, which we name Alice and Bob
respectively. Alice and Bob communicate with each other to learn $A\Delta B$,
the difference between A and B, and as a result the reconciled set $A\bigcup
B$.
  Current set reconciliation schemes are based on either Invertible Bloom
Filters (IBF) or Error-Correction Codes (ECC). The former has a low
computational complexity of O(d), where d is the cardinality of $A\Delta B$,
but has a high communication overhead that is several times larger than the
theoretical minimum. The latter has a low communication overhead close to the
theoretical minimum, but has a much higher computational complexity of
$O(d^2)$. In this work, we propose Parity Bitmap Sketch (PBS), an ECC- based
set reconciliation scheme that gets the better of both worlds: PBS has both a
low computational complexity of O(d) just like IBF-based solutions and a low
communication overhead of roughly twice the theoretical minimum. A separate
contribution of this work is a novel rigorous analytical framework that can be
used for the precise calculation of various performance metrics and for the
near-optimal parameter tuning of PBS.

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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: q-fin