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arXiv · 2007.14569

Space- and Computationally-Efficient Set Reconciliation via Parity Bitmap Sketch (PBS)

Long Gong·Ziheng Liu·Liang Liu·Jun Xu·Mitsunori Ogihara·Tong Yang
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Abstract

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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Long Gong, Ziheng Liu, Liang Liu, Jun Xu, Mitsunori Ogihara, Tong Yang. 2020-07-29. Space- and Computationally-Efficient Set Reconciliation via Parity Bitmap Sketch (PBS). https://arxiv.org/abs/2007.14569

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