Archive for the ‘Set Reconciliation’ Category

Biff (Bloom Filter) Codes:…

Tuesday, August 7th, 2012

Biff (Bloom Filter) Codes: Fast Error Correction for Large Data Sets by M. Mitzenmacher and George Varghese.

Abstract:

Large data sets are increasingly common in cloud and virtualized environments. For example, transfers of multiple gigabytes are commonplace, as are replicated blocks of such sizes. There is a need for fast error-correction or data reconciliation in such settings even when the expected number of errors is small.

Motivated by such cloud reconciliation problems, we consider error-correction schemes designed for large data, after explaining why previous approaches appear unsuitable. We introduce Biff codes, which are based on Bloom filters and are designed for large data. For Biff codes with a message of length L and E errors, the encoding time is O(L), decoding time is O(L + E) and the space overhead is O(E). Biff codes are low-density parity-check codes; they are similar to Tornado codes, but are designed for errors instead of erasures. Further, Biff codes are designed to be very simple, removing any explicit graph structures and based entirely on hash tables. We derive Biff codes by a simple reduction from a set reconciliation algorithm for a recently developed data structure, invertible Bloom lookup tables. While the underlying theory is extremely simple, what makes this code especially attractive is the ease with which it can be implemented and the speed of decoding. We present results from a prototype implementation that decodes messages of 1 million words with thousands of errors in well under a second.

I followed this paper’s citation on set reconciliation to find the paper reported at: What’s the Difference? Efficient Set Reconciliation without Prior Context.

Suspect this line of work is far from finished and that you will find immediate and future applications of it for topic map applications.

What’s the Difference? Efficient Set Reconciliation without Prior Context

Monday, August 6th, 2012

What’s the Difference? Efficient Set Reconciliation without Prior Context by David Eppstein, Michael T. Goodrich, Frank Uyeda, and George Varghese.

Abstract:

We describe a synopsis structure, the Difference Digest, that allows two nodes to compute the elements belonging to the set difference in a single round with communication overhead proportional to the size of the difference times the logarithm of the keyspace. While set reconciliation can be done efficiently using logs, logs require overhead for every update and scale poorly when multiple users are to be reconciled. By contrast, our abstraction assumes no prior context and is useful in networking and distributed systems applications such as trading blocks in a peer-to-peer network, and synchronizing link-state databases after a partition.

Our basic set-reconciliation method has a similarity with the peeling algorithm used in Tornado codes [6], which is not surprising, as there is an intimate connection between set difference and coding. Beyond set reconciliation, an essential component in our Difference Digest is a new estimator for the size of the set difference that outperforms min-wise sketches [3] for small set differences.

Our experiments show that the Difference Digest is more efficient than prior approaches such as Approximate Reconciliation Trees [5] and Characteristic Polynomial Interpolation [17]. We use Difference Digests to implement a generic KeyDiff service in Linux that runs over TCP and returns the sets of keys that differ between machines.

Distributed topic maps anyone?