NDLI: Maximally recoverable codes for grid-like topologies

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Proximity in the age of distraction: robust approximate nearest neighbor search

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Optimal hashing-based time-space trade-offs for approximate near neighbors

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Distance sensitive bloom filters without false negatives

Optimal approximate polytope membership

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Maximally recoverable codes for grid-like topologies

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The complexity of simulation and matrix multiplication

Better approximations for tree sparsity in nearly-linear time

Counting matchings in irregular bipartite graphs and random lifts

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Extension complexity lower bounds for mixed-integer extended formulations

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Time-space trade-offs in population protocols

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Fair scheduling via iterative quasi-uniform sampling

A logarithmic additive integrality gap for bin packing

Tight algorithms for vertex cover with hard capacities on multigraphs and hypergraphs

Iterative partial rounding for vertex cover with hard capacities

Unrelated machine scheduling of jobs with uniform smith ratios

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Deciding contractibility of a non-simple curve on the boundary of a 3-manifold

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Parameter-free topology inference and sparsification for data on manifolds

Maximally recoverable codes for grid-like topologies

Content Provider	ACM Digital Library
Author	Yekhanin, Sergey Gopalan, Parikshit Kopparty, Swastik Hu, Guangda Wang, Carol Saraf, Shubhangi
Abstract	The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we view as the main coding theoretic barrier to deploying longer codes in storage: at large lengths, failures are not independent and correlated failures are inevitable. This motivates designing codes that allow quick data recovery even after large correlated failures, and which have efficient encoding and decoding. We propose that code design for distributed storage be viewed as a two step process. The first step is choose a topology of the code, which incorporates knowledge about the correlate d failures that need to be handled, and ensures local recovery from such failures. In the second step one specifies a code with the chosen topology by choosing coefficients from a finite field $𝔽_{q}.$ In this step, one tries to balance reliability (which is better over larger fields) with encoding and decoding efficiency (which is better over smaller fields). This work initiates an in-depth study of this reliability/efficiency tradeoff. We consider the field-size needed for achieving maximal recoverability: the strongest reliability possible with a given topology. We propose a family of topologies called grid-like topologies which unify a number of topologies considered both in theory and practice, and prove the following results about codes for such topologies: • The first super-polynomial lower bound on the field size needed for achieving maximal recoverability in a simple grid-like topology. To our knowledge, there was no super-linear lower bound known before, for any topology. • A combinatorial characterization of erasure patterns correctable by Maximally Recoverable codes for a topology which corresponds to tensoring MDS codes with a parity check code. This topology is used in practice (for instance see $[MLR^{+}14]).$ We conjecture a similar characterization for Maximally Recoverable codes instantiating arbitrary tensor product topologies.
Starting Page	2092
Ending Page	2108
Page Count	17
File Format	PDF
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-01-16
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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