## SSS Abstracts |

Our result on list decoding follows from a much more general result: any local property satisfied with high probability by a random linear code is also satisfied with high probability by a random LDPC code from Gallager's distribution. Local properties are properties characterized by the exclusion of small sets of codewords, and include list-decoding, list-recovery and average-radius list-decoding. Along the way, we give a characterization of sets of codewords that are likely to appear in a random linear code, which may be of independent interest.

In the first part of this talk I will present theoretically efficient implementations of parallel graph algorithms for a set of 20 important graph problems. Our codes, which we have publicly open-sourced as part of the Graph Based Benchmark Suite (GBBS) solve these problems on the Hyperlink Web graph using a single commodity multicore machine with a terabyte of RAM, with most of the codes running in under a minute on this graph. The running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs, and for many of the problems that we consider, this is the first time they have been solved on graphs at this scale.

In the second part of this talk I will present Aspen, a framework for processing streaming graphs, which are graphs that evolve over time via a stream of updates (batches of edge insertions/deletions). The key idea is to represent the adjacency information using a purely-functional compressed tree data structure called a C-tree, which can be efficiently updated. Aspen achieves millisecond latency for processing small batches, and achieves throughputs of hundreds of millions of updates per second for very large batches, while providing strict serializability for both queries and updates. Using Aspen, we are able to concurrently update and run analytics on the Hyperlink Web graph using a single commodity multicore server with a terabyte of RAM.

Based on joint work with Guy Blelloch and Julian Shun.

We introduce parity models, a new approach for enabling erasure-coded resilience in prediction serving systems. A parity model is a neural network trained to transform erasure-coded queries into a form that enables a decoder to reconstruct slow or failed predictions. We implement parity models in ParM, a prediction serving system that makes use of erasure-coded resilience. ParM encodes multiple queries into a ``parity query'', performs inference over parity queries using parity models, and decodes approximations of unavailable predictions by using the output of a parity model. We showcase the applicability of parity models to image classification, speech recognition, and object localization tasks. Parity models enable accurate reconstructions of unavailable predictions and reduce tail latency in the presence of resource contention. These results highlight the potential of parity models to open new doors in imparting resource-efficient resilience to prediction serving systems.