We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial erasures in adjacency entries. We focus on two computational tasks: testing if a graph is connected ... more >>>

A binary code $\text{Enc}:\{0,1\}^k \rightarrow \{0,1\}^n$ is $(\frac{1}{2}-\varepsilon,L)$-list decodable if for every $w \in \{0,1\}^n$, there exists a set $\text{List}(w)$ of size at most $L$, containing all messages $m \in \{0,1\}^k$ such that the relative Hamming distance between $\text{Enc}(m)$ and $w$ is at most $\frac{1}{2}-\varepsilon$.
A $q$-query local list-decoder is ... more >>>

We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure-resilient and tolerant property testing. Local decoding in the presence of errors has been extensively studied, but has not been considered explicitly in the presence of erasures.

Motivated by ... more >>>