# Local Computation Algorithms for Graphs of Non-Constant Degrees

arXiv: https://arxiv.org/abs/1502.04022 · HTML: https://mlsanity.com/paper/1502.04022/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2015.

## Built on by (most cited first, 2 of 2)

- [Agnostic proper learning of monotone functions: beyond the black-box correction barrier](https://mlsanity.com/paper/2304.02700/) (2023)
- [PAC Learning is just Bipartite Matching (Sort of)](https://mlsanity.com/paper/2502.00607/) (2025)

## Abstract (arXiv)

In the model of local computation algorithms (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with subexponential dependence on d, while maintaining polylogarithmic dependence on n. We present: a randomized LCA for computing maximal independent sets whose time and space complexities are quasi-polynomial in d and polylogarithmic in n; for constant ε > 0, a randomized LCA that provides a (1-ε)-approximation to maximum matching whose time and space complexities are polynomial in d and polylogarithmic in n.