# Silent MST approximation for tiny memory

## TL;DR

This paper introduces a silent self-stabilizing algorithm for the minimum spanning tree problem that balances solution quality with memory efficiency in the state model of network communication.

## Contribution

It presents the first approximation algorithm for MST that is silent and self-stabilizing, reducing space requirements compared to exact solutions.

## Key findings

- Achieves a trade-off between solution quality and space used.
- Operates in the classic state model with silent stabilization.
- Reduces memory usage for MST approximation in distributed networks.

## Abstract

In this paper we show that approximation can help reduce the space used for self-stabilization. In the classic \emph{state model}, where the nodes of a network communicate by reading the states of their neighbors, an important measure of efficiency is the space: the number of bits used at each node to encode the state. In this model, a classic requirement is that the algorithm has to be \emph{silent}, that is, after stabilization the states should not change anymore. We design a silent self-stabilizing algorithm for the problem of minimum spanning tree, that has a trade-off between the quality of the solution and the space needed to compute it.