# A Linear-Time and Linear-Space Algorithm for the Minimum Vertex Cover Problem on Giant Graphs

**Hong Xu**, T. K. Satish Kumar, and Sven Koenig.
**A linear-time and linear-space algorithm for the minimum vertex cover problem on giant graphs.**
In *Proceedings of the 10th International Symposium on Combinatorial Search (SoCS)*, 173–174. 2017.
URL: https://aaai.org/ocs/index.php/SOCS/SOCS17/paper/viewFile/15789/15080.

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## Abstract

In this paper, we develop the message passing based linear-time and linear-space MVC algorithm (MVC-MPL) for solving the minimum vertex cover (MVC) problem. MVC-MPL is based on heuristics derived from a theoretical analysis of message passing algorithms in the context of belief propagation. We show that MVC-MPL produces smaller vertex covers than other linear-time and linear-space algorithms.

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