Genome assembly from error-prone reads
For short reads, the typical and the most widely used solution is to correct away sequencing errors before assembly. You can correct errors with k-mer spectrum, a trie or multi-alignment. There are many papers on this topic.

Error correction alone won't fix all sequencing errors. Remaining errors may lead to bubbles and tips in the overlap/de Bruijn graph. You can identify them by inspecting the local topology of assembly graph.