A highly scalable assembler for processing massive sequencing data using thousands of cores, where SWAP is an acronym for Small World Asynchronous Parallel model. In SWAP-Assembler, two fundamental improvements are crucial for its scalability. Firstly, multi-step bi-directed graph (MSG) is presented as a comprehensive mathematical abstraction for genome assembly. With MSG the computational interdependence is resolved. Secondly, SWAP computational framework triggers the parallel computation of all operations without interference. Two additional steps are included to improve the quality of contigs. One is graph cleaning, which adopts the traditional methods of removing k-molecules and edges with low frequency, and the other is contig extension, which resolves special edges and some cross nodes with a heuristic method. Compared with several other assemblers, it showed very good performance in terms of scalability and contig quality.