Recent years have witnessed an increase in research activity for the detection of structural variants (SVs) and their association to human disease. The advent of next-generation sequencing technologies make it possible to extend the scope of structural variation studies to a point previously unimaginable as exemplified by the 1000 Genomes Project. Although various computational methods have been described for the detection of SVs, no such algorithm is yet fully capable of discovering transposon insertions, a very important class of SVs to the study of human evolution and disease. In this article, we provide a complete and novel formulation to discover both loci and classes of transposons inserted into genomes sequenced with high-throughput sequencing technologies. In addition, we also present conflict resolution improvements to our earlier combinatorial SV detection algorithm (VariationHunter) by taking the diploid nature of the human genome into consideration. We test our algorithms with simulated data from the Venter genome (HuRef) and are able to discover >85% of transposon insertion events with precision of >90%. We also demonstrate that our conflict resolution algorithm (denoted as VariationHunter-CR) outperforms current state of the art (such as original VariationHunter, BreakDancer and MoDIL) algorithms when tested on the genome of the Yoruba African individual (NA18507).