Transcriptomic structural variants (TSVs) --- structural variants that affect expressed regions --- are common, especially in cancer. Detecting TSVs is a challenging computational problem. Sample heterogeneity (including differences between alleles in diploid organisms) is a critical confounding factor when identifying TSVs.
To improve TSV detection in heterogeneous RNA-seq samples, we introduce the Multiple Compatible Arrangement Problem (MCAP), which seeks k genome rearrangements to maximize the number of reads that are concordant with at least one rearrangement. This directly models the situation of a heterogeneous or diploid sample.
We prove that MCAP is NP-hard and provide a 1/4-approximation algorithm for k=1 and a 3/4-approximation algorithm for the diploid case (k=2) assuming an oracle for k=1. Combining these, we obtain a 3/16-approximation algorithm for MCAP when k=2 (without an oracle). We also present an integer linear programming formulation for general k. We completely characterize the graph structures that require k>1 to satisfy all edges and show such structures are prevalent in cancer samples.
We evaluate our algorithms on 381 TCGA samples and 2 cancer cell lines and show improved performance from the state-of-the-art TSV-calling tool, SQUID.