Somatically acquired DNA rearrangements are characteristic of many cancers. The use of these mutations as diagnostic markers is challenging, because tumor cells are frequently admixed with normal cells, particularly in early stage tumor samples, and thus the samples contain a high background of normal DNA. Detection is further confounded by the fact that the rearrangement boundaries are not conserved across individuals, and might vary over hundreds of kilobases. Here, we present an algorithm for designing PCR primers and oligonucleotide probes to assay for these variant rearrangements. Specifically, the primers and probes tile the entire genomic region surrounding a rearrangement, so as to amplify the mutant DNA over a wide range of possible breakpoints and robustly assay for the amplified signal on an array. Our solution involves the design of a complex combinatorial optimization problem, and also includes a novel alternating multiplexing strategy that makes efficient detection possible. Simulations show that we can achieve near-optimal detection in many different cases, even when the regions are highly non-symmetric. Additionally, we prove that the suggested multiplexing strategy is optimal in breakpoint detection. We applied our technique to create a custom design to assay for genomic lesions in several cancer cell-lines associated with a disruption in the CDKN2A locus. The CDKN2A deletion has highly variable boundaries across many cancers. We successfully detect the breakpoint in all cell-lines, even when the regionhas undergone multiple rearrangements. These results point to the development of a successful protocol for early diagnosis and monitoring of cancer.