Since the discovery of the "Philadelphia chromosome" in chronic myelogenous leukemia in 1960, there is an ongoing intensive research of chromosomal aberrations in cancer. These aberrations, which result in abnormally structured genomes, became a hallmark of cancer. Many studies give evidence to the connection between chromosomal alterations and aberrant genes involved in the carcinogenesis process. An important problem in the analysis of cancer genomes, is inferring the history of events leading to the observed aberrations. Cancer genomes are usually described in form of karyotypes, which present the global changes in the genomes' structure. In this study, we propose a mathematical framework for analyzing chromosomal aberrations in cancer karyotypes. We introduce the problem of sorting karyotypes by elementary operations, which seeks for a shortest sequence of elementary chromosomal events transforming a normal karyotype into a given (abnormal) cancerous karyotype. Under...