States. Previous matching programs limited kidney-transplant patients and their families to connect with other incompatible pairs on their own. Together, Segev and Gentry devised a nationwide system to match donor-patient pairs. Based on an algorithm created by the Canadian mathematician Jack Edmonds in 1965, the system improves paired donation by ensuring the maximum number of matches while still factoring in age, location and willingness to travel. Under the direction of Segev and Robert Montgomery, Johns Hopkins completed the first five-way donor kidney swap among 10 individuals. The longest kidney-pair chain to date included 70 participants and was completed in 2014. HOPE Act and HIV positive transplantation in the U.S. Before 2013, it was illegal to use organs from HIV+ donors for transplantation. Any organ whose donor was diagnosed with HIV would be immediately thrown out, despite them being otherwise healthy organs. In May 2010, Brian Boyarsky sought out Segev's advice after doing previous research comparing transplant programs in different countries. During his research, Boyarsky met Elmi Muller, who had been successfully transplanting organs between HIV+ donors and recipients in South Africa. With that in mind, Segev and Boyarsky looked at both the Nationwide Inpatient Sample to study in-hospital deaths of HIV+ patients and the HIV Research Network, which provided granular disease-specific data, to calculate the impact of using organs from HIV+ donors on the organ transplant waitlist. Both data sources allowed Segev and Boyarsky to estimate a possible 500 to 600 HIV+ donors in the United States, whose organs were currently being discarded. After appearing on the front page of The New York Times and Boyarsky's article appearing in the American Journal of Transplantation, Segev and his mentee visited every major national transplant and AIDS advocacy group in the US. Within weeks, they had every group officially supporting their campaign to legalize using organs from HIV+ donors for HIV+ recipients. In August 2011, Segev and Boyarsky sought out bipartisan support to change the existing law. California Senator Barbara Boxer (D) and Oklahoma Senator Tom Coburn (R) became the main sponsors of the bill first drafted by Segev and Boyarsky. They were later joined by congressional representatives Lois Capps (D) and Andy Harris (R) to support the bill in the House of Representatives. The HIV Organ Policy Equity Act (or HOPE Act) was introduced in the Senate on February 14, 2013. President Barack Obama signed the HOPE Act into law on