Legal scholars have discussed whether or not to impose term limits on the Supreme Court of the United States. Currently, Supreme Court Justices are appointed for life "during good behavior". A sentiment has developed, among certain scholars, that the Supreme Court may not be accountable in a way that is most in line with the spirit of checks and balances .  Equally, scholars have argued that life tenure has taken on a new meaning in a modern context.  Changes in medical care have markedly raised life expectancy and therefore has allowed Justices to serve for longer than ever before.   Steven G. Calebresi and James Lindgren, professors of law at Northwestern University, argued that, because vacancies in the court are occurring with less frequency and justices served on average, between 1971 and 2006, for years, the "efficacy of the democratic check that the appointment process provides on the Court's membership" is reduced.  There have been several similar proposals to implement term limits for the nation's highest court, including Professor of Law at Duke University , Paul Carrington's 2005 "The Supreme Court Renewal Act of 2005". 
Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have running time quadratic in the sample size. As our main contribution, we provide new sample near-linear time algorithms for the problem that – while not being minimax optimal – achieve a significantly better sample-time tradeoff on large datasets compared to the DP approach. Our experimental evaluation shows that, compared with the DP approach, our algorithms provide a convergence rate that is only off by a factor of 2 to 4, while achieving speedups of three orders of magnitude.