  Gradecast is a simple three-round algorithm presented by Feldman and Micali.
The current work presents a very simple algorithm that utilized Gradecast to
achieve Byzantine agreement. Two small variations of the presented algorithm
lead to improved algorithms for solving the Approximate agreement problem and
the Multi-consensus problem.
  An optimal approximate agreement algorithm was presented by Fekete, which
supports up to 1/4 n Byzantine nodes and has message complexity of O(n^k),
where n is the number of nodes and k is the number of rounds.
  Our solution to the approximate agreement problem is optimal, simple and
reduces the message complexity to O(k * n^3), while supporting up to 1/3 n
Byzantine nodes.
  Multi consensus was first presented by Bar-Noy et al. It consists of
consecutive executions of l Byzantine consensuses. Bar-Noy et al., show an
optimal amortized solution to this problem, assuming that all nodes start each
consensus instance at the same time, a property that cannot be guaranteed with
early stopping. Our solution is simpler, preserves round complexity optimality,
allows early stopping and does not require synchronized starts of the consensus
instances.
