• 1 Introduction
    • 1.1 Problem Definition
    • 1.2 Previous Work
    • 1.3 Contribution
      • Outline.
  • 2 Preliminaries
    • 2.1 Divisor Sequences
    • 2.2 Ties, Rounding Rules, and Seat Allocations
    • 2.3 Highest Averages
  • 3 Fast Apportionment through Selection
    • 3.1 Cheng and Eppstein's Algorithm
    • 3.2 Our Algorithm
    • 3.3 Proof of Main Result
  • 4 Comparison of algorithms
    • 4.1 Iterative methods
    • 4.2 Running Time Comparison
    • 4.3 Super-linear worst case for JumpAndStep
  • 5 Conclusion
  • A Notation Index