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Main Results and Claims

The results and accompanying claims are enumerated below.

  1. Figure 2 compares the runtime of localization using two MPC libraries, EMP and ABY. Claim: EMP is better suited to localization than ABY.
  2. Figure 3 measures the runtime of arithmetic operations on various data representations. Claim: 64 bit fixed point multiplication is slower than 32 bit floating.
  3. Figure 4 counts the number of arithmetic operations performed during localization. Claim: Multiplication is the dominant operation.
  4. Figure 6 compares the time to localize using data oblivious (DO) vs. single iteration localization (SIL). Claim: SIL localizes faster than DO with the Levenburg Marquardt (LM) optimization algorithm being faster than Gauss Newton (GN).
  5. Figure 7 measures runtime and network IO for different localization configurations at large input sizes. Claim: LM better scales to large input sizes than GN, making LM the better approach of the two.

Main Result 1: Figure 2

The EMP MPC library is better suited to localization than the ABY MPC library. Open the file plots/emp_vs_aby.pdf and compare it to Figure 2 in the paper. The EMP LM and EMP GN bars should be smaller than the ABY bars.

Main Result 2: Figure 3

64 bit fixed point multiplication is slower than 32 bit floating point. Open plots/emp_float_vs_fixed_benchmark_add_mul.pdf and verify the size of these two bars noting the y axis for multiplication is is on the right.

Main Result 3: Figure 4

Multiplication is the dominant operation in LM-based localization. Open plots/emp_arith_ops.pdf and verify the green multiplication bars are larger than all other bars at any of the measured number of features.

Main Result 4: Figure 6

Single iteration localization (SIL) localizes faster than the data oblivious (DO) adaptation with LM being the faster optimization algorithm. Open plots/loopleak_vs_dataobl.pdf and verify the DO lines are (much) higher than the SIL lines. Also check the purple LM SIL line is the lowest in the figure for all the numbers of features.

Main Result 5: Figure 7

LM better scales to large input size i.e. large numbers of input features. Open plots/emp_float_runtime_long.pdf and verify the GN lines are higher than their respective LM lines for the same latency. Next open plots/netio.pdf and verify the LM lines are below their respective GN lines.