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Table 2 Average and 95 % confidence interval of the time, in seconds, to solve each problem using ε=10−3

From: Reachability-based model reduction for Markov decision process

Problem ReachMRFS-V2 + TVI ReachMRFS-V2 + VI ReachMRFS-V2 + LRTDP TVI VI LRTDP
Cross. 1 3.64 ± 0.04 4.10 ± 0.03 5.71 ± 0.08 4.51 ± 0.03 2594.45 ± 58.66 3.16 ±0.05
  2 3.65 ± 0.03 4.14 ± 0.05 6.53 ± 0.16 4.47 ± 0.04 2007.41 ± 37.64 2.92 ±0.04
  3 15.29 ± 0.11 22.74 ± 0.21 26.72 ± 0.40 18.95 ± 0.16 - 12.79 ±0.18
  4 15.17 ±0.14 22.49 ± 0.34 25.05 ± 0.34 19.50 ± 0.31 - 17.43,0.18
Elevators 1 4.45 ±0.04 4.90 ± 0.07 16.08 ± 0.33 5.83 ± 0.16 135.46 ± 3.61 13.50 ± 0.38
  2 161.60 ± 1.42 155.99 ±1.35 1788.44 ± 14.60 240.45 ± 6.25 - 555.47 ± 7.06
  3 146.87 ±1.04 149.76 ± 1.24 1468.64 ± 11.85 217.75 ± 5.41 - 980.74 ± 8.64
  4 16.86 ± 0.65 15.35 ± 0.26 146.66 ± 1.22 14.61 ±0.20 1964.44 ± 32.10 82.39 ± 1.09
  7 72.25 ±0.83 90.99 ± 0.86 3599.00 ± 0.11 78.90 ± 1.17 208.30 ± 3.48 1363.33 ± 11.72
Game 1 137.10 ±0.48 192.98 ± 0.80 215.95 ± 1.31 557.46 ± 6.35 514.48 ± 4.60 917.27 ± 14.06
  2 118.89 ±0.35 174.03 ± 0.97 239.72 ± 1.27 440.28 ± 5.33 399.34 ± 3.72 1263.55 ± 9.63
  3 114.57 ±0.49 168.88 ± 0.48 233.54 ± 1.51 406.64 ± 4.95 369.03 ± 3.74 1399.49 ± 7.12
Navigation 1 1.76 ± 0.01 1.97 ± 0.01 2.41 ± 0.03 1.40 ±0.01 43.49 ± 0.96 2.01 ± 0.02
  2 2.29 ± 0.02 2.59 ± 0.02 2.91 ± 0.03 1.47 ±0.01 365.03 ± 10.71 2.16 ± 0.04
  3 2.72 ± 0.07 3.45 ± 0.03 3.26 ± 0.02 1.64 ±0.01 - 2.46 ± 0.03
  4 4.61 ± 0.04 4.80 ± 0.04 4.83 ± 0.04 3.30 ±0.03 - 3.85 ± 0.23
  5 4.32 ± 0.05 4.80 ± 0.05 5.18 ± 0.06 2.56 ±0.03 - 3.50 ± 0.08
  6 6.66 ± 0.07 7.17 ± 0.07 8.03 ± 0.09 3.60 ±0.05 - 6.62 ± 0.40
  7 8.53 ± 0.06 8.84 ± 0.07 9.64 ± 0.07 5.10 ±0.09 - 5.66 ± 0.26
  8 11.40 ± 0.09 12.24 ± 0.11 13.39 ± 0.10 4.61 ±0.03 - 5.69 ± 0.10
  9 20.33 ± 0.21 21.58 ± 0.21 22.94 ± 0.22 5.59 ±0.07 - 6.66 ± 0.14
  10 36.53 ± 0.51 37.55 ± 0.47 38.55 ± 0.45 7.93 ± 0.09 - 7.73 ±0.12
Skill 1 2.76 ± 0.02 2.86 ± 0.03 4.48 ± 0.07 4.09 ± 0.02 38.62 ± 0.98 1.49 ±0.02
  2 2.75 ± 0.04 2.87 ± 0.03 4.51 ± 0.12 4.11 ± 0.03 41.03 ± 1.00 1.56 ±0.02
  3 27.91 ± 0.23 26.15 ± 0.23 112.63 ± 0.80 38.25 ± 0.71 - 12.44 ±0.38
  4 27.55 ± 0.26 25.92 ± 0.30 100.38 ± 0.79 38.84 ± 0.75 - 11.95 ±0.34
  1. If a solution is not found in the given time and memory thresholds, then ‘-’ is shown. Best performance over all planners (columns) is shown in bold font. Results for all Reach MRFS planners are the same as in Table 1