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Table 1 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 MRFS + TVI MRFS + VI MRFS + LRTDP
Cross. 1 3.64 ±0.04 4.10 ± 0.03 5.71 ± 0.08 19.41 ± 0.60 19.87 ± 0.65 20.86 ± 0.59
  2 3.65 ±0.03 4.14 ± 0.05 6.53 ± 0.16 19.36 ± 0.60 19.80 ± 0.58 21.82 ± 0.67
  3 15.29 ±0.11 22.74 ± 0.21 26.72 ± 0.40 - - -
  4 15.17 ±0.14 22.49 ± 0.34 25.05 ± 0.34 - - -
Elevators 1 4.45 ±0.04 4.90 ± 0.07 16.08 ± 0.33 100.10 ± 4.56 97.57 ± 5.49 101.99 ± 4.07
  2 161.60 ± 1.42 155.99 ±1.35 1788.44 ± 14.60 - - -
  3 146.87 ±1.04 149.76 ± 1.24 1468.64 ± 11.85 - - -
  4 16.86 ± 0.65 15.35 ±0.26 146.66 ± 1.22 - - -
  7 72.25 ±0.83 90.99 ± 0.86 3599.00 ± 0.11 - - -
Game 1 137.10 ±0.48 192.98 ± 0.80 215.95 ± 1.31 161.62 ± 1.04 211.74 ± 1.31 234.31 ± 1.65
  2 118.89 ±0.35 174.03 ± 0.97 239.72 ± 1.27 140.83 ± 0.97 191.77 ± 1.16 260.07 ± 2.40
  3 114.57 ±0.49 168.88 ± 0.48 233.54 ± 1.51 137.38 ± 0.83 187.54 ± 1.21 253.25 ± 1.87
Navigation 1 1.76 ±0.01 1.97 ± 0.01 2.41 ± 0.03 21.09 ± 0.76 20.36 ± 1.00 21.39 ± 0.82
  2 2.29 ±0.02 2.59 ± 0.02 2.91 ± 0.03 189.90 ± 8.69 191.50 ± 6.66 194.26 ± 6.82
  3 2.72 ±0.07 3.45 ± 0.03 3.26 ± 0.02 - - -
  4 4.61 ±0.04 4.80 ± 0.04 4.83 ± 0.04 - - -
  5 4.32 ±0.05 4.80 ± 0.05 5.18 ± 0.06 - - -
  6 6.66 ±0.07 7.17 ± 0.07 8.03 ± 0.09 - - -
  7 8.53 ±0.06 8.84 ± 0.07 9.64 ± 0.07 - - -
  8 11.40 ±0.09 12.24 ± 0.11 13.39 ± 0.10 - - -
  9 20.33 ±0.21 21.58 ± 0.21 22.94 ± 0.22 - - -
  10 36.53 ±0.51 37.55 ± 0.47 38.55 ± 0.45 - - -
Skill 1 2.76 ±0.02 2.86 ± 0.03 4.48 ± 0.07 19.24 ± 1.17 18.98 ± 1.00 18.07 ± 0.85
  2 2.75 ±0.04 2.87 ± 0.03 4.51 ± 0.12 18.72 ± 0.95 18.20 ± 0.87 17.46 ± 0.60
  3 27.91 ± 0.23 26.15 ±0.23 112.63 ± 0.80 175.94 ± 5.73 176.50 ± 7.12 328.26 ± 11.62
  4 27.55 ± 0.26 25.92 ±0.30 100.38 ± 0.79 178.21 ± 7.62 172.60 ± 7.85 311.95 ± 12.43
  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. In the columns, Algorithm ?? + Algorithm ?? refers to the algorithm used in reduction phase (Algorithm ??) and the algorithm used to solve the reduced MDP (Algorithm ??)