Table 2: The performance of robust methods under the perturbation in the discrete setting.
Methods	β = 0	β = 25	β = 50	β = 75	β = 100
Uti.(%)	Std.	Num.	Uti.(%)	Std.	Num.	Uti.(%)	Std.	Num.	Uti.(%)	Std.	Num.	Uti.(%)	Std.	Num.
PCT	76.2	6.8	29.9	73.6	7.9	29.9	70.6	9.2	28.5	67.5	9.1	27.8	64.9	8.2	27.1
CPPO	75.5	6.9	29.6	73.1	8.0	29.0	70.7	8.4	28.5	67.9	8.2	27.9	65.2	7.3	27.4
RARL	74.6	6.2	29.2	73.1	7.3	29.2	70.8	8.4	29.0	67.8	8.4	28.4	66.7	8.1	28.5
ExactAR2L(0.3)	76.3	6.6	29.8	73.8	8.5	29.6	71.0	9.1	29.2	67.5	9.6	28.4	64.5	9.4	27.7
ExactAR2L(0.5)	76.5	7.1	30.1	73.5	8.8	29.4	70.5	10.4	28.8	68.2	10.3	28.1	65.3	10.0	27.6
ExactAR2L(0.7)	76.8	6.1	30.1	74.4	7.7	29.7	71.1	8.9	29.1	68.8	9.7	28.7	66.3	8.6	28.5
ExactAR2L(1.0)	77.4	6.5	30.2	74.3	9.3	29.5	72.0	9.5	29.0	69.5	10.0	28.4	66.5	8.7	27.9
RfMDP	75.5	6.7	29.6	71.8	9.8	28.8	69.6	9.4	28.5	67.1	9.0	28.0	63.9	8.1	27.3
ApproxAR2L(0.3)	75.3	6.3	29.6	72.6	7.7	28.9	70.0	8.6	28.4	66.4	9.7	27.6	63.2	9.5	26.9
ApproxAR2L(0.5)	76.1	5.8	29.8	72.6	8.4	29.0	69.8	9.9	28.4	67.3	9.6	27.7	64.7	8.8	27.4
ApproxAR2L(0.7)	76.9	5.7	30.0	73.7	8.0	29.1	71.6	8.5	28.7	68.2	8.4	27.8	65.2	7.9	27.0
ApproxAR2L(1.0)	76.5	6.5	30.1	73.4	8.9	29.2	70.8	9.3	28.6	68.4	9.3	28.0	65.7	8.5	27.5
PCT	76.4	6.6	29.9	70.6	12.4	28.5	65.1	14.5	27.3	61.4	14.8	26.4	55.7	12.9	25.2
CPPO	75.6	7.2	29.8	70.7	11.6	28.6	66.2	12.7	27.7	62.3	12.9	26.9	57.4	11.4	25.8
RARL	74.3	7.2	29.4	71.1	8.7	29.0	69.2	8.5	28.7	65.6	8.6	28.0	63.3	8.2	27.7
ExactAR2L(0.3)	76.5	5.9	29.9	71.5	12.1	28.9	66.8	14.0	27.8	62.9	14.1	27.0	59.2	12.7	26.4
ExactAR2L(0.5)	77.6	5.8	30.3	73.1	10.2	29.5	68.0	13.1	28.8	64.0	12.7	28.0	59.7	10.2	27.4
ExactAR2L(0.7)	77.4	5.6	30.2	73.1	9.7	29.5	69.5	11.2	28.9	65.6	11.1	28.1	62.3	9.7	27.4
ExactAR2L(1.0)	76.0	7.0	29.8	72.4	9.7	30.0	70.3	9.4	30.3	66.7	9.3	30.3	63.8	8.0	30.6
RfMDP	74.4	7.2	29.7	70.5	11.4	28.7	65.7	14.3	28.0	60.8	14.4	26.8	55.9	12.5	25.9
ApproxAR2L(0.3)	76.1	5.9	29.7	70.5	12.5	28.8	66.1	14.6	28.2	61.3	14.5	27.2	55.7	11.8	26.2
ApproxAR2L(0.5)	76.2	5.9	29.9	72.1	11.7	29.2	66.9	14.7	28.1	62.1	15.0	26.9	56.1	13.6	25.5
ApproxAR2L(0.7)	73.0	7.0	28.8	70.1	9.5	29.2	65.4	11.1	28.4	61.0	10.7	27.9	56.2	8.4	27.1
ApproxAR2L(1.0)	73.6	6.8	28.9	69.3	10.7	29.2	66.1	11.8	29.3	61.9	11.6	29.4	57.1	9.1	29.8
PCT	76.8	6.9	29.9	69.4	15.4	28.1	62.0	18.3	26.3	55.2	18.2	24.3	48.6	14.7	22.5
CPPO	75.2	7.7	29.3	69.9	13.1	28.2	63.8	15.2	26.8	58.0	15.7	25.2	52.3	13.3	23.9
RARL	73.2	7.2	28.7	70.3	9.1	28.7	67.2	10.9	28.4	63.1	12.4	28.0	58.7	11.0	27.5
ExactAR2L(0.3)	76.8	6.4	30.1	71.4	11.4	29.3	65.3	13.8	28.4	59.7	14.0	27.3	53.4	11.6	26.5
ExactAR2L(0.5)	77.7	5.8	30.3	72.0	11.9	29.3	68.0	13.8	28.8	61.2	15.4	27.2	55.0	13.3	26.0
ExactAR2L(0.7)	76.5	7.5	30.0	71.5	13.4	29.0	66.4	14.8	28.0	62.0	14.5	26.7	56.3	12.3	25.6
ExactAR2L(1.0)	76.6	5.4	30.0	71.7	10.8	29.4	67.7	12.3	29.0	63.3	11.9	28.2	58.5	11.1	27.6
RfMDP	73.6	8.0	29.0	68.4	12.8	29.1	62.2	15.0	28.9	58.2	14.7	29.2	54.1	12.5	29.6
ApproxAR2L(0.3)	75.4	7.3	29.5	69.9	12.3	29.4	65.5	13.5	29.2	59.3	13.2	28.0	54.5	10.6	27.5
ApproxAR2L(0.5)	75.2	6.4	29.6	69.9	10.6	29.5	65.2	11.9	29.5	60.1	10.9	29.2	55.1	6.8	29.4
ApproxAR2L(0.7)	74.6	7.5	29.2	70.2	10.3	29.1	65.0	11.9	28.8	60.6	11.5	28.6	55.8	8.0	28.6
ApproxAR2L(1.0)	73.5	7.5	29.1	69.1	10.2	29.0	65.0	12.4	29.3	60.4	11.6	29.0	55.8	8.8	29.2
PCT	77.0	5.5	30.1	68.4	17.0	28.6	59.7	19.3	27.0	50.9	18.2	25.5	41.9	12.2	24.2
CPPO	74.1	7.5	29.2	66.7	16.2	27.9	59.1	18.5	26.5	53.2	17.3	25.3	45.8	13.6	24.0
RARL	72.0	6.4	28.4	68.6	9.4	29.1	64.6	10.6	29.3	61.7	10.0	30.0	58.7	8.4	30.4
ExactAR2L(0.3)	76.7	6.7	30.0	70.8	13.3	29.4	65.6	15.8	28.9	59.4	16.3	28.0	52.7	14.3	27.4
ExactAR2L(0.5)	76.8	6.2	30.1	70.0	14.3	30.2	64.7	15.8	30.5	60.0	15.3	30.6	54.4	13.3	30.8
ExactAR2L(0.7)	76.3	6.1	30.0	71.1	11.4	29.6	66.2	14.1	29.3	61.9	14.2	29.2	57.0	12.3	28.8
ExactAR2L(1.0)	76.1	7.3	30.0	70.9	11.8	29.4	66.7	12.7	29.0	62.8	12.6	28.6	58.5	10.3	28.2
RfMDP	73.8	7.0	29.0	69.4	11.0	26.6	64.7	13.3	24.2	59.4	15.1	21.5	54.4	13.0	19.2
ApproxAR2L(0.3)	76.1	6.1	29.8	70.3	12.1	30.4	64.1	14.1	30.8	57.7	12.3	31.0	51.7	6.7	31.5
ApproxAR2L(0.5)	75.0	7.6	29.5	70.1	12.2	30.1	63.9	15.4	30.5	58.8	14.4	30.7	53.1	11.7	31.1
ApproxAR2L(0.7)	74.1	6.9	29.0	68.9	10.8	29.3	64.0	11.9	30.0	59.4	11.3	30.4	54.1	7.1	30.5
ApproxAR2L(1.0)	73.4	8.2	28.9	68.2	13.2	28.7	65.6	13.9	29.0	61.9	14.6	28.9	57.6	12.9	28.8