Table 4.

Distances for the IRTD problem with and without the use of our partition algorithm

OP	$|\mathrm{\Sigma }|$	With partition							Without partition
		Minimum distance			Average distance			Time	Minimum distance			Average distance			Time
		Min.	Avg.	Max.	Min.	Avg.	Max.		Min.	Avg.	Max.	Min.	Avg.	Max.
25	10	34	42.01	52	35.07	43.70	52.51	6.86	95	97.08	98	99.61	100.12	100.50	12.59
25	20	32	41.89	50	32.53	43.38	51.06	6.74	91	94.79	98	97.78	99.10	99.84	12.53
25	30	34	41.79	48	34.74	43.18	49.83	6.76	85	92.07	96	95.73	97.69	99.68	12.39
25	40	34	41.39	47	35.55	42.60	48.38	6.78	81	89.38	94	91.59	95.91	98.63	12.31
25	50	35	41.97	48	35.00	43.03	50.70	6.68	79	87.64	94	89.88	94.51	98.58	12.28
25	60	37	41.65	48	37.00	42.60	48.27	6.64	77	85.67	93	87.68	93.16	97.16	12.07
25	70	34	41.73	49	34.98	42.68	49.44	6.73	73	82.57	92	85.13	90.79	97.24	11.84
25	80	37	42.26	49	37.54	43.05	50.05	6.83	69	81.44	89	79.81	89.54	95.94	11.73
25	90	35	41.57	48	35.76	42.34	48.57	6.62	71	79.51	89	79.79	87.65	95.32	11.54
25	100	35	41.84	48	36.00	42.57	49.22	6.71	66	79.31	89	77.86	87.45	94.45	11.43
50	10	59	66.72	75	60.61	67.91	76.42	10.13	95	97.64	99	99.91	100.26	100.50	12.59
50	20	57	66.93	74	58.60	68.14	74.67	10.03	94	96.08	98	98.93	99.63	100.39	12.50
50	30	60	67.11	76	61.56	68.25	77.61	10.10	90	94.31	97	97.01	98.73	99.85	12.45
50	40	56	66.21	73	56.47	67.35	74.62	9.97	86	92.72	96	95.12	97.72	99.91	12.36
50	50	59	66.79	74	60.41	67.96	75.60	10.04	87	91.76	96	94.44	96.98	99.49	12.29
50	60	57	66.32	75	57.74	67.39	76.48	10.12	81	89.80	94	92.17	95.72	98.76	12.33
50	70	53	66.66	75	53.77	67.86	76.61	9.88	83	89.43	95	88.72	94.97	98.51	12.16
50	80	59	66.69	72	59.68	67.74	73.50	9.84	77	88.68	95	89.37	94.34	98.27	12.25
50	90	53	66.24	75	54.56	67.30	76.58	10.09	80	87.89	94	87.04	93.64	97.91	12.16
50	100	59	66.36	76	59.44	67.33	76.59	9.85	80	87.03	94	87.12	92.81	96.63	12.06
75	10	71	79.44	86	72.64	80.61	86.68	11.86	96	97.82	99	100.07	100.35	100.61	12.62
75	20	74	79.92	88	74.53	81.05	88.75	11.84	95	96.88	99	98.85	99.94	100.45	12.55
75	30	71	79.72	87	72.55	80.99	88.57	11.94	92	95.69	98	97.62	99.37	100.19	12.50
75	40	69	79.47	88	70.51	80.64	89.64	11.84	90	94.72	97	96.37	98.67	99.91	12.43
75	50	70	80.38	88	70.72	81.49	89.60	12.00	86	93.89	97	95.04	98.09	100.15	12.44
75	60	72	80.04	89	72.59	81.13	89.67	11.88	88	93.55	97	94.59	97.71	99.60	12.43
75	70	72	80.72	89	72.52	81.78	89.68	12.00	88	92.89	97	93.54	97.06	99.82	12.29
75	80	71	79.91	89	72.68	81.05	89.76	11.86	87	91.95	97	93.33	96.27	99.12	12.44
75	90	73	79.81	88	73.65	80.84	88.63	11.98	88	91.74	96	92.58	96.00	99.04	12.37
75	100	73	80.26	89	73.63	81.32	90.53	11.84	85	91.36	96	90.71	95.55	99.20	12.18
100	10	80	86.23	95	80.56	87.44	96.71	13.20	97	98.18	99	100.13	100.42	100.72	12.62
100	20	81	86.61	94	81.70	87.78	94.59	13.26	95	97.20	99	99.28	100.09	100.56	12.54
100	30	79	87.14	93	80.63	88.39	93.81	13.29	94	96.59	98	98.59	99.73	100.30	12.59
100	40	80	87.15	92	81.57	88.31	93.67	13.19	93	95.84	98	97.28	99.29	100.17	12.50
100	50	79	86.92	93	80.53	88.02	94.68	13.18	91	95.26	97	96.09	98.81	100.18	12.47
100	60	79	87.14	93	80.47	88.27	94.56	13.15	90	94.89	98	96.08	98.52	100.15	12.42
100	70	81	87.61	92	82.67	88.71	93.64	13.21	90	94.70	98	94.98	98.21	100.08	12.37
100	80	78	87.98	96	79.69	89.09	96.57	13.47	91	94.55	97	95.46	98.01	99.97	12.50
100	90	79	87.04	93	80.66	88.22	93.65	13.16	89	94.14	97	93.84	97.64	99.72	12.32
100	100	78	87.46	93	80.53	88.50	94.68	13.13	88	93.65	98	92.55	97.19	100.04	12.24