Heuristic Algorithms for MapReduce Scheduling Problem with Open-Map Task and Series-Reduce Tasks

Table 1

Experimental results for small-scale instances of the processing time of operations range from 1 to 5.

(m, n, k)	CPLEX		GA			SA			L-F
	obj	Time	obj	Time	gap	obj	Time	gap	obj	Time	gap
(2, 3, 3)	10.90	0.24	11.40	1.75	0.05	11.50	2.75	0.06	12.40	0.00	0.14
(2, 3, 4)	14.40	5.24	15.20	2.18	0.06	15.30	3.17	0.06	17.00	0.00	0.18
(2, 3, 5)	16.00	45.95	16.90	2.53	0.06	17.60	3.63	0.10	18.40	0.00	0.15
(2, 4, 3)	13.50	7.14	13.80	2.07	0.02	13.90	3.12	0.03	15.00	0.00	0.11
(2, 4, 4)	16.70	545.07	18.10	2.61	0.08	18.40	3.82	0.10	19.70	0.00	0.18
(2, 5, 3)	16.70	32.14	17.30	2.42	0.04	17.10	3.67	0.02	17.70	0.00	0.06
(3, 4, 3)	8.00	1.07	9.50	2.07	0.19	9.90	3.22	0.24	9.40	0.00	0.18
(3, 4, 4)	10.60	112.79	12.80	2.61	0.21	13.60	3.80	0.28	13.30	0.00	0.25
(3, 5, 3)	9.40	25.75	11.30	2.41	0.20	11.30	3.61	0.20	11.10	0.00	0.18
(3, 6, 3)	11.60	7231.70	13.30	2.74	0.15	13.90	4.02	0.20	13.90	0.00	0.20
(4, 5, 3)	7.30	1.35	9.40	2.43	0.29	9.90	3.58	0.36	8.20	0.00	0.12
(4, 5, 4)	9.30	243.26	13.40	3.13	0.44	14.10	4.46	0.52	12.60	0.00	0.35
(4, 6, 3)	8.30	49.19	10.90	2.82	0.31	11.80	4.04	0.42	9.50	0.00	0.14
(5, 5, 4)	7.50	12.23	11.20	3.13	0.49	12.60	4.40	0.68	9.40	0.00	0.25
(5, 6, 3)	6.20	2.52	8.90	2.78	0.44	10.50	3.99	0.69	7.60	0.00	0.23
(5, 6, 4)	8.20	177.18	12.80	3.51	0.56	14.60	4.95	0.78	10.60	0.00	0.29
(5, 7, 3)	6.90	251.84	11.10	3.16	0.61	11.80	4.19	0.71	8.40	0.00	0.22
(8, 10, 3)	5.70	304.38	11.00	4.16	0.93	12.00	5.71	1.11	6.80	0.00	0.19
Average	10.40	502.83	12.68	2.70	0.28	13.32	3.90	0.36	12.28	0.00	0.19

Note. gap = .