The MapReduce-based approach to improve the shortest path computation in large-scale road networks: the case of A* algorithm

Journal of Big Data

Table 3 Comparison of computational time in seconds time between \(A^\) and \(MRA^\) into a 1-node cluster

n	No. data	\(G_{size}\)	Time with A*	Time with MRA*			Ratio
n	No. data	\(G_{size}\)	\(T_{A^*}\)	\(t_{map}\)	\(t_{red}\)	\(T_{MRA^*}\)	\(\frac{T_{A^_{ }}}{T_{MRA^}}\)
8000	64 × 10⁶	0.25	1,5752	157	11	168	94
15,000	22.5 × 10⁷	0.5	35,331	183	18	201	159
20,000	40 × 10⁷	0.8	51,469	233	36	269	191
25,000	62.5 × 10⁷	1.2	77,378	330	53	366	211
30,000	90 × 10⁷	2	101,909	405	76	481	212
40,000	16 × 10⁸	3	129,343	698	91	789	164
50,000	25 × 10⁸	5	152,863	1035	103	1137	134
60,000	36 × 10⁸	7	177,948	1397	203	1600	111
80,000	64 × 10⁸	11.5	269,102	1790	408	2198	122
90,000	81 × 10⁸	14	31,4425	2100	568	2668	118
100,000	10 × 10⁹	16.6	359,747	2257	682	2939	122
Average ratio of time improvement							149