A Novel Mathematical Model for Radio Mean Square Labeling Problem

Table 2

Comparison between standard radio mean square number, algorithm, and integer linear programming for the upper bound of radio mean square number for the path graph.

Path graph
N	Standard RMS	Proposed algorithm		Integer linear programming
		rmsn (Pn)	CPU time	rmsn (Pn)	CPU time
1	1	—	—	—	—
2	2	2	0.0001565	2	0.0135961
3	3	3	0.0007495	3	0.0137607
4	4	4	0.0009242	4	0.0142838
5	5	6	0.0009259	9	0.0148360
6	6	7	0.0011930	11	0.0149701
7	7	8	0.0028154	13	0.0151607
8	8	9	0.0031659	15	0.0153437
9	9	10	0.0086583	17	0.0153530
10	10	12	0.0092995	28	0.0153602
11	11	13	0.0178153	31	0.0154630
12	12	14	0.0179739	34	0.0158122
13	13	15	0.0195242	37	0.0159264
14	14	16	0.0214671	40	0.0160664
15	15	17	0.0323685	43	0.0165312
16	17	18	0.0397062	46	0.0165756
17	18	20	0.0488390	65	0.0166756
18	19	21	0.0521773	69	0.0168593
19	20	22	0.0635412	73	0.0168673
20	21	23	0.0773853	77	0.0173017
21	22	24	0.0926470	81	0.0173982
22	23	25	0.1082337	85	0.0174649
23	25	26	0.1321028	89	0.0176519
24	26	27	0.1680530	93	0.0178209
25	27	28	0.1819503	97	0.0178319
26	28	30	0.2174177	126	0.0178408
27	29	31	0.2423215	131	0.0178502
28	30	32	0.2838989	135	0.0179323
29	31	33	0.3306090	142	0.0181244
30	32	34	0.3907487	146	0.0182150
50	54	56	3.3044964	344	0.0295531