A New Length-Based Algebraic Multigrid Clustering Algorithm

Table 5

Placement wire length and runtime results comparing one- and two-level AMG-LE clustering with length-driven unclustering without detailed placement to baseline placements without using clustering with three placers on the ICCAD04 benchmark suite.

(a) HPWL

Circuit	Capo			Fastplace			mPL
		AMG-LE			AMG-LE			AMG-LE
	Baseline (×10^5)	1Lvl (%)	2Lvl (%)	Baseline (×10^5)	1Lvl (%)	2Lvl (%)	Baseline (×10^5)	1Lvl (%)	2Lvl (%)
ibm01	25	−1.0	−1.7	24	−7.7	−4.9	24	−3.2	−3.4
ibm02	51	1.6	1.2	54	1.3	2.5	52	−3.8	−3.8
ibm03	77	4.2	4.6	80	1.3	3.4	82	5.0	5.1
ibm04	93	10.6	10.4	86	4.0	4.7	109	11.3	15.9
ibm05	103	0.3	−1.1	101	−1.9	−2.7	93	−10.1	−13.4
ibm06	67	1.3	0.3	99	35.8	31.1	88	15.4	17.1
ibm07	126	10.2	9.9	123	3.3	7.0	124	−4.4	1.2
ibm08	137	2.6	1.9	147	−3.0	3.3	211	13.0	20.0
ibm09	145	0.6	1.5	155	4.3	3.9	189	11.9	15.9
ibm10	318	−1.0	−0.5	362	7.4	9.0	363	3.2	5.7
ibm11	210	1.9	1.9	225	7.6	6.3	243	4.3	4.1
ibm12	413	9.6	9.6	410	7.4	10.4	461	6.4	6.9
ibm13	266	3.3	3.4	273	7.7	7.3	324	9.7	14.3
ibm14	392	2.4	1.0	478	11.5	18.4	824	30.0	35.2
ibm15	544	2.6	−0.1	577	5.0	8.6	1001	23.3	23.4
ibm16	629	5.1	2.5	680	8.5	7.9	931	16.8	21.8
ibm17	737	1.9	1.2	810	7.0	9.0	1144	13.0	21.5
ibm18	458	0.9	0.0	574	15.3	15.8	885	18.8	28.9
Average	—	3.2	2.6	—	6.4	7.8	—	8.9	12.0

(b) Runtime

Circuit	Capo			Fastplace			mPL
		AMG-LE			AMG-LE			AMG-LE
	Baseline (s)	1Lvl (%)	2Lvl (%)	Baseline (s)	1Lvl (%)	2Lvl (%)	Baseline (s)	1Lvl (%)	2Lvl (%)
ibm01	193	16	12	26	−12	−22	109	47	54
ibm02	329	−8	2	46	1	−28	236	27	38
ibm03	487	−5	5	46	−16	−36	221	10	32
ibm04	512	−1	−4	51	−13	−42	250	39	40
ibm05	411	−1	−1	36	−29	−63	174	−2	32
ibm06	580	12	5	96	34	15	390	39	51
ibm07	920	7	8	96	−8	−57	387	28	35
ibm08	941	6	−11	99	−22	−110	1109	62	67
ibm09	1198	−8	1	122	−3	−42	898	55	62
ibm10	1868	3	−3	286	8	−11	1450	8	38
ibm11	1834	−1	−5	135	−64	−94	1084	56	56
ibm12	1996	−1	−7	282	−3	−17	1517	29	39
ibm13	2387	−7	−6	239	−32	−81	1235	54	56
ibm14	3327	−2	−14	530	−51	−125	2189	27	49
ibm15	5781	0	−22	624	−38	−188	3969	32	43
ibm16	4917	−4	−11	722	−58	−167	5457	50	53
ibm17	5286	−4	−26	1133	−40	−84	2788	3	12
ibm18	4215	−8	−36	1589	2	−43	3106	2	14
Average	—	0	−6	—	−19	−66	—	32	43