dmcs

Experiments

Log-IC 2011 experimental results for streaming dmcs

Test name	#answers	DMCSOPT	DMCS STREAMING
			k=0	k=10	k=100
tree(10,10,5,5)	18	1.21	0.24	0.39	6.80
	308	7.46	0.34	0.27	0.65
tree(50,10,5,5)	32	8.98	2.28	3.22	139.83
	24	5.92	2.27	1.80	156.18
tree(100,10,5,5)	16	24.87	9.10	5.43	—
	4	13.95	6.94	86.26	—
tree(10,40,20,20)	—	—	—	0.15	0.76
	—	—	—	0.14	0.68
tree(50,40,20,20)	—	—	—	1.66	8.45
	—	—	—	1.64	8.04
tree(100,40,20,20)	—	—	—	5.04	27.84
	—	—	—	5.00	26.30
ring(10,10,5,5)	12	2.17	0.99	2.44	—
	16	3.11	3.31	0.17	143.83
ring(50,10,5,5)	21	15.49	13.43	—	—
	12	10.30	6.43	—	—
ring(10,40,20,20)	—	—	—	0.86	6.27
	—	—	—	0.51	5.66
ring(50,40,20,20)	—	—	—	3.06	29.81
	—	—	—	4.29	43.94

Experimental Results for dynamic dmcs

Running with inequality atoms

Test name	Heuristics	Running time (secs)	Size	Density	Quality
rand(100, 4974)	None	0.22	5	10	0.604167
	H1	6.16	9	18	0.45
	H2	0.18	4	8	0.605263
	H3	2.39	26	54	0.975491
	H4	1.42	8	16	0.859375
rand(100, 4886)	None	0.18	7	14	0.642857
	H1	1.01	9	18	0.603571
	H2	0.19	6	12	0.584211
	H3	6.65	17	34	0.97541
	H4	0.36	8	16	0.703846
rand(200, 19953)	None	0.62	6	12	0.584
	H1	2.23	7	14	0.48
	H2	0.4	6	12	0.588
	H3	8.92	44	91	0.995732
	H4	0.82	7	14	0.851613
rand(200, 19896)	None	1.02	6	12	0.51
	H1	0.84	6	12	0.604545
	H2	1.12	6	12	0.51
	H3	18.88	37	76	0.998611
	H4	1.29	7	14	0.793548

Test name	Heuristics	Running time (secs)	Size	Density	Quality
rake(100, 5575)	None	10.61	99	198	0.529282
	H1	1	35	70	0.529458
	H2	1.01	10	20	0.509091
	H3	7.65	28	57	0.983333
	H4	0.48	10	20	0.908333
rake(100, 5597)	None	22.76	100	200	0.557895
	H1	1.01	26	52	0.514852
	H2	1.29	10	20	0.497619
	H3	0.96	22	45	0.937931
	H4	1.51	9	18	0.866667
rake(200, 22579)	None	230.1	197	394	0.540533
	H1	17.11	73	146	0.507042
	H2	0.82	9	18	0.517647
	H3	64.24	59	119	0.998734
	H4	0.88	5	11	0.790476
rake(200, 22510)	None	277.04	199	398	0.54967
	H1	4.84	54	108	0.579188
	H2	1.65	9	18	0.520513
	H3	4.4	36	72	0.993939
	H4	0.74	9	18	0.746154

Test name	Heuristics	Running time (secs)	Size	Density	Quality
grid(10 x 10, 279)	None	1.82	100	198	0.54
	H1	1.6	66	130	0.567811
	H2	4.02	100	198	0.544789
	H3	2.87	74	154	0.630233
	H4	2.02	64	128	0.735556
grid(20 x 5, 274)	None	2.52	100	198	0.562431
	H1	1.84	57	112	0.564878
	H2	5.05	82	162	0.557432
	H3	2.38	67	134	0.622951
	H4	2.04	52	104	0.723936
grid(25 x 4, 270)	None	3.44	100	198	0.5192
	H1	1.81	50	98	0.534408
	H2	8.64	100	198	0.527467
	H3	1.46	50	98	0.591398
	H4	1.94	55	109	0.623415
grid(20 x 10, 569)	None	5.32	200	398	0.543836
	H1	6.9	130	258	0.540812
	H2	25.62	200	398	0.550548
	H3	9.1	152	323	0.631351
	H4	9.86	104	206	0.677445
grid(25 x 8, 566)	None	6.78	200	398	0.562888
	H1	10.6	142	282	0.563428
	H2	31.54	200	398	0.55668
	H3	2.61	87	178	0.62263
	H4	10.15	83	164	0.704761
grid(40 x 5, 554)	None	8.44	200	398	0.557206
	H1	5.1	102	202	0.577102
	H2	29.46	162	322	0.570833
	H3	5.35	103	215	0.629737
	H4	5.88	91	184	0.686319

Running without inequality atoms

Test name	Heuristics	Running time (secs)	Size	Density	Quality
rand(100, 4974)	None	0.39	2	2	0.566667
	H1	0.46	3	3	0.638461
	H2	0.37	2	2	0.566667
	H3	2.61	23	44	0.981522
	H4	0.37	4	4	0.764706
rand(100, 4886)	None	0.43	3	3	0.572727
	H1	0.47	3	3	0.572727
	H2	0.15	3	3	0.572727
	H3	9.74	17	33	0.977049
	H4	0.46	4	4	0.833333
rand(200, 19953)	None	0.38	2	2	0.711111
	H1	0.78	5	5	0.415789
	H2	0.1	2	2	0.711111
	H3	8.13	42	80	0.99557
	H4	0.13	3	3	0.630769
rand(200, 19896)	None	0.39	2	2	0.483333
	H1	0.46	2	2	0.466667
	H2	0.43	2	2	0.483333
	H3	36.58	36	70	0.998561
	H4	0.2	3	3	0.685714

Test name	Heuristics	Running time (secs)	Size	Density	Quality
rake(100, 5575)	None	3.08	91	91	0.521365
	H1	0.52	32	32	0.533058
	H2	0.34	6	6	0.366667
	H3	8.46	27	49	0.983505
	H4	0.08	5	5	0.74375
rake(100, 5597)	None	3.15	90	90	0.567638
	H1	0.25	22	22	0.508139
	H2	0.69	5	5	0.445
	H3	0.82	20	38	0.95065
	H4	0.16	3	3	0.681818
rake(200, 22579)	None	11.7	174	174	0.550709
	H1	1.09	66	66	0.490804
	H2	0.42	4	4	0.494737
	H3	39.95	57	111	0.998696
	H4	0.64	4	4	0.815385
rake(200, 22510)	None	6.04	173	173	0.540757
	H1	0.81	48	48	0.592737
	H2	2.91	4	4	0.48125
	H3	4.47	36	72	0.993939
	H4	0.55	3	3	0.666667

Test name	Heuristics	Running time (secs)	Size	Density	Quality
grid(10 x 10, 279)	None	0.13	19	18	0.557971
	H1	0.13	16	16	0.553571
	H2	0.12	19	18	0.557971
	H3	0.73	20	25	0.588571
	H4	0.1	17	17	0.591525
grid(20 x 5, 274)	None	0.17	24	23	0.597368
	H1	0.19	28	28	0.547525
	H2	0.16	24	23	0.597368
	H3	1.1	30	37	0.598148
	H4	0.16	24	23	0.658441
grid(25 x 4, 270)	None	0.22	28	27	0.528972
	H1	0.22	31	31	0.579032
	H2	0.2	28	27	0.528972
	H3	1.42	37	50	0.622759
	H4	0.25	34	34	0.616279
grid(20 x 10, 569)	None	0.2	29	28	0.479808
	H1	0.21	30	30	0.459048
	H2	0.2	29	28	0.479808
	H3	1.54	49	61	0.605759
	H4	0.2	26	25	0.711905
grid(25 x 8, 566)	None	0.25	32	31	0.565854
	H1	0.26	32	32	0.592126
	H2	0.25	32	31	0.565854
	H3	1.73	35	41	0.637857
	H4	0.91	28	28	0.616667
grid(40 x 5, 554)	None	0.49	44	43	0.538194
	H1	0.85	46	46	0.535152
	H2	0.37	44	43	0.538194
	H3	2.02	53	65	0.627778
	H4	0.53	53	52	0.630435

Experimental Results for ordinary dmcs

We present some results for a SAT-solver based prototype implementation of DMCS and DMCSOPT under Ubuntu Linux 9.10, written in C++. The host system was using a Pentium Core2 Duo 2.53GHz processor with 4GB RAM. We used clasp 1.3.3 as a SAT solver, which accepts DIMACS CNF as input. Specifically, all generated instantiations of MCS systems have contexts with ASP logics. The translation defined in defk2010-kr is used to create SAT instances at all contexts and clasp builds all models.

For initial experimentation, we created random MCS instances of fixed topologies generalizing the diamond, ring, zig-zag, and house. A parameter setting P=(n,s,b,r) specifies

• the number n of contexts,
• the local alphabet size |Σ|=s (each context C has a random ASP program on s atoms with 2^k answer sets, 0 ≤ k ≤ s/2),
• the maximum interface size b (number of atoms exported),
• and the maximum number r of bridge rules per context, each having at most 2 body literals.

JELIA 2010 experimental results

The tables below show some experimental results for parameter settings (n,10,5,5), where n varies between 9 and 301, with the respective topologies. Each row displays the number of answers/models, the running time for tasks such as local solving, projection, combination, transfering models between contexts, and the total running time, in the cases of DMCS and DMCSOPT.

Diamond

A diamond stack combines multiple diamonds in a row (stacking m diamonds in a tower of 3m+1 contexts).

	DMCS						DMCSOPT
Test	#answers	lsolve	projection	combine	transfer	total	#answers	lsolve	projection	combine	transfer	total
10-10-5-5	8704	0.393	0.011	3.557	0.015	4.09	256	0.374	0.005	0.005	0.001	0.43
	2688	0.375	0.009	1.682	0.024	2.16	24	0.355	0.009	0.001	0.003	0.41
	384	0.535	0.017	0.022	0	0.62	14	0.523	0.017	0	0	0.57
	672	0.325	0.004	0.343	0.006	0.72	9	0.288	0.003	0	0	0.32
	1536	0.431	0.009	0.611	0.009	1.11	64	0.413	0.002	0.001	0.002	0.47
	2520	0.191	0	0.277	0.014	0.54	42	0.179	0	0	0	0.23
	768	0.338	0.005	0.122	0.002	0.51	32	0.305	0.003	0	0	0.35
	198	0.294	0.003	0.015	0	0.38	9	0.27	0.002	0	0	0.30
	832	0.407	0.014	0.163	0.013	0.64	32	0.391	0.004	0.002	0	0.45
	480	0.406	0.009	0.014	0.004	0.48	128	0.447	0.005	0	0	0.49
13-10-5-5	2688	0.986	0.037	1.742	0.024	2.90	40	1.28	0.021	0.004	0	1.38
	25200	1.43	0.082	112.524	0.171	114.57	14	0.974	0.036	0.002	0.001	1.09
	3136	0.696	0.021	8.642	0.073	9.54	36	1.364	0.046	0.017	0	1.52
	5376	0.739	0.024	3.769	0.051	4.73	4	0.723	0.019	0.001	0	0.81
	1296	0.899	0.049	0.598	0.017	1.64	24	0.702	0.004	0	0	0.78
	6144	0.794	0.021	10.249	0.06	11.25	72	1.001	0.015	0.006	0	1.19
	11520	0.638	0.012	17.61	0.038	18.47	16	0.91	0.045	0	0	1.02
	—	—	—	—	—	—	32	1.015	0.031	0.004	0	1.12
	—	—	—	—	—	—	48	0.798	0.017	0	0	0.88
	—	—	—	—	—	—	96	0.623	0.008	0.004	0	0.70
25-10-5-5	—	—	—	—	—	—	4	13.28	0.71	0.179	0	15.32
	—	—	—	—	—	—	12	10.996	0.285	0.064	0.002	12.39
	—	—	—	—	—	—	56	12.379	0.822	0.095	0	14.38
	—	—	—	—	—	—	48	8.052	0.165	0.043	0.016	9.30
	—	—	—	—	—	—	8	9.841	0.232	0.13	0.002	11.35
	—	—	—	—	—	—	32	10.129	0.467	0.06	0.001	11.77
	—	—	—	—	—	—	22	11.54	0.267	0.059	0.001	12.89
	—	—	—	—	—	—	56	13.754	0.661	0.224	0	16.01
	—	—	—	—	—	—	12	10.85	0.511	0.136	0.001	12.51
	—	—	—	—	—	—	90	10.553	0.279	0.088	0.012	11.98
31-10-5-5	—	—	—	—	—	—	480	35.973	0.955	0.193	0.013	41.14
	—	—	—	—	—	—	120	56.003	3.354	0.308	0.005	63.79
	—	—	—	—	—	—	68	57.188	5.998	0.599	0.016	68.79
	—	—	—	—	—	—	24	46.188	1.943	0.614	0.01	53.46
	—	—	—	—	—	—	176	51.909	3.38	0.285	0.009	59.81
	—	—	—	—	—	—	12	60.984	3.085	1.358	0.007	71.03
	—	—	—	—	—	—	16	108.088	13.371	0.978	0.01	127.74
	—	—	—	—	—	—	48	55.346	4.793	0.686	0.006	65.33
	—	—	—	—	—	—	96	42.596	1.786	0.329	0.014	49.17
	—	—	—	—	—	—	96	38.698	1.345	0.254	0.015	44.57

Ring

A ring of n contexts is a cycle in which context i queries context i+1 for 1 ≤ i ≤ n-1, and context n queries context 1.

	DMCS						DMCSOPT
Test	#answers	lsolve	projection	combine	transfer	total	#answers	lsolve	projection	combine	transfer	total
10-10-5-5	216	0.123	0	0.029	0.033	0.20	12	0.073	0	0	0	0.09
	2400	0.085	0	0.096	0.084	0.30	7	0.056	0	0	0.004	0.09
	192	0.084	0.001	0.007	0.008	0.12	2	0.08	0.001	0	0.004	0.12
	192	0.061	0	0.004	0.005	0.09	2	0.099	0	0	0	0.12
	384	0.07	0	0.002	0.013	0.11	4	0.077	0	0	0	0.09
	60	0.078	0	0.008	0.008	0.11	1	0.076	0	0	0	0.09
	640	0.068	0	0.016	0.029	0.14	6	0.062	0	0	0	0.08
	4320	0.159	0.003	0.382	0.201	0.80	3	0.134	0	0	0.003	0.18
	880	0.097	0	0.091	0.064	0.32	12	0.098	0	0	0.005	0.14
	1008	0.096	0	0.091	0.074	0.29	9	0.098	0	0.001	0.008	0.18
13-10-5-5	70840	0.125	0	7.262	8.718	17.26	24	0.124	0	0	0.001	0.17
	10560	0.131	0	0.356	0.643	1.27	7	0.106	0	0	0.001	0.14
	280	0.093	0	0.037	0.026	0.19	6	0.083	0	0	0	0.10
	14720	0.128	0.001	2.228	2.869	5.51	8	0.107	0	0	0	0.14
	6384	0.103	0	0.172	0.274	0.67	4	0.101	0	0	0.001	0.14
	998400	0.146	0	110.619	71.125	196.01	7	0.12	0	0	0.004	0.18
	3024	0.204	0.002	0.56	0.558	1.38	6	0.16	0.002	0	0.002	0.20
	416	0.112	0	0.038	0.143	0.36	3	0.094	0	0	0	0.11
	11616	0.093	0	0.745	1.511	2.55	8	0.106	0	0	0	0.14
	3744	0.109	0	0.394	0.452	1.09	6	0.103	0	0	0	0.13
301-10-5-5	—	—	—	—	—	—	4	3.674	0.314	0.076	2.744	12.14
	—	—	—	—	—	—	10	3.104	0.036	0	1.612	5.94
	—	—	—	—	—	—	2	5.508	0.048	0.004	1.705	11.55
	—	—	—	—	—	—	8	3.433	0.059	0.001	1.626	6.13
	—	—	—	—	—	—	18	5.298	0.073	0.016	2.097	11.98
	—	—	—	—	—	—	8	4.765	0.184	0.003	1.687	8.67
	—	—	—	—	—	—	6	4.055	0.075	0.022	2.159	9.85
	—	—	—	—	—	—	28	3.636	0.074	0.087	2.881	12.79
	—	—	—	—	—	—	16	4.482	0.084	0.132	2.988	18.48
	—	—	—	—	—	—	16	3.625	0.182	0.014	2.067	8.52

Zig-zag

This topology is incremented from the diamond topology by adding an edge between two middle contexts.

	DMCS						DMCSOPT
Test	#answers	lsolve	projection	combine	transfer	total	#answers	lsolve	projection	combine	transfer	total
10-10-5-5	240	0.587	0.006	0.037	0.005	0.74	40	0.113	0	0	0	0.13
	3264	0.995	0.049	1.914	0.011	3.08	192	0.245	0.014	0.003	0	0.29
	6144	1.201	0.102	12.785	0.021	14.24	72	0.426	0.073	0.004	0	0.53
	110	0.776	0.023	0.036	0.002	0.91	10	0.193	0.012	0	0	0.23
	6240	3.422	0.637	10.907	0.035	15.18	88	0.811	0.18	0.019	0.002	1.04
	528	1.71	0.229	0.054	0.006	2.10	24	0.362	0.051	0	0	0.44
	864	2.471	0.32	0.917	0.029	3.83	16	0.314	0.023	0.002	0	0.36
	1120	2.513	0.272	0.143	0.006	3.04	48	0.406	0.047	0	0	0.47
	4608	2.47	0.425	3.64	0.034	6.69	48	0.4	0.049	0.001	0	0.48
	1260	1.927	0.439	1.637	0.014	4.11	21	0.233	0.042	0	0	0.30
13-10-5-5	5376	10.112	2.346	2.211	0.027	14.99	128	0.759	0.13	0.003	0.001	0.92
	3024	5.792	0.924	4.055	0.024	11.05	108	0.495	0.068	0.002	0	0.60
	3840	7.045	1.385	1.801	0.034	10.54	36	0.477	0.085	0.006	0	0.60
	1440	3.088	0.138	0.258	0.012	3.72	32	0.478	0.067	0.001	0.001	0.58
	1344	3.904	0.376	0.408	0.005	4.91	288	1.048	0.209	0.013	0.003	1.32
	3920	6.416	0.952	8.304	0.121	16.16	48	0.229	0.008	0.003	0.009	0.28
	10248	4.538	0.438	26.313	0.079	31.72	16	0.71	0.117	0.007	0	0.87
	—	—	—	—	—	—	112	0.407	0.039	0.002	0	0.49
	—	—	—	—	—	—	9	0.897	0.177	0.002	0.001	1.11
	—	—	—	—	—	—	28	0.376	0.026	0	0	0.43
70-10-5-5	—	—	—	—	—	—	48	4.941	4.809	0.054	0.09	10.26
	—	—	—	—	—	—	24	5.033	5.345	0.015	0.074	10.64
	—	—	—	—	—	—	56	4.204	4.278	0.071	0.094	9.49
	—	—	—	—	—	—	64	3.594	3.591	0.055	0.085	7.51
	—	—	—	—	—	—	32	3.311	2.551	0.04	0.082	6.16
	—	—	—	—	—	—	96	4.374	6.704	0.095	0.098	11.48
	—	—	—	—	—	—	24	4.86	7.982	0.116	0.106	13.28
	—	—	—	—	—	—	256	5.385	11.151	0.077	0.112	16.93
	—	—	—	—	—	—	6	5.401	7.669	0.073	0.081	13.42
	—	—	—	—	—	—	160	5.042	17.092	0.274	0.12	22.86
151-10-5-5	—	—	—	—	—	—	72	7.981	18.51	0.181	0.486	27.60
	—	—	—	—	—	—	60	9.78	16.614	0.17	0.387	27.43
	—	—	—	—	—	—	8	6.712	8.964	0.104	0.422	16.62
	—	—	—	—	—	—	4	9.582	42.139	0.306	0.435	52.92
	—	—	—	—	—	—	80	9.258	15.862	0.222	0.448	26.28
	—	—	—	—	—	—	10	7.631	12.203	0.209	0.449	20.96
	—	—	—	—	—	—	60	8.991	34.029	0.188	0.458	44.13
	—	—	—	—	—	—	56	9.456	24.58	0.181	0.456	35.43
	—	—	—	—	—	—	672	9.645	26.849	0.258	0.416	37.74
	—	—	—	—	—	—	8	9.014	28.105	0.327	0.469	38.41

House

A house consists of 5 nodes with 6 edges (the ridge context has directed edges to the two middle contexts, which form with the two base contexts a cycle with 4 edges); house stacks are subsequently built up by using the basement nodes as ridges for the next houses (thus, m houses have 4m+1 contexts).

	DMCS						DMCSOPT
Test	#answers	lsolve	projection	combine	transfer	total	#answers	lsolve	projection	combine	transfer	total
9-10-5-5	1344	0.446	0.04	0.173	0.014	0.68	112	0.205	0.039	0.004	0	0.28
	528	0.622	0.058	0.113	0.007	0.83	12	0.127	0.004	0.005	0.004	0.22
	1352	1.551	0.433	0.326	0.01	2.31	24	0.225	0.016	0.002	0	0.27
	2560	0.776	0.099	0.475	0.008	1.41	32	0.229	0.035	0.003	0.001	0.30
	13056	2.17	1.575	25.36	0.295	29.48	144	0.173	0.003	0.018	0.004	0.27
	840	1.251	0.563	0.242	0.013	2.05	40	0.17	0.015	0.004	0.003	0.23
	72	1.252	0.658	0.022	0.004	1.92	24	0.145	0.004	0	0	0.17
	296	0.487	0.02	0.119	0.003	0.65	4	0.116	0.003	0.001	0.001	0.15
	408	1.155	0.369	0.176	0.027	1.67	63	0.15	0.006	0.007	0.002	0.20
	4416	1.912	1.345	1.991	0.044	5.30	144	0.185	0.015	0.008	0.002	0.26
13-10-5-5	19200	3.786	7.811	40.847	0.315	53.33	120	0.354	0.084	0.023	0.006	0.52
	10240	1.551	0.474	11.354	0.18	13.72	512	0.467	0.027	0.04	0.016	0.71
	1848	1.475	0.325	0.829	0.144	2.78	64	0.119	0.001	0.001	0.002	0.16
	5120	5.784	15.878	3.841	0.052	25.68	4	0.131	0.002	0	0.001	0.16
	—	—	—	—	—	—	90	0.185	0.008	0.004	0.002	0.31
	—	—	—	—	—	—	24	0.271	0.033	0.01	0.009	0.39
	—	—	—	—	—	—	288	0.414	0.121	0.035	0.002	0.62
	—	—	—	—	—	—	44	0.353	0.046	0.027	0.006	0.50
	—	—	—	—	—	—	208	0.382	0.043	0.016	0.005	0.49
	—	—	—	—	—	—	624	0.279	0.028	0.034	0.004	0.44
41-10-5-5	—	—	—	—	—	—	80	0.907	0.133	0.038	0.056	1.54
	—	—	—	—	—	—	24	0.69	0.016	0.017	0.041	0.94
	—	—	—	—	—	—	16	0.793	0.014	0.007	0.04	1.04
	—	—	—	—	—	—	96	0.646	0.016	0.022	0.03	0.87
	—	—	—	—	—	—	64	0.56	0.016	0.01	0.025	0.74
	—	—	—	—	—	—	8	0.778	0.015	0.005	0.023	0.94
	—	—	—	—	—	—	28	0.584	0.009	0.012	0.043	1.27
	—	—	—	—	—	—	64	0.805	0.103	0.019	0.033	1.13
	—	—	—	—	—	—	12	0.603	0.026	0.014	0.036	0.84
	—	—	—	—	—	—	56	0.699	0.032	0.015	0.036	0.95
101-10-5-5	—	—	—	—	—	—	22	1.776	0.246	0.194	0.309	7.02
	—	—	—	—	—	—	48	1.669	0.159	0.098	0.238	2.97
	—	—	—	—	—	—	64	1.976	0.12	0.075	0.297	3.64
	—	—	—	—	—	—	27	1.932	0.188	0.127	0.287	3.55
	—	—	—	—	—	—	48	1.767	0.08	0.044	0.198	2.74
	—	—	—	—	—	—	384	1.808	0.149	0.183	0.272	3.69
	—	—	—	—	—	—	136	1.986	0.235	0.138	0.244	3.21
	—	—	—	—	—	—	272	1.78	0.173	0.101	0.243	3.05
	—	—	—	—	—	—	56	1.258	0.099	0.079	0.254	3.35
	—	—	—	—	—	—	40	1.338	0.08	0.163	0.292	6.47

Binary Tree

	DMCS						DMCSOPT
Test	#answers	lsolve	projection	combine	transfer	total	#answers	lsolve	projection	combine	transfer	total
100-9-4-4	—	—	—	—	—	—	8	0.667	0	0	0.108	0.95
	—	—	—	—	—	—	6	0.779	0.003	0	0.101	1.06
	—	—	—	—	—	—	10	0.666	0	0	0.105	0.94
	—	—	—	—	—	—	8	0.677	0	0	0.1	0.94
	—	—	—	—	—	—	8	0.576	0	0	0.107	0.86
	—	—	—	—	—	—	56	0.816	0.003	0	0.102	1.10
	—	—	—	—	—	—	14	0.807	0.002	0	0.108	1.09
	—	—	—	—	—	—	8	0.583	0	0	0.105	0.85
	—	—	—	—	—	—	16	0.625	0	0	0.101	0.90
	—	—	—	—	—	—	64	0.601	0	0	0.107	0.88
200-9-4-4	—	—	—	—	—	—	8	1.299	0.039	0	0.409	2.30
	—	—	—	—	—	—	6	1.763	0.011	0	0.419	2.76
	—	—	—	—	—	—	24	1.383	0.003	0	0.405	2.30
	—	—	—	—	—	—	56	1.377	0.008	0	0.417	2.40
	—	—	—	—	—	—	8	1.629	0.002	0	0.436	2.86
	—	—	—	—	—	—	32	1.3	0.005	0	0.407	2.17
	—	—	—	—	—	—	32	1.582	0.01	0	0.408	2.63
	—	—	—	—	—	—	16	1.528	0.009	0	0.425	2.38
	—	—	—	—	—	—	10	1.651	0.007	0	0.413	2.69
	—	—	—	—	—	—	9	1.392	0.004	0	0.41	2.57
400-9-4-4	—	—	—	—	—	—	32	2.799	0.041	0	1.669	5.36
	—	—	—	—	—	—	24	2.586	0.036	0	1.706	5.19
	—	—	—	—	—	—	32	2.348	0.026	0	1.657	4.86
	—	—	—	—	—	—	6	2.7	0.031	0	1.704	5.29
	—	—	—	—	—	—	6	2.995	0.052	0	1.716	5.64
	—	—	—	—	—	—	8	2.885	0.041	0	1.75	5.55
	—	—	—	—	—	—	64	2.738	0.038	0.001	1.762	5.41
	—	—	—	—	—	—	4	2.757	0.039	0	1.728	5.37
	—	—	—	—	—	—	4	2.636	0.033	0	1.75	5.25
	—	—	—	—	—	—	28	2.733	0.044	0	1.667	5.30
600-9-4-4	—	—	—	—	—	—	4	34.46	1.631	0.573	16.445	175.59

KR 2010 experimental results

The table below shows the experimental result in defk2010-kr. We experemented on two topologies, namely diamond (D) and ring (R). For each topology and each of the two set of parameters P1 and P2, there are 5 test cases. Each row of the table reports the total running time and number of models/answers for the respective test cases.

Topoloy	P1=(7, 8, 4, 4)	#answers	P2=(10, 12, 6, 6)	#answers
D1	0.248	1014	19.520	1944
D2	0.129	56	3.361	5240
D3	0.159	32	18.948	15088
D4	0.121	348	46.249	14596
D5	0.085	12	11.289	5220
R1	0.109	176	33.020	120736
R2	0.106	208	2.285	10548
R3	0.185	80	0.637	2200
R4	0.135	111	12.176	98656
R5	0.320	2119	6.870	19388

Streaming DMCS experiment
Dynamic DMCS experiment
DMCSOPT experiment
DMCS experiment