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\begin{document}

\appendix

\section{Comprehensive Computational Results} \label{s:ResultsALL}

Tables \ref{supptab:all_large}, \ref{supptab:all_medium}, \ref{supptab:all_small}, and \ref{supptab:all_tiny} present exhaustive computational results for large (those requiring $\geq1$ hour of run time), medium (those requiring between 1 hour and 1 minute of run time), small (those requiring between 1 minute and $0.1$ seconds of run time) and tiny (those requiring less than $0.1$ seconds) instances, respectively. In each table, the first five columns give the name (or index from SJ database), dimension, number of nonzeros, MATLAB estimated condition number, and MATLAB estimated sparse norm in each matrix. Column 6 gives the run time of SPEX Left LU using the selected pivoting scheme tol 0. Lastly, columns 7 and 8 give the relative run time of Wiedemann and Lanczos, respectively. Note that those instances in which these algorithms seg-fault are indicated with {\bf \red SF} and those instances whose solutions were incorrect are indicated with bold red text.

\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & & & \multicolumn{2}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{norm} & \multicolumn{1}{c|}{SPEX time (hr)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos}  \\  \hline \endhead
350	&	6774	&	33744	&	7.68E+13	&	1.26E+06	&	10.40	&	0.01	&	0.01	\\
367	&	7337	&	156508	&	7.64E+13	&	1.83E+01	&	10.12	&	0.04	&	0.04	\\
696	&	14454	&	147972	&	4.44E+12	&	5.31E+03	&	9.78	&	{\bf \red SF}	&	{\bf \red SF}	\\
695	&	14454	&	147972	&	3.10E+12	&	5.31E+03	&	9.67	&	{\bf \red SF}	&	{\bf \red SF}	\\
213	&	3402	&	130371	&	2.67E+16	&	3.98E+14	&	8.31	&	0.02	&	0.02	\\
352	&	5773	&	71701	&	8.77E+12	&	1.29E+08	&	8.09	&	0.03	&	0.03	\\
119	&	3251	&	65875	&	2.62E+16	&	1.27E+07	&	7.54	&	0.01	&	0.01	\\
344	&	3363	&	99471	&	4.08E+13	&	3.79E+09	&	7.37	&	0.02	&	0.02	\\
337	&	5321	&	65693	&	2.10E+13	&	4.68E+06	&	6.74	&	0.02	&	0.02	\\
117	&	3973	&	79077	&	1.49E+19	&	1.28E+02	&	6.51	&	0.02	&	0.02	\\
346	&	7055	&	30082	&	1.65E+12	&	4.02E+02	&	6.35	&	0.03	&	0.03	\\
347	&	7055	&	30082	&	6.34E+17	&	4.02E+02	&	6.09	&	{\bf \red *0.02}	&	{\bf \red *0.02}	\\
140	&	3937	&	25407	&	1.04E+17	&	3.27E+11	&	5.06	&	0.01	&	0.01	\\
221	&	4257	&	37465	&	2.52E+16	&	1.46E+02	&	4.50	&	{\bf \red *0.01}	&	{\bf \red *0.01}	\\
222	&	4257	&	37465	&	2.52E+16	&	1.46E+02	&	4.49	&	{\bf \red *0.01}	&	{\bf \red *0.01}	\\
223	&	4257	&	37465	&	1.21E+19	&	1.46E+02	&	4.49	&	{\bf \red *0.01}	&	{\bf \red *0.01}	\\
142	&	3937	&	25407	&	1.04E+17	&	3.27E+11	&	4.41	&	0.01	&	0.01	\\
341	&	2880	&	18229	&	9.74E+13	&	1.39E+04	&	4.25	&	0.01	&	0.01	\\
349	&	4101	&	82682	&	1.44E+13	&	1.34E+01	&	3.54	&	0.03	&	0.04	\\
pilot87.pre	&	1540	&	30916	&	Inf	&	Inf	&	2.70	&	0.01	&	0.01	\\
118	&	2568	&	75628	&	4.01E+15	&	1.26E+10	&	2.18	&	0.04	&	0.04	\\
pilot87	&	1625	&	31396	&	Inf	&	Inf	&	1.85	&	0.01	&	0.01	\\
gen4	&	375	&	8919	&	8.43E+236	&	Inf	&	1.25	&	0.01	&	0.01	\\
217	&	4720	&	20042	&	3.51E+48	&	1.89E+02	&	1.16	&	0.06	&	0.06	\\
self	&	924	&	157411	&	1.20E+07	&	1.57E+11	&	1.15	&	0.02	&	0.02	\\
gen4.pre	&	367	&	9322	&	Inf	&	Inf	&	1.12	&	0.01	&	0.01	\\
\hline
\caption{Comprehensive Results: Large Instances}
\small
\centering
\label{supptab:all_large}
\end{longtable}


\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & & & \multicolumn{2}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{Norm}  & \multicolumn{1}{c|}{SPEX time (min)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\  \hline \endhead
slptsk	&	2315	&	34430	&	4.35E+185	&	NaN	&	54.85	&	0.19	&	0.19	\\
gen1	&	329	&	11016	&	Inf	&	Inf	&	44.42	&	0.03	&	0.03	\\
207	&	1919	&	32399	&	3.73E+18	&	2.92E+00	&	33.82	&	0.04	&	0.04	\\
335	&	6747	&	29195	&	2.22E+18	&	5.41E+08	&	32.89	&	0.21	&	0.21	\\
87	&	2500	&	12349	&	4.35E+17	&	9.83E+03	&	26.86	&	0.05	&	0.05	\\
pla8\_sig185	&	39835	&	196256	&	4.29E+09	&	1.04E+03	&	17.17	&	0.16	&	0.17	\\
355	&	1409	&	42760	&	2.28E+13	&	2.67E+05	&	13.90	&	0.08	&	0.08	\\
159	&	1050	&	26198	&	9.00E+15	&	2.10E+07	&	12.37	&	0.04	&	0.04	\\
pilot	&	1132	&	16624	&	1.12E+175	&	NaN	&	10.04	&	0.03	&	0.03	\\
maros-r7	&	1350	&	31923	&	7.43E+06	&	3.99E+10	&	8.62	&	0.03	&	0.03	\\
320	&	1733	&	22189	&	1.20E+13	&	1.18E+11	&	8.30	&	0.14	&	0.15	\\
stat96v4	&	3139	&	23752	&	9.62E+17	&	1.63E+21	&	6.47	&	0.17	&	0.17	\\
pla85900.nov21	&	40304	&	230558	&	5.46E+08	&	9.76E+02	&	6.17	&	0.49	&	0.50	\\
153	&	765	&	24382	&	1.67E+14	&	1.35E+17	&	5.68	&	0.08	&	0.08	\\
58	&	3083	&	11767	&	2.30E+21	&	1.21E+09	&	5.62	&	0.23	&	0.23	\\
momentum3	&	3254	&	15159	&	Inf	&	Inf	&	5.36	&	0.31	&	0.31	\\
jendrec1	&	1779	&	34196	&	9.54E+217	&	NaN	&	4.12	&	3.64	&	3.64	\\
296	&	1258	&	7682	&	1.03E+13	&	2.05E+07	&	3.99	&	0.07	&	0.06	\\
brd14051	&	16360	&	180847	&	2.96E+08	&	2.74E+02	&	3.07	&	0.41	&	0.41	\\
fome13	&	24884	&	70839	&	7.99E+15	&	4.02E+11	&	3.07	&	0.34	&	0.34	\\
240	&	1000	&	1000000	&	1.61E+21	&	6.46E+00	&	2.69	&	{\bf \red *6.22}	&	{\bf \red *6.09}	\\
236	&	1000	&	1000000	&	3.25E+19	&	3.23E+00	&	2.38	&	{\bf \red *6.53}	&	{\bf \red *6.73}	\\
mod2.pre	&	4422	&	12914	&	3.72E+246	&	NaN	&	2.29	&	1.48	&	1.48	\\
260	&	1000	&	1000000	&	1.15E+14	&	5.36E-01	&	2.23	&	{\bf \red *7.04}	&	{\bf \red *7.03} 	\\
world	&	4261	&	12190	&	5.65E+241	&	NaN	&	2.18	&	1.26	&	1.27	\\
l30	&	2492	&	12653	&	1.73E+08	&	2.61E+09	&	2.15	&	0.21	&	0.22	\\
340	&	8765	&	42471	&	6.15E+14	&	1.00E+15	&	1.82	&	11.26	&	11.13	\\
cont11\_l	&	58936	&	179556	&	3.65E+26	&	7.37E+00	&	1.80	&	9.68	&	9.67	\\
mod2	&	4435	&	12985	&	1.38E+223	&	NaN	&	1.74	&	1.77	&	1.79	\\
309	&	2837	&	10967	&	5.85E+12	&	7.41E+05	&	1.58	&	0.82	&	0.81	\\
314	&	2836	&	10965	&	5.85E+12	&	7.41E+05	&	1.58	&	0.81	&	0.83	\\
232	&	1000	&	1000000	&	1.85E+21	&	8.11E-01	&	1.44	&	{\bf \red *10.48} 	&	{\bf \red *10.32} 	\\
gen2	&	328	&	8894	&	1.84E+11	&	4.51E+18	&	1.35	&	0.04	&	0.04	\\
scfxm1-2r-256	&	11812	&	44985	&	3.12E+12	&	2.84E+08	&	1.11	&	2.95	&	2.94	\\
\hline
\caption{Comprehensive Results: Medium Instances}
\small
\centering
\label{supptab:all_medium}
\end{longtable}






\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & & & \multicolumn{2}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{Norm} & \multicolumn{1}{c|}{SPEX time (s)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\  \hline \endhead
nemswrld	&	2205	&	13323	&	NaN	&	Inf	&	53.50	&	0.34	&	0.34	\\
cont4	&	2802	&	11862	&	3.85E+05	&	3.98E+03	&	44.81	&	0.28	&	0.29	\\
rat5	&	902	&	12026	&	4.19E+06	&	7.48E+05	&	40.77	&	0.10	&	0.10	\\
nug30	&	14681	&	45627	&	1.06E+06	&	7.88E+00	&	37.07	&	0.68	&	0.63	\\
nug20	&	7733	&	31455	&	8.84E+07	&	7.26E+00	&	35.20	&	0.26	&	0.28	\\
stat96v1	&	5013	&	20325	&	6.35E+32	&	8.22E+20	&	34.16	&	0.45	&	0.44	\\
stat96v2	&	12928	&	48009	&	1.06E+13	&	1.32E+10	&	32.85	&	1.07	&	1.08	\\
210	&	1484	&	6110	&	5.57E+17	&	1.26E+16	&	29.97	&	0.95	&	0.96	\\
pla33810	&	18940	&	123445	&	1.05E+08	&	2.20E+02	&	29.57	&	1.64	&	1.61	\\
stat96v3	&	13485	&	49917	&	3.93E+12	&	6.98E+09	&	27.62	&	1.29	&	1.31	\\
nug15	&	5486	&	24736	&	2.41E+07	&	7.73E+00	&	26.99	&	0.19	&	0.17	\\
pilot.ja	&	567	&	3781	&	Inf	&	Inf	&	25.13	&	0.32	&	0.31	\\
model10	&	1341	&	6403	&	1.71E+164	&	Inf	&	24.62	&	0.50	&	0.50	\\
rat7a	&	641	&	10542	&	1.38E+20	&	5.06E+05	&	18.88	&	0.12	&	0.13	\\
d2q06c	&	1047	&	5717	&	1.82E+188	&	Inf	&	18.27	&	0.48	&	0.48	\\
128	&	760	&	5739	&	1.12E+16	&	3.10E+08	&	18.26	&	0.29	&	0.29	\\
d15112	&	9197	&	47335	&	2.33E+18	&	2.25E+11	&	17.95	&	2.21	&	2.23	\\
141	&	511	&	2796	&	6.37E+15	&	4.21E+10	&	16.60	&	0.17	&	0.16	\\
144	&	511	&	2796	&	6.37E+15	&	4.21E+10	&	16.49	&	0.17	&	0.17	\\
progas	&	1167	&	6500	&	8.15E+103	&	6.78E+100	&	14.19	&	0.91	&	0.91	\\
co9	&	2287	&	13481	&	2.32E+49	&	1.56E+42	&	13.06	&	0.98	&	0.99	\\
stat96v5	&	812	&	3795	&	1.42E+63	&	3.93E+64	&	13.00	&	1.11	&	1.11	\\
l30.pre	&	1199	&	6030	&	1.79E+06	&	2.61E+09	&	12.56	&	0.24	&	0.24	\\
scfxm1-2b-64	&	5966	&	22682	&	1.30E+12	&	2.84E+08	&	12.11	&	3.96	&	3.94	\\
158	&	416	&	8562	&	2.41E+25	&	2.54E+03	&	12.08	&	0.24	&	0.25	\\
scfxm1-2r-128	&	5671	&	21943	&	1.64E+12	&	2.84E+08	&	11.80	&	3.89	&	3.85	\\
332	&	4101	&	36879	&	6.72E+20	&	2.02E+06	&	11.67	&	12.63	&	12.65	\\
NSR8K	&	5387	&	46157	&	2.64E+07	&	2.06E+03	&	11.62	&	0.66	&	0.66	\\
qap12	&	2740	&	12014	&	2.46E+07	&	6.84E+00	&	10.96	&	0.11	&	0.11	\\
newman2	&	468	&	7917	&	1.39E+225	&	Inf	&	10.85	&	0.23	&	0.23	\\
watson\_1	&	5729	&	14544	&	7.98E+58	&	9.72E+55	&	9.00	&	10.75	&	10.84	\\
209	&	415	&	2779	&	1.04E+18	&	6.47E+00	&	8.66	&	0.23	&	0.25	\\
pilotnov	&	549	&	3337	&	2.82E+264	&	NaN	&	8.64	&	0.54	&	0.54	\\
239	&	500	&	250000	&	3.27E+20	&	6.46E+00	&	8.38	&	{\bf \red *15.04}	&	{\bf \red *15.55}	\\
momentum2	&	2113	&	6516	&	2.52E+39	&	1.88E+37	&	8.35	&	1.10	&	1.08	\\
238	&	200	&	40000	&	8.07E+19	&	6.46E+00	&	8.32	&	0.68	&	0.68	\\
pilot4	&	289	&	2805	&	Inf	&	Inf	&	7.75	&	0.57	&	0.57	\\
235	&	500	&	250000	&	1.01E+19	&	3.23E+00	&	7.52	&	{\bf \red *16.55} 	&	{\bf \red *16.30} 	\\
231	&	500	&	250000	&	8.95E+20	&	8.11E-01	&	7.43	&	{\bf \red *15.82} 	&	{\bf \red *16.21} 	\\
dbic1	&	4795	&	23403	&	1.04E+11	&	4.53E+06	&	7.18	&	1.05	&	1.04	\\
perold	&	440	&	2584	&	4.45E+256	&	NaN	&	7.13	&	0.56	&	0.56	\\
259	&	500	&	250000	&	1.65E+14	&	5.36E-01	&	7.12	&	{\bf \red *16.58} 	&	{\bf \red *16.49} 	\\
watson\_1.pre	&	4642	&	12991	&	3.44E+58	&	9.72E+55	&	7.05	&	10.03	&	9.87	\\
cont1\_l	&	1070	&	4649	&	1.22E+09	&	2.51E+05	&	6.23	&	0.47	&	0.46	\\
scfxm1-2r-96	&	4504	&	17205	&	1.35E+12	&	2.84E+08	&	6.22	&	4.32	&	4.30	\\
126	&	1220	&	5884	&	1.06E+14	&	9.34E+00	&	5.99	&	2.16	&	2.19	\\
291	&	1220	&	5860	&	1.80E+13	&	8.78E+00	&	5.91	&	2.14	&	2.16	\\
212	&	882	&	3354	&	7.98E+16	&	6.69E+12	&	5.87	&	1.52	&	1.51	\\
125	&	1220	&	5892	&	1.58E+17	&	2.88E+00	&	5.69	&	2.25	&	2.24	\\
nug12	&	2736	&	12037	&	2.25E+07	&	6.97E+00	&	5.62	&	0.22	&	0.23	\\
288	&	1220	&	5852	&	2.74E+13	&	1.23E+01	&	5.55	&	2.35	&	2.29	\\
pcb3038	&	3588	&	46560	&	2.00E+06	&	1.55E+02	&	5.41	&	0.72	&	0.72	\\
127	&	1220	&	5855	&	6.25E+14	&	3.70E+02	&	5.39	&	2.36	&	2.38	\\
model11	&	2039	&	7606	&	1.40E+32	&	3.38E+29	&	5.28	&	1.11	&	1.10	\\
294	&	1220	&	5892	&	2.74E+13	&	1.23E+01	&	5.20	&	2.49	&	2.43	\\
287	&	1220	&	5888	&	4.14E+13	&	1.63E+01	&	4.65	&	2.78	&	2.79	\\
289	&	1220	&	5884	&	1.42E+13	&	4.95E+00	&	4.39	&	2.87	&	2.86	\\
292	&	1220	&	5888	&	3.45E+13	&	2.02E+01	&	4.29	&	2.94	&	2.93	\\
nemspmm2	&	949	&	6478	&	2.61E+222	&	Inf	&	4.24	&	1.02	&	1.02	\\
211	&	768	&	2934	&	1.29E+17	&	1.36E+13	&	4.01	&	1.69	&	1.67	\\
293	&	1220	&	5892	&	1.58E+13	&	8.37E+00	&	3.40	&	3.65	&	3.69	\\
stormg2\_1000.pre	&	13926	&	32547	&	2.13E+11	&	2.59E+05	&	3.27	&	31.02	&	31.19	\\
124	&	1220	&	5892	&	2.24E+34	&	2.87E+00	&	2.91	&	3.98	&	3.92	\\
stormg2\_1000	&	14075	&	32597	&	3.77E+09	&	1.05E+04	&	2.90	&	32.90	&	32.98	\\
152	&	180	&	2659	&	3.59E+17	&	2.04E+19	&	2.60	&	0.32	&	0.32	\\
fome12	&	12652	&	35969	&	8.93E+05	&	4.65E+01	&	2.53	&	4.63	&	4.58	\\
nl	&	890	&	2919	&	5.83E+293	&	Inf	&	2.46	&	3.32	&	3.33	\\
fnl4461	&	5044	&	46977	&	4.12E+06	&	2.35E+02	&	2.36	&	2.28	&	2.31	\\
model6	&	790	&	3425	&	5.17E+63	&	4.11E+61	&	2.35	&	1.22	&	1.21	\\
scfxm1-2r-64	&	1870	&	11122	&	8.23E+11	&	2.84E+08	&	2.31	&	4.92	&	4.93	\\
co5	&	928	&	6173	&	3.86E+185	&	Inf	&	2.26	&	2.21	&	2.20	\\
pla7397	&	5059	&	42683	&	8.55E+06	&	3.36E+02	&	2.17	&	2.11	&	2.13	\\
nemspmm1	&	982	&	5023	&	4.94E+23	&	1.59E+20	&	2.12	&	1.30	&	1.30	\\
315	&	2053	&	18447	&	6.71E+16	&	2.03E+04	&	2.09	&	16.27	&	16.18	\\
rl11849	&	6769	&	40885	&	1.21E+08	&	1.92E+02	&	2.09	&	3.40	&	3.36	\\
d18512	&	10815	&	55880	&	8.61E+05	&	2.09E+02	&	1.99	&	7.06	&	7.00	\\
cq9	&	1187	&	5786	&	4.94E+165	&	Inf	&	1.52	&	3.14	&	3.13	\\
qap10	&	1510	&	6381	&	4.45E+06	&	6.13E+00	&	1.49	&	0.21	&	0.20	\\
de080285	&	368	&	1493	&	1.06E+78	&	1.36E+79	&	1.41	&	1.12	&	1.11	\\
rail4284	&	2463	&	11802	&	3.58E+04	&	7.23E+00	&	1.37	&	0.63	&	0.63	\\
pilot.we	&	554	&	2367	&	5.11E+137	&	4.03E+133	&	1.27	&	2.60	&	2.63	\\
newman	&	334	&	2156	&	6.20E+233	&	Inf	&	1.24	&	0.97	&	0.98	\\
ge	&	1675	&	4758	&	3.29E+130	&	7.56E+127	&	1.14	&	7.58	&	7.65	\\
rat1	&	452	&	2893	&	3.93E+27	&	2.26E+30	&	1.10	&	0.70	&	0.68	\\
dano3mip.pre	&	1091	&	5239	&	3.46E+10	&	1.36E+05	&	1.08	&	0.41	&	0.41	\\
342	&	10001	&	49999	&	4.17E+18	&	5.00E+03	&	0.98	&	{\bf \red *846.53} 	&	{\bf \red *845.32}	\\
t0331-4l	&	520	&	5034	&	2.75E+04	&	1.10E+01	&	0.91	&	0.25	&	0.25	\\
132	&	216	&	812	&	8.10E+14	&	1.39E+00	&	0.89	&	0.48	&	0.44	\\
model5	&	492	&	2247	&	7.35E+109	&	1.03E+108	&	0.88	&	2.13	&	2.09	\\
dano3mip	&	1135	&	5390	&	2.47E+10	&	1.36E+05	&	0.85	&	0.55	&	0.52	\\
grow22	&	434	&	4711	&	2.09E+17	&	4.39E+16	&	0.85	&	1.29	&	1.30	\\
rl5915	&	3853	&	28829	&	3.43E+06	&	1.03E+02	&	0.82	&	3.22	&	3.24	\\
model9	&	902	&	4361	&	3.90E+23	&	6.53E+20	&	0.75	&	2.31	&	2.31	\\
siena1	&	1265	&	11573	&	6.40E+05	&	7.85E+02	&	0.67	&	0.63	&	0.62	\\
fome11	&	6226	&	17749	&	6.31E+05	&	5.09E+01	&	0.64	&	4.35	&	4.28	\\
model7	&	646	&	2850	&	2.89E+137	&	2.87E+134	&	0.64	&	2.59	&	2.61	\\
rl5934	&	3773	&	23917	&	2.94E+06	&	1.11E+02	&	0.63	&	3.26	&	3.21	\\
nesm	&	279	&	895	&	1.01E+127	&	1.12E+125	&	0.63	&	3.20	&	3.22	\\
model4	&	409	&	1898	&	9.08E+213	&	NaN	&	0.57	&	2.61	&	2.59	\\
de063155	&	313	&	1233	&	1.09E+95	&	6.12E+69	&	0.54	&	2.33	&	2.30	\\
lp22.pre	&	1811	&	13146	&	3.89E+05	&	1.27E+01	&	0.52	&	1.44	&	1.36	\\
orna1	&	810	&	2842	&	2.66E+13	&	2.55E+15	&	0.51	&	3.36	&	3.38	\\
lp22	&	1796	&	13076	&	1.32E+05	&	1.29E+01	&	0.49	&	1.60	&	1.55	\\
scfxm1-2r-32	&	1447	&	5658	&	2.93E+11	&	2.84E+08	&	0.46	&	6.37	&	6.50	\\
233	&	100	&	10000	&	1.69E+20	&	3.23E+00	&	0.44	&	1.66	&	1.71	\\
van	&	7417	&	21681	&	4.24E+04	&	7.23E+00	&	0.44	&	7.33	&	7.27	\\
usa13509	&	3595	&	19919	&	2.89E+08	&	1.70E+02	&	0.43	&	6.23	&	6.11	\\
237	&	100	&	10000	&	1.08E+19	&	6.46E+00	&	0.40	&	1.92	&	1.85	\\
arki001	&	160	&	893	&	4.46E+299	&	Inf	&	0.37	&	4.08	&	4.07	\\
230	&	200	&	40000	&	9.06E+19	&	8.11E-01	&	0.37	&	{\bf \red *15.47} 	&	{\bf \red *15.07}	\\
greenbeb	&	713	&	3278	&	1.17E+25	&	9.16E+21	&	0.36	&	3.26	&	3.27	\\
234	&	200	&	40000	&	1.74E+18	&	3.23E+00	&	0.35	&	{\bf \red *15.54} 	&	{\bf \red *16.51} 	\\
280	&	430	&	1544	&	2.91E+13	&	2.00E+06	&	0.35	&	4.89	&	4.87	\\
258	&	200	&	40000	&	1.40E+14	&	5.36E-01	&	0.35	&	{\bf \red *15.23} 	&	{\bf \red *15.24}	\\
grow15	&	297	&	3614	&	1.65E+13	&	4.24E+16	&	0.34	&	1.62	&	1.60	\\
complex	&	327	&	10738	&	9.05E+04	&	5.39E+01	&	0.33	&	0.44	&	0.43	\\
scfxm1-2r-27	&	1222	&	4753	&	5.08E+10	&	2.84E+08	&	0.33	&	6.63	&	6.65	\\
newman3	&	369	&	3662	&	1.58E+23	&	3.91E+19	&	0.30	&	1.45	&	1.47	\\
momentum1	&	932	&	2792	&	1.18E+146	&	2.49E+141	&	0.30	&	7.92	&	7.89	\\
dfl001	&	3271	&	9276	&	4.54E+05	&	4.33E+01	&	0.27	&	2.82	&	2.81	\\
dfl001.pre	&	2097	&	6501	&	4.10E+05	&	3.99E+01	&	0.27	&	1.33	&	1.31	\\
stair	&	324	&	3431	&	1.27E+19	&	4.02E+15	&	0.27	&	1.18	&	1.15	\\
stocfor3	&	1782	&	4562	&	2.03E+31	&	3.50E+27	&	0.26	&	23.01	&	22.94	\\
large000	&	823	&	2282	&	1.39E+31	&	1.02E+34	&	0.25	&	14.33	&	14.49	\\
ulevimin	&	697	&	1879	&	8.89E+103	&	5.41E+96	&	0.24	&	5.86	&	5.95	\\
t1717	&	549	&	3657	&	1.89E+04	&	7.40E+00	&	0.24	&	0.40	&	0.44	\\
de063157	&	282	&	1102	&	1.10E+97	&	6.45E+77	&	0.24	&	4.26	&	4.30	\\
car4	&	122	&	4384	&	1.30E+14	&	4.51E+15	&	0.22	&	1.35	&	1.35	\\
greenbea	&	664	&	2706	&	2.17E+38	&	2.38E+32	&	0.21	&	4.38	&	4.46	\\
pcb3000	&	3058	&	27446	&	5.01E+04	&	6.24E+01	&	0.21	&	6.87	&	6.91	\\
25fv47	&	416	&	2061	&	1.42E+35	&	7.33E+32	&	0.21	&	2.01	&	1.94	\\
277	&	183	&	1069	&	2.69E+13	&	1.15E+09	&	0.20	&	{\bf \red *1.46} 	&	{\bf \red *1.45}	\\
stp3d	&	10642	&	25936	&	4.12E+05	&	4.28E+00	&	0.20	&	28.09	&	27.93	\\
trento1	&	1070	&	10010	&	1.54E+05	&	6.57E+02	&	0.19	&	1.23	&	1.23	\\
cq5	&	570	&	2615	&	1.05E+164	&	Inf	&	0.19	&	5.51	&	5.48	\\
dc1l	&	851	&	5171	&	1.68E+05	&	9.70E+02	&	0.18	&	0.72	&	0.72	\\
gran	&	284	&	1958	&	7.38E+32	&	1.25E+27	&	0.17	&	3.00	&	3.00	\\
dg012142	&	892	&	3627	&	9.32E+07	&	2.13E+04	&	0.15	&	2.51	&	2.42	\\
nug08	&	732	&	3004	&	2.49E+05	&	5.71E+00	&	0.15	&	0.42	&	0.43	\\
watson\_2	&	1011	&	2703	&	7.02E+42	&	1.78E+40	&	0.15	&	10.16	&	10.25	\\
dc1c	&	808	&	4698	&	1.26E+06	&	9.63E+02	&	0.14	&	0.79	&	0.81	\\
scfxm1-2r-16	&	752	&	2962	&	1.94E+10	&	2.84E+08	&	0.13	&	5.99	&	6.02	\\
air04	&	630	&	4187	&	1.29E+04	&	8.67E+00	&	0.12	&	0.55	&	0.55	\\
aa01	&	630	&	4187	&	1.29E+04	&	8.67E+00	&	0.12	&	0.57	&	0.56	\\
nemsemm2	&	789	&	2440	&	1.78E+124	&	1.79E+123	&	0.12	&	16.53	&	16.46	\\
scfxm1-2b-16	&	784	&	2975	&	3.37E+10	&	2.84E+08	&	0.12	&	6.69	&	6.76	\\
pf2177	&	406	&	1772	&	9.40E+03	&	4.65E+00	&	0.12	&	0.27	&	0.28	\\
dolom1	&	806	&	5681	&	3.47E+05	&	2.27E+03	&	0.11	&	1.11	&	1.13	\\
model3	&	310	&	1417	&	3.11E+95	&	6.44E+93	&	0.10	&	3.27	&	3.25	\\
\hline
\caption{Comprehensive Results: Small Instances}
\small
\centering
\label{supptab:all_small}
\end{longtable}



\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & & & \multicolumn{2}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{Norm} & \multicolumn{1}{c|}{SPEX Left LU time (ms)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\  \hline \endhead
ds	&	647	&	12193	&	1.01E+04	&	2.08E+01	&	9.85	&	2.83	&	2.68	\\
ch	&	393	&	1304	&	4.36E+110	&	3.12E+106	&	9.21	&	8.74	&	8.84	\\
nug07	&	450	&	1780	&	5.45E+04	&	5.28E+00	&	8.92	&	0.80	&	0.31	\\
229	&	100	&	10000	&	6.48E+18	&	8.11E-01	&	8.51	&	{\bf \red *8.37}	&	{\bf \red *8.24}	\\
cr42	&	304	&	608	&	1.52E+35	&	1.86E+84	&	8.10	&	40.60	&	40.68	\\
143	&	131	&	536	&	1.49E+15	&	9.77E+09	&	8.05	&	2.95	&	1.90	\\
delf000	&	593	&	1606	&	1.27E+18	&	1.44E+20	&	7.23	&	18.52	&	18.91	\\
257	&	100	&	10000	&	3.09E+14	&	5.36E-01	&	6.99	&	{\bf \red *9.84} 	&	{\bf \red *10.18} 	\\
air06	&	562	&	3420	&	1.07E+04	&	9.00E+00	&	6.79	&	0.60	&	0.61	\\
protfold	&	574	&	2562	&	8.36E+03	&	6.50E+00	&	6.71	&	0.66	&	0.65	\\
pldd000b	&	537	&	1448	&	9.92E+18	&	1.27E+22	&	6.59	&	16.57	&	16.59	\\
279	&	261	&	2319	&	7.54E+16	&	2.03E+04	&	6.46	&	9.95	&	9.87	\\
msc98-ip	&	2897	&	10006	&	1.63E+07	&	4.26E+02	&	6.32	&	21.45	&	21.58	\\
l9	&	241	&	1381	&	7.65E+21	&	1.74E+19	&	6.18	&	2.44	&	2.44	\\
model2	&	149	&	757	&	1.15E+112	&	4.60E+108	&	6.16	&	2.54	&	2.56	\\
pcb1000	&	1156	&	9955	&	2.28E+04	&	4.37E+01	&	6.15	&	3.06	&	3.11	\\
aa03	&	562	&	3420	&	1.07E+04	&	9.00E+00	&	5.79	&	0.72	&	0.71	\\
lpl1	&	2692	&	7211	&	8.18E+08	&	1.02E+04	&	5.16	&	16.99	&	17.30	\\
biella1	&	813	&	5726	&	2.72E+04	&	1.18E+01	&	5.03	&	2.78	&	2.76	\\
grow7	&	138	&	1744	&	8.45E+12	&	3.53E+16	&	4.91	&	2.86	&	2.83	\\
bg512142	&	560	&	2140	&	6.92E+06	&	1.95E+03	&	4.71	&	3.18	&	3.20	\\
139	&	131	&	536	&	1.49E+15	&	9.77E+09	&	4.53	&	3.45	&	3.40	\\
rosen10	&	989	&	6916	&	2.01E+03	&	1.35E+03	&	4.23	&	10.79	&	10.86	\\
stormg2-125.pre	&	1780	&	4138	&	1.96E+09	&	5.43E+04	&	4.04	&	35.78	&	35.58	\\
df2177	&	414	&	1825	&	4.61E+03	&	4.74E+00	&	3.96	&	1.99	&	0.60	\\
stormg2-125	&	1886	&	4372	&	2.63E+07	&	2.26E+03	&	3.94	&	39.34	&	39.82	\\
rosen2	&	431	&	4143	&	7.85E+02	&	3.19E+02	&	3.63	&	3.88	&	3.87	\\
degen3	&	744	&	5431	&	1.66E+04	&	2.00E+01	&	3.52	&	1.70	&	1.71	\\
10teams	&	177	&	885	&	1.12E+03	&	5.63E+00	&	3.50	&	0.87	&	0.81	\\
scsd8	&	247	&	655	&	9.59E+18	&	1.58E+17	&	3.44	&	5.35	&	5.26	\\
pds-80	&	9225	&	19432	&	1.12E+04	&	5.66E+00	&	3.36	&	115.71	&	115.40	\\
bas1lp	&	502	&	6651	&	9.77E+04	&	9.80E+01	&	3.28	&	3.22	&	3.12	\\
pilot4i	&	134	&	1220	&	1.50E+33	&	4.19E+28	&	3.15	&	4.41	&	4.41	\\
cycle	&	284	&	878	&	1.46E+79	&	3.19E+75	&	2.99	&	6.23	&	5.80	\\
pds-100	&	8377	&	17555	&	1.79E+04	&	5.48E+00	&	2.97	&	109.88	&	108.16	\\
scfxm1-2r-8	&	403	&	1608	&	7.45E+09	&	2.84E+08	&	2.94	&	7.89	&	7.92	\\
air05	&	323	&	1789	&	2.79E+04	&	6.94E+00	&	2.87	&	1.90	&	0.62	\\
pds-60	&	7586	&	16067	&	8.18E+03	&	4.48E+00	&	2.56	&	104.72	&	104.84	\\
gosh	&	379	&	1379	&	8.05E+27	&	4.51E+24	&	2.49	&	12.14	&	12.47	\\
pds-90	&	7914	&	16673	&	1.48E+04	&	4.13E+00	&	2.43	&	114.84	&	117.41	\\
pds-70	&	7822	&	16545	&	1.11E+04	&	5.84E+00	&	2.14	&	132.65	&	133.20	\\
maros	&	289	&	1143	&	2.76E+14	&	2.54E+11	&	2.13	&	4.07	&	4.08	\\
ganges	&	344	&	1123	&	4.19E+26	&	3.03E+25	&	2.01	&	10.46	&	9.90	\\
fast0507	&	401	&	1908	&	3.72E+03	&	6.99E+00	&	1.94	&	3.54	&	1.26	\\
bandm	&	122	&	609	&	1.12E+27	&	1.05E+26	&	1.94	&	3.02	&	3.03	\\
pds-50	&	5962	&	12592	&	1.04E+04	&	3.49E+00	&	1.87	&	81.12	&	81.91	\\
rail507	&	413	&	2005	&	5.39E+03	&	6.85E+00	&	1.87	&	3.09	&	1.44	\\
30\_70\_4.5\_0.95\_100	&	2754	&	8381	&	6.12E+03	&	4.34E+00	&	1.83	&	36.49	&	30.40	\\
baxter.pre	&	470	&	1274	&	3.55E+94	&	8.48E+88	&	1.61	&	13.78	&	13.99	\\
modszk1	&	263	&	765	&	1.52E+21	&	1.25E+20	&	1.59	&	9.74	&	9.81	\\
30\_70\_4.5\_0.95\_98	&	2451	&	7364	&	7.84E+03	&	4.35E+00	&	1.54	&	28.46	&	26.87	\\
30\_70\_4.5\_0.5\_100	&	2098	&	6197	&	1.98E+03	&	4.28E+00	&	1.48	&	21.62	&	21.47	\\
d6cube	&	223	&	1424	&	9.56E+05	&	4.24E+02	&	1.47	&	2.78	&	2.44	\\
rentacar	&	327	&	1080	&	3.64E+05	&	1.01E+03	&	1.41	&	2.27	&	1.70	\\
qiulp	&	603	&	1717	&	8.25E+10	&	1.31E+09	&	1.38	&	9.67	&	9.95	\\
nug06	&	267	&	1007	&	1.04E+04	&	4.81E+00	&	1.35	&	2.36	&	2.46	\\
qiu	&	603	&	1717	&	5.99E+10	&	1.31E+09	&	1.33	&	10.16	&	9.95	\\
scfxm1-2c-4	&	233	&	965	&	5.92E+09	&	2.84E+08	&	1.23	&	6.22	&	6.34	\\
rosen1	&	217	&	2528	&	1.23E+03	&	5.80E+02	&	1.15	&	3.85	&	3.82	\\
pds-40	&	4028	&	8478	&	6.64E+03	&	3.02E+00	&	1.10	&	50.46	&	50.21	\\
bnl2	&	459	&	1488	&	1.22E+15	&	1.10E+12	&	1.07	&	20.38	&	20.21	\\
mitre	&	801	&	2466	&	4.18E+05	&	2.81E+03	&	1.07	&	37.24	&	36.80	\\
pds-30	&	2643	&	5641	&	3.27E+03	&	3.04E+00	&	1.07	&	30.21	&	30.34	\\
rail516	&	268	&	936	&	1.31E+03	&	5.64E+00	&	0.98	&	4.05	&	3.70	\\
fome21	&	3291	&	7240	&	9.21E+03	&	3.18E+00	&	0.98	&	48.53	&	48.54	\\
south31	&	112	&	460	&	1.68E+265	&	Inf	&	0.95	&	12.15	&	11.65	\\
rail582	&	384	&	1387	&	4.55E+03	&	5.10E+00	&	0.93	&	7.41	&	1.87	\\
seymour	&	537	&	1881	&	5.24E+03	&	5.81E+00	&	0.92	&	4.72	&	3.52	\\
scfxm1-2b-4	&	233	&	965	&	5.92E+09	&	2.84E+08	&	0.84	&	9.50	&	9.27	\\
sp97ar	&	271	&	2400	&	2.40E+04	&	3.93E+01	&	0.82	&	5.84	&	3.53	\\
neos6	&	174	&	1580	&	3.33E+03	&	7.20E+01	&	0.82	&	4.64	&	5.31	\\
neos	&	2342	&	5098	&	3.29E+04	&	5.88E+00	&	0.77	&	25.92	&	27.98	\\
r05	&	919	&	2717	&	4.06E+04	&	3.06E+01	&	0.75	&	12.87	&	12.91	\\
manna81	&	1392	&	2784	&	3.00E+00	&	2.00E+00	&	0.73	&	11.09	&	11.15	\\
p05	&	919	&	2717	&	4.06E+04	&	3.06E+01	&	0.67	&	14.18	&	14.56	\\
scfxm1-2r-4	&	233	&	965	&	5.92E+09	&	2.84E+08	&	0.65	&	12.17	&	12.22	\\
bnl1	&	223	&	824	&	3.34E+23	&	2.35E+20	&	0.65	&	13.63	&	13.63	\\
rosen8	&	264	&	1850	&	2.53E+02	&	8.87E+01	&	0.57	&	6.49	&	6.40	\\
scagr7-2r-864	&	680	&	1697	&	6.99E+06	&	3.42E+03	&	0.57	&	49.66	&	48.56	\\
sp98ar	&	223	&	1782	&	1.69E+04	&	4.43E+01	&	0.55	&	10.46	&	4.20	\\
fome20	&	1718	&	3811	&	5.39E+03	&	3.14E+00	&	0.55	&	27.11	&	26.91	\\
scrs8-2r-512	&	992	&	1984	&	1.92E+01	&	9.13E+00	&	0.54	&	29.88	&	29.67	\\
disctom	&	192	&	565	&	5.92E+02	&	3.41E+00	&	0.52	&	3.41	&	3.34	\\
scfxm3	&	262	&	1005	&	1.67E+17	&	7.58E+13	&	0.52	&	18.62	&	18.57	\\
danoint	&	196	&	790	&	2.11E+07	&	6.31E+03	&	0.51	&	9.36	&	4.55	\\
mzzv11	&	1098	&	3189	&	8.92E+05	&	2.46E+02	&	0.47	&	27.67	&	28.68	\\
80bau3b	&	154	&	396	&	3.31E+46	&	1.75E+45	&	0.46	&	17.53	&	17.59	\\
dbir2.pre	&	281	&	1879	&	5.86E+06	&	1.10E+05	&	0.43	&	8.86	&	8.28	\\
capri	&	138	&	507	&	3.72E+68	&	3.01E+65	&	0.43	&	23.65	&	23.64	\\
p010	&	839	&	2486	&	3.96E+04	&	3.06E+01	&	0.41	&	19.48	&	19.82	\\
degen2	&	217	&	1138	&	2.58E+03	&	1.15E+01	&	0.40	&	4.24	&	4.93	\\
scfxm2	&	178	&	658	&	1.67E+17	&	7.58E+13	&	0.37	&	12.38	&	12.29	\\
baxter	&	256	&	697	&	3.06E+21	&	6.81E+15	&	0.37	&	15.96	&	15.58	\\
dbir1	&	154	&	845	&	4.54E+06	&	1.42E+06	&	0.35	&	17.05	&	17.36	\\
small000	&	140	&	383	&	6.77E+19	&	5.59E+23	&	0.34	&	29.03	&	29.08	\\
stormg2-27	&	449	&	1019	&	3.67E+06	&	1.77E+03	&	0.34	&	21.32	&	21.95	\\
roll3000	&	177	&	1101	&	2.19E+06	&	1.47E+03	&	0.34	&	18.49	&	15.37	\\
woodw	&	168	&	589	&	1.44E+12	&	3.80E+10	&	0.32	&	19.94	&	20.28	\\
route	&	339	&	1290	&	7.27E+08	&	2.03E+07	&	0.32	&	22.68	&	8.86	\\
nsct1	&	120	&	595	&	4.25E+06	&	7.67E+05	&	0.31	&	16.26	&	12.14	\\
neos.pre	&	2080	&	4578	&	1.60E+04	&	5.86E+00	&	0.29	&	56.91	&	56.44	\\
mzzv42z	&	787	&	2124	&	5.68E+05	&	2.01E+02	&	0.27	&	24.22	&	24.24	\\
crew1	&	127	&	861	&	7.82E+02	&	8.18E+00	&	0.27	&	7.76	&	11.03	\\
neos7	&	590	&	1434	&	1.46E+08	&	1.00E+06	&	0.26	&	54.87	&	55.02	\\
sgpf5y6	&	787	&	1870	&	6.24E+02	&	3.37E+00	&	0.22	&	34.46	&	12.04	\\
neos1	&	309	&	944	&	8.24E+02	&	4.83E+00	&	0.22	&	8.65	&	14.13	\\
neos11	&	365	&	1116	&	3.06E+03	&	5.06E+00	&	0.22	&	23.94	&	24.55	\\
nsct2.pre	&	156	&	1140	&	3.84E+06	&	3.22E+05	&	0.21	&	18.44	&	7.87	\\
stocfor2	&	224	&	576	&	3.54E+26	&	1.50E+24	&	0.21	&	46.90	&	46.41	\\
scrs8-2r-256	&	416	&	832	&	1.92E+01	&	9.13E+00	&	0.20	&	38.34	&	12.82	\\
neos4	&	454	&	944	&	2.63E+08	&	5.59E+06	&	0.20	&	38.63	&	9.84	\\
blp-ar98	&	148	&	876	&	3.94E+03	&	9.40E+01	&	0.19	&	25.82	&	27.74	\\
dsbmip	&	220	&	568	&	3.06E+46	&	2.19E+41	&	0.19	&	31.23	&	31.43	\\
sgpf5y6.pre	&	755	&	1744	&	1.20E+02	&	3.22E+00	&	0.18	&	42.42	&	14.08	\\
neos823206	&	220	&	547	&	3.15E+05	&	2.24E+03	&	0.15	&	24.58	&	26.84	\\
sc205	&	184	&	487	&	1.18E+04	&	2.10E+01	&	0.15	&	21.46	&	21.34	\\
rosen7	&	127	&	649	&	8.23E+01	&	5.75E+01	&	0.14	&	39.64	&	14.59	\\
scrs8-2r-64	&	256	&	512	&	1.60E+05	&	1.41E+05	&	0.14	&	54.87	&	20.84	\\
pp08aCUTS	&	131	&	332	&	1.44E+04	&	4.27E+02	&	0.13	&	14.12	&	12.34	\\
scorpion	&	131	&	507	&	7.19E+06	&	2.00E+05	&	0.13	&	39.44	&	35.93	\\
lpl3	&	212	&	461	&	3.06E+02	&	2.61E+00	&	0.13	&	4.52	&	8.85	\\
p19	&	117	&	555	&	4.13E+05	&	4.37E+04	&	0.12	&	64.73	&	20.09	\\
iiasa	&	113	&	262	&	6.06E+18	&	6.37E+17	&	0.12	&	28.25	&	28.10	\\
pds-20.pre	&	370	&	851	&	1.07E+03	&	3.38E+00	&	0.12	&	25.30	&	23.88	\\
rd-rplusc-21	&	148	&	454	&	7.35E+16	&	4.38E+13	&	0.11	&	58.47	&	22.21	\\
neos19	&	228	&	487	&	7.19E+04	&	5.23E+01	&	0.11	&	59.49	&	35.86	\\
gesa2\_o	&	102	&	214	&	6.47E+09	&	4.13E+08	&	0.11	&	51.49	&	38.52	\\
boeing1	&	122	&	415	&	7.36E+10	&	6.29E+07	&	0.11	&	46.04	&	47.62	\\
gesa3\_o	&	148	&	365	&	1.73E+29	&	1.19E+26	&	0.10	&	52.90	&	32.00	\\
gesa3	&	134	&	336	&	1.73E+29	&	1.19E+26	&	0.10	&	69.71	&	27.82	\\
UMTS	&	268	&	828	&	4.40E+20	&	3.24E+18	&	0.10	&	67.24	&	38.74	\\
scrs8	&	109	&	280	&	2.97E+27	&	8.93E+24	&	0.10	&	81.52	&	24.12	\\
scrs8-2r-128	&	192	&	384	&	1.92E+01	&	9.13E+00	&	0.10	&	19.11	&	24.55	\\
scrs8-2c-64	&	168	&	336	&	4.80E+01	&	2.66E+01	&	0.09	&	35.05	&	38.88	\\
ceria3d	&	130	&	647	&	2.40E+04	&	1.09E+01	&	0.09	&	11.93	&	10.00	\\
stormg2-8	&	117	&	263	&	4.82E+05	&	1.77E+03	&	0.09	&	24.41	&	35.78	\\
nsct2	&	107	&	544	&	2.74E+06	&	2.40E+05	&	0.09	&	20.69	&	24.29	\\
mkc	&	106	&	250	&	1.27E+06	&	2.89E+04	&	0.09	&	16.57	&	13.55	\\
scrs8-2r-32	&	128	&	256	&	4.16E+01	&	3.54E+01	&	0.09	&	26.58	&	46.92	\\
dbir2	&	157	&	784	&	1.71E+06	&	7.27E+04	&	0.09	&	30.31	&	33.46	\\
neos818918	&	265	&	678	&	4.29E+02	&	3.22E+00	&	0.09	&	26.79	&	25.53	\\
mkc1	&	106	&	250	&	1.27E+06	&	2.89E+04	&	0.08	&	13.77	&	15.81	\\
bienst1	&	102	&	253	&	7.61E+02	&	6.09E+00	&	0.06	&	11.97	&	9.59	\\
nug05	&	107	&	362	&	1.14E+03	&	4.15E+00	&	0.06	&	5.53	&	11.20	\\
dcmulti	&	120	&	303	&	7.03E+03	&	6.26E+02	&	0.05	&	35.72	&	38.40	\\
\hline
\caption{Comprehensive Results: Tiny Instances}
\small
\centering
\label{supptab:all_tiny}
\end{longtable}
\end{document}