## Optimal sparse matrix bipartitioning

### A matrix a day will keep the doctor away

This page presents a data base of optimal partitionings which can be used to benchmark heuristic sparse matrix partitioners for their quality in terms of communication volume of a parallel sparse matrix-vector multiplication. This page is under perpetual construction. New matrices will be added as we go. Currently we have a batch of 839 optimally partitioned matrices (and a few more). Comments are welcome.

### Papers

The data base accompanies the following papers:

### Programs

The initial set of 355 solutions has been obtained by the program MondriaanOpt, developed by Daan Pelt and Rob Bisseling, which is included as a tool in the Mondriaan package, but is a separate program with a separate version number. It uses the matrix reading functions of Mondriaan, but is otherwise self-contained (so that its correctness can be verified independently). MondriaanOpt v1.0 has been included in Mondriaan v4.1, released November 7, 2016.

A larger set of 839 solutions has been obtained by an improved program called MP (MatrixPartitioner) with stronger bounds developed by Timon Knigge, which is available from GitHub, matrix partitioner MP. The optimal communication volumes computed by both programs are the same. (This has been verified for all 368 matrices that both could solve.)

### Splitting into 2 parts

The partitioning results are for bipartitionings only, i.e. for p=2 processors. The main reason is that heuristic partitioners are often based on recursive bipartitioning, which thus determines the overall quality of the partitioning. Furthermore, exact algorithms can only solve small problems to optimality within a reasonable time, and problems for 2 processors are easier to solve than those for more processors. Symmetric matrices stored in lower triangular form are first expanded to the full sparse matrix, which also includes the nonzeros of the upper triangle. Symmetry is not imposed in the partitioning.

### Imbalance

The allowed imbalance is ε = 3%, which is a value commonly used in the literature for testing partitioners of sparse matrices, graphs, and hypergraphs. Having a single value keeps the database limited in size. Results for any other desired value of ε can be obtained by running the MondriaanOpt program or the program MP with that value as input parameter. The allowed imbalance is defined by the constraint

nz(A[i])(1+ ε) ceil(nz(A)/2), for i=0,1.

Here, nz(A) is the number of nonzeros of the matrix A and nz(A)[i] the number of nonzeros assigned to processor P(i). The ceiling is taken to guarantee that a feasible solution always exists, also for ε= 0 and an odd number of nonzeros. Note that for matrices with an odd number of nonzeros this differs slightly from the formula without the ceiling commonly used in heuristic solvers. To compare soltions, the input value of ε has to be slightly adapted for the heuristic solvers in the odd case.

### Results

The results are presented in two different ways: a set of files containing the solution by MP of a batch of 839 matrices, and a picture gallery presented as a table containing the initial set of 355 matrices obtained by using MondriaanOpt. The picture gallery will over time be extended to include the MP batch of matrices.

Ongoing work will provided more solutions than the 839-matrix batch. These newer solutions will be provided in a separate set of files, which will be regularly updated.

### MP matrices

This set of solutions has been obtained by running the MP program for 24 hours on all sparse matrices with at most 100,000 nonzeros from the SuiteSparse Matrix collection (formerly the University of Florida sparse matrix collection). This succeeded in 839 out of 1602 cases. (cases with duplicate names were removed). The hardware used for each run of MP is a single core of an Intel Ivy Bridge E5-2695 v2 processor running at 2.4 GHz, part of a 24-core node of the Dutch National Supercomputer Cartesius at SURFsara in Amsterdam.

A Comma Separated Values file mp_solutions.csv presents all the statistics of the solutions by MP in the same format as the table of the picture galley, see below. The CSV file can easily be handled by a spreadsheet program for further analysis. The number of rows and columns in the CSV file is the number after removal of empty rows and columns. Thus these numbers may be less than the original numbers. The timings in the CSV file are given in seconds.

The solutions themselves, i.e., the bipartitioned matrices, are collected in a single file mp_matrices.tar.gz in gzipped tar format. The file size is 24 Mbyte, but it expands to a directory with a total size of 845 Mbyte when uncompressed. The directory contains the matrices as a textfile (with extension .mtx-I2f) giving the partitioning. Images of the bipartitioned matrices are collected in a single file mp_SVG.tar.gz in gzipped tar format. The file size is 59 Mbyte, but it expands to a directory with a total size of 1.4 Gbyte when uncompressed. The images are given in .svg format. The .mtx-I2f and .svg formats are described below.

### Picture gallery: table rows

Each row of the table represents a sparse matrix. The rows are sorted by increasing number of matrix nonzeros (nz).

### Picture gallery: table columns

The table contains 10 columns. The meaning of the headers is as follows.
• Name: matrix name in the SuiteSparse sparse matrix collection. If the same matrix name (like `football') appears in two different matrix groups, the group name is also given. If you click on the name you get the details from the SuiteSparse page.
• Rows: number of matrix rows (m).
• Columns: number of matrix columns (n).
• Nonzeros: number of nonzero matrix elements (nz). Note that explicitly stored zeros are also treated as nonzeros. See e.g. bcsstm01 which has 24 explicitly stored zeros.
• Volume: communication volume in a parallel sparse matrix-vector multiplication (in data words).
• Imbalance: achieved imbalance, expressed as the difference between the maximum number of nonzeros per processor and the minimum.
• Solution: link to the solution given as an integer matrix in Matrix-Market format, with a header line, one line of the form m, n, nz, and then nz lines of the form

i j proc

where i is the row number of a nonzero, j the column number, and proc the processor number assigned by the solution, either 1 for processor P(1), or 2 for processor P(2), or a special value 3 meaning the nonzero is free, so that it can be assigned either way, to P(1) or P(2), without affecting communication. Still, their assignment must satisfy the load imbalance constraint (e.g. for the matrix jgl009, at least one of the free nonzeros in row 4 must be assigned to P(2), blue, as here the constraint requires perfect balance). Free nonzeros can be assigned such as to give the best possible load balance. The matrix name is extended by the postfix -I2f, to denote that the matrix has been partitioned into 2 parts, and that free nonzeros are displayed. The numerical values of the original matrix are discarded. The processor numbering is 1-based, in line with the Matrix-Market conventions, and to facilitate plotting by Matlab.
• Date: date when the solution has been added to the table, in dd-mm-yyyy format. Keeps track of history.
• Mond means MondriaanOpt was used to produce the solution. MP means the MatrixPartitioner program MP was used. Mond/MP means MondriaanOpt was used, and MP was used to verify the volume bound.
• Time: time needed to solve the problem, either less than a second, minute, hour, day, week, month, year, decade on the current computer used. This is only a rough indication, as it depends on the initial upper bound on the volume given (for MondriaanOpt, the volume obtained by a run of the medium-grain method from Mondriaan v4.0 +1; for MP, trying increasing upper bounds, each time multiplying a failed bound by a factor 1.25) and the computer used (for MondriaanOpt, 1 core of an Apple iMac with 3.4 GHz Intel Core i5 processor; for MP, 1 core of a 2.4 GHZ Intel Ivy Bridge E5-2695 v2 processor).
• Picture: a picture in Scalable Vector Graphics (SVG) format with red nonzeros corresponding to P(1), blue nonzeros to P(2), and yellow ones to the free nonzeros. For matrices that are too large (nz >1000) to show within the table in SVG format, you have to click on a link to see the picture. For matrices that are very large (nz > 100000), the picture will most likely not display on your browser.
Name Rows Columns Nonzeros Volume Imbalance Solution Date Version Time Picture
Trec3 1 2 1 0 1 solution 24-06-2015 Mond/MPsecond
Trec4 2 3 3 1 1 solution 24-06-2015 Mond/MP second
GL7d10 1 60 8 1 0 solution 04-08-2015 Mond/MP second
Trec5 3 7 12 2 0 solution 06-08-2015 Mond/MP second
b1_ss 7 7 15 3 1 solution 23-06-2015 Mond/MP second
rel3 12 5 18 3 0 solution 23-06-2015 Mond/MP second
ch3-3-b2 6 18 18 0 0 solution 15-12-2015 Mond/MP second
cage3 5 5 19 4 1 solution 19-06-2015 Mond/MP second
lpi_galenet 8 14 22 2 0 solution 10-08-2015 Mond/MP second
relat3 12 5 24 3 0 solution 12-08-2015 Mond/MP second
lpi_itest2 9 13 26 3 0 solution 13-08-2015 Mond/MP second
lpi_itest6 11 17 29 2 1 solution 14-08-2015 Mond/MP second
Tina_AskCal 11 11 29 3 1 solution 17-08-2015 Mond/MP second
n3c4-b1 15 6 30 5 0 solution 18-08-2015 Mond/MP second
n3c4-b4 6 15 30 5 0 solution 15-12-2015 Mond/MP second
Tina_AskCog 11 11 36 4 0 solution 21-08-2015 Mond/MP second
ch3-3-b1 18 9 36 5 0 solution 21-08-2015 Mond/MP second
GD01_b 18 18 37 1 1 solution 25-08-2015 Mond/MP second
Trec6 6 15 40 5 0 solution 25-08-2015 Mond/MP second
farm 7 17 41 4 1 solution 25-08-2015 Mond/MP second
Tina_DisCal 11 11 41 5 1 solution 26-08-2015 Mond/MP second
kleemin 8 16 44 6 0 solution 26-08-2015 Mond/MP second
LFAT5 14 14 46 4 0 solution 27-08-2015 Mond/MP second
Tina_DisCog 11 11 48 6 0 solution 27-08-2015 Mond/MP second
bcsstm01 48 48 48 0 0 solution 11-08-2015 Mond/MP second
cage4 9 9 49 9 1 solution 07-08-2015 Mond/MP second
jgl009 9 9 50 5 0 solution 28-08-2015 Mond/MP second
GD98_a 38 38 50 0 0 solution 28-08-2015 Mond/MP second
GD95_a 36 36 57 1 1 solution 28-08-2015 Mond/MP second
klein-b1 30 10 60 5 0 solution 28-08-2015 Mond/MP second
klein-b2 20 30 60 6 0 solution 31-08-2015 Mond/MP second
n3c4-b2 20 15 60 9 0 solution 02-09-2015 Mond/MP second
n3c4-b3 15 20 60 9 0 solution 02-09-2015 Mond/MP second
Ragusa18 23 23 64 5 0 solution 03-09-2015 Mond/MP second
bcsstm02 66 66 66 0 0 solution 07-09-2015 Mond/MP second
lpi_bgprtr 20 40 70 4 0 solution 07-09-2015 Mond/MP second
wheel_3_1 21 25 74 8 2 solution 10-09-2015 Mond/MP second
rgg010 10 10 76 8 0 solution 10-09-2015 Mond/MP second
jgl011 11 11 76 7 0 solution 10-09-2015 Mond/MP second
Ragusa16 24 24 81 7 1 solution 11-09-2015 Mond/MP second
LF10 18 18 82 4 0 solution 13-09-2015 Mond/MP second
problem 12 46 86 2 2 solution 13-09-2015 Mond/MP second
GD02_a 23 23 87 7 1 solution 15-09-2015 Mond/MP second
n3c5-b1 45 10 90 8 2 solution 17-09-2015 Mond/MP second
Stranke94 10 10 90 10 0 solution 17-09-2015 Mond/MP second
ch4-4-b3 24 96 96 0 0 solution 20-09-2015 Mond/MP second
GD95_b 73 73 96 2 0 solution 20-09-2015 Mond/MP second
Hamrle1 32 32 98 5 2 solution 20-09-2015 Mond/MP second
lp_afiro 27 51 102 5 0 solution 20-09-2015 Mond/MP second
rel4 66 12 104 5 0 solution 25-09-2015 Mond/MP second
bcsstm03 112 112 112 0 0 solution 07-09-2015 Mond/MP second
p0033 15 48 113 5 3 solution 25-09-2015 Mond/MP second
Pajek/football 35 35 118 8 0 solution 25-09-2015 Mond second
n4c5-b11 10 120 120 0 0 solution 30-09-2015 Mond/MP second
wheel_4_1 36 41 122 12 2 solution 30-09-2015 Mond/MP hour
GlossGT 72 72 122 5 2 solution 30-09-2015 Mond/MP second
ibm32 32 32 126 13 0 solution 05-10-2015 Mond/MP minute
bcspwr01 39 39 131 6 1 solution 05-10-2015 Mond/MP second
bcsstm04 132 132 132 0 0 solution 07-09-2015 Mond/MP second
p0040 23 63 133 3 1 solution 11-09-2015 Mond/MP second
GD01_c 33 33 135 7 1 solution 05-10-2015 Mond/MP second
bcsstm22 138 138 138 0 0 solution 06-10-2015 Mond/MP second
lpi_woodinfe 35 89 140 0 2 solution 06-10-2015 Mond/MP second
ch4-4-b1 72 16 144 11 2 solution 06-10-2015 Mond/MP minute
Trec7 11 36 147 8 3 solution 09-10-2015 Mond/MP second
Trefethen_20b 19 19 147 16 5 solution 14-10-2015 Mond/MP second
lp_sc50b 50 78 148 5 4 solution 14-10-2015 Mond/MP minute
d_ss 53 53 149 4 3 solution 09-10-2015 Mond/MP second
GD99_c 105 105 149 0 1 solution 15-10-2015 Mond/MP second
bcsstm05 153 153 153 0 1 solution 15-10-2015 Mond/MP second
refine 29 62 153 3 5 solution 16-10-2015 Mond/MP second
karate 34 34 156 8 0 solution 15-12-2015 Mond/MP second
Trefethen_20 20 20 158 17 4 solution 16-10-2015 Mond/MP second
can_24 24 24 160 8 0 solution 08-12-2015 Mond/MP second
lp_sc50a 50 78 160 5 4 solution 10-12-2015 Mond/MP minute
bcspwr02 49 49 167 4 5 solution 11-12-2015 Mond/MP second
lap_25 25 25 169 10 1 solution 11-12-2015 Mond/MP second
relat4 66 12 172 4 4 solution 14-12-2015 Mond/MP second
pores_1 30 30 180 9 2 solution 31-08-2015 Mond/MP second
wheel_5_1 57 61 182 13 4 solution 14-12-2015 Mond/MP day
GD96_b 111 111 193 3 5 solution 15-12-2015 Mond/MP second
GD98_b 121 121 207 0 1 solution 16-12-2015 Mond/MP second
n2c6-b1 105 15 210 11 2 solution 17-12-2015 Mond/MP second
n3c6-b1 105 105 210 11 2 solution 17-12-2015 Mond/MP second
n4c5-b1 105 15 210 11 2 solution 17-12-2015 Mond/MP second
can_62 62 62 218 6 6 solution 18-12-2015 Mond/MP second
dwt_72 72 72 222 4 2 solution 18-12-2015 Mond/MP second
divorce 50 9 225 8 1 solution 25-06-2015 Mond/MP second
GD96_d 180 180 229 0 1 solution 06-01-2016 Mond/MP second
GD02_b 80 80 232 5 4 solution 25-06-2015 Mond/MP minute
cage5 37 37 233 14 1 solution06-07-2015 Mond/MP second
Maragal_1 32 14 234 14 0 solution 08-01-2016 Mond/MP second
d_dyn 87 87 238 5 4 solution 07-01-2016 Mond/MP minute
d_dyn1 87 87 238 5 4 solution 07-01-2016 Mond/MP minute
n3c5-b7 30 120 240 14 0 solution 12-01-2016 Mond/MP hour
lpi_forest6 66 131 246 5 2 solution 13-01-2016 Mond/MP second
Sandi_authors 86 86 248 4 0 solution 21-08-2015 Mond/MP second
GD96_c 65 65 250 5 6 solution 13-01-2016 Mond/MP minute
IG5-6 30 77 251 18 5 solution 14-01-2016 Mond/MP second
bibd_9_3 36 84 252 22 0 solution 25-01-2016 Mond/MP week
cat_ears_2_1 85 85 254 14 4 solution 01-02-2016 Mond/MP week
dwt_59 59 59 267 8 1 solution 05-02-2016 Mond/MP minute
GD97_b 47 47 264 11 0 solution 19-08-2015 Mond/MP second
ex5 27 27 279 9 9 solution 05-02-2016 Mond/MP second
will57 57 57 281 4 7 solution 29-01-2016 Mond/MP second
GD95_c 62 62 287 6 1 solution 05-02-2016 Mond/MP second
curtis54 54 54 291 7 7 solution 05-02-2016 Mond/MP second
west0067 67 67 294 12 8 solution 02-09-2015 Mond/MP hour
pivtol 102 102 306 4 8 solution 03-09-2015 Mond/MP minute
mesh1e1 48 48 306 18 6 solution 21-08-2015 Mond/MP hour
mesh1em1 48 48 306 18 6 solution 09-02-2016 Mond/MP hour
mesh1em6 48 48 306 18 6 solution 09-02-2016 Mond/MP hour
impcol_b 59 59 312 10 8 solution 14-08-2015 Mond/MP hour
lp_kb2 43 68 313 14 9 solution 09-02-2016 Mond/MP hour
dolphins 62 62 318 18 6 solution 06-07-2015 Mond/MP hour
dwt_66 66 66 320 4 0 solution 29-01-2016 Mond/MP second
n2c6-b10 30 306 330 0 0 solution 17-09-2015 Mond/MP second
wheel_7_1 114 113 338 17 10 solution 25-06-2018 MP minute
chesapeake 39 39 340 16 6 solution 21-08-2015 Mond/MP second
lp_sc105 105 163 340 5 4 solution 10-02-2016 Mond/MP hour
bfwb62 62 62 342 8 2 solution 09-02-2016 Mond/MP second
west0156 156 156 371 5 5 solution 10-02-2016 Mond/MP day
can_73 73 73 377 18 1 solution 09-02-2016 Mond/MP minute
GD06_theory 101 101 380 0 0 solution 18-01-2016 Mond/MP second
olm100 100 100 396 2 0 solution 21-09-2015 Mond/MP second
tub100 100 100 396 4 10 solution 29-01-2016 Mond/MP minute
odepb400 400 400 399 0 1 solution 18-01-2016 Mond/MP second
bcsstk01 48 48 400 24 0 solution 10-02-2016 Mond/MP hour
ch5-5-b1 200 25 400 17 0 solution 10-02-2016 Mond/MP hour
gams10a 114 171 407 2 5 solution 22-09-2015 Mond/MP second
gams10am 114 171 407 2 5 solution 22-09-2015 Mond/MP second
impcol_c 137 137 411 14 13 solution 15-02-2016 Mond/MP day
west0132 132 132 414 6 12 solution 17-02-2016 Mond/MP minute
n4c6-b1 210 21 420 15 4 solution 17-02-2016 Mond/MP minute
cis-n4c6-b1 210 21 420 15 4 solution 17-02-2016 Mond/MP minute
bcsstm06 420 420 420 0 0 solution 19-01-2016 Mond/MP second
lp_adlittle 56 138 424 9 0 solution 17-02-2016 Mond/MP second
ash219 219 85 438 7 8 solution 18-02-2016 Mond/MP hour
bfwa62 62 62 450 11 2 solution 17-02-2016 Mond/MP second
lpi_ex73a 193 211 457 4 3 solution 24-02-2016 Mond/MP month
GD00_a 352 352 458 0 0 solution 26-01-2016 Mond/MP second
GD97_c 452 452 460 1 8 solution 17-02-2016 Mond/MP second
lp_scagr7 129 185 465 6 13 solution 17-02-2016 Mond/MP second
bcspwr03 118 118 476 8 12 solution 17-02-2016 Mond/MP hour
bcsstm20 485 485 485 0 1 solution 26-01-2016 Mond/MP second
lp_stocfor1 117 165 501 9 15 solution 26-02-2016 Mond/MP hour
west0167 167 167 507 7 15 solution 25-02-2016 Mond/MP minute
lesmis 77 77 508 10 0 solution 26-02-2016 Mond/MP second
lp_blend 74 114 522 11 14 solution 26-02-2016 Mond/MP minute
ash85 85 85 523 14 1 solution 25-02-2016 Mond/MP hour
lns_131 131 131 536 22 16 solution 04-03-2016 Mond/MP day
lnsp_131 131 131 536 22 16 solution 03-03-2016 Mond/MP day
dwt_87 87 87 541 12 1 solution 25-02-2016 Mond/MP minute
IG5-7 62 150 549 26 1 solution 25-02-2016 Mond/MP minute
Trec8 23 84 549 17 1 solution 25-02-2016 Mond/MP second
can_61 61 61 557 10 1 solution 29-02-2016 Mond/MP second
impcol_a 207 207 572 7 16 solution 04-05-2016 Mond/MP day
08blocks 300 300 592 0 0 solution 21-09-2015 Mond/MP second
nos4 100 100 594 14 16 solution 04-05-2016 Mond/MP hour
ch5-5-b4 120 600 600 0 10 solution 28-01-2016 Mond/MP second
Sandi_sandi 314 360 613 0 1 solution 29-02-2016 Mond/MP second
bcsstk03 112 112 640 0 0 solution 02-02-2016 Mond/MP second
GD01_a 311 311 645 22 19 solution 17-05-2016 Mond/MP week
lpi_box1 231 261 651 4 11 solution 04-03-2016 Mond/MP minute
gent113 113 113 655 17 19 solution 04-03-2016 Mond/MP minute
rel5 340 35 656 10 16 solution 04-03-2016 Mond/MP minute
ash331 331 104 662 9 6 solution 07-03-2016 Mond/MP day
zed 116 142 666 10 2 solution 08-03-2016 Mond/MP second
lp_recipe 91 204 687 11 1 solution 08-03-2016 Mond/MP hour
bcsstk22 138 138 696 8 20 solution 07-03-2016 Mond/MP day
rotor1 100 100 708 14 20 solution 04-03-2016 Mond/MP minute
n3c6-b11 60 675 720 0 0 solution 03-02-2016 Mond/MP second
lpi_klein1 54 108 750 33 0 solution 08-03-2016 Mond/MP hour
lp_share2b 96 162 777 9 1 solution 20-08-2015 Mond/MP day
bwm200 200 200 796 4 20 solution 08-03-2016 Mond/MP minute
rajat11 135 135 812 8 22 solution 07-03-2016 Mond/MP hour
bcsstm19 817 817 817 0 1 solution 02-02-2016 Mond/MP second
dwt_234 234 234 834 4 22 solution 09-03-2016 Mond/MP minute
grid1_dual 224 224 840 0 0 solution 08-02-2016 Mond/MP second
robot 120 120 870 12 12 solution 09-03-2016 Mond/MP minute
polbooks 105 105 882 18 0 solution 09-03-2016 Mond/MP hour
spaceStation_1 99 99 927 42 9 solution 29-06-2016 Mond week
steam3 80 80 928 8 0 solution 25-06-2015 Mond/MP hour
grid1 252 252 952 0 0 solution 04-02-2016 Mond/MP second
cis-n4c6-b15 60 920 960 0 0 solution 03-02-2016 Mond/MP second
ck104 104 104 992 0 0 solution 03-02-2016 Mond/MP second
SmallW 396 396 994 12 28 solution 08-03-2016 Mond/MP minute
CAG_mat72 72 72 1012 13 6 solution 14-03-2016 Mond/MP second click here (large picture)
GD00_c 638 638 1041 15 29 solution 25-07-2016 Mond/MP week click here (large picture)
lp_vtp_base 198 346 1051 16 1 solution 15-03-2016 Mond/MP hour click here (large picture)
relat5 340 35 1058 10 18 solution 14-03-2016 Mond/MP second click here (large picture)
bcsstm08 1074 1074 1074 0 0 solution 04-02-2016 Mond/MP second click here (large picture)
bcsstm09 1083 1083 1083 0 1 solution 08-02-2016 Mond/MP second click here (large picture)
lp_share1b 117 253 1179 7 35 solution 15-03-2016 Mond/MP minute click here (large picture)
ww_36_pmec_36 66 66 1194 29 4 solution 15-03-2016 Mond/MP hour click here (large picture)
odepa400 400 400 1201 3 31 solution 11-09-2015 Mond/MP hour click here (large picture)
lpi_cplex2 224 378 1215 15 35 solution 25-07-2016 Mond/MP week click here (large picture)
bibd_9_5 36 126 1260 34 24 solution 28-04-2016 Mond/MP day click here (large picture)
arc130 130 130 1282 13 12 solution 14-03-2016 Mond/MP second click here (large picture)
gams30a 354 531 1287 2 31 solution 18-09-2015 Mond/MP second click here (large picture)
gams30am 354 531 1287 2 31 solution 24-09-2015 Mond/MP second click here (large picture)
can_144 144 144 1296 12 0 solution 21-03-2016 Mond/MP hour click here (large picture)
n4c5-b10 120 630 1320 14 0 solution 04-08-2016 Mond/MP week click here (large picture)
Cities 55 46 1342 38 40 solution 28-04-2016 Mond/MP hour click here (large picture)
rajat05 301 301 1384 6 0 solution 21-03-2016 Mond/MP minute click here (large picture)
lp_bore3d 233 334 1448 21 0 solution 12-05-2016 Mond/MP day click here (large picture)
dwt_245 245 245 1461 8 41 solution 10-05-2016 Mond/MP minute click here (large picture)
bcsstm11 1473 1473 1473 0 1 solution 08-02-2016 Mond/MP second click here (large picture)
oscil_dcop_01 430 430 1544 2 16 solution 24-09-2015 Mond/MP second click here (large picture)
oscil_dcop_02 430 430 1544 2 16 solution 11-04-2016 Mond/MP second click here (large picture)
oscil_dcop_03 430 430 1544 2 16 solution 11-04-2016 Mond/MP second click here (large picture)
oscil_dcop_04 430 430 1544 2 16 solution 22-04-2016 Mond/MP second click here (large picture)
oscil_dcop_05 430 430 1544 2 16 solution 22-04-2016 Mond/MP second click here (large picture)
oscil_dcop_06 430 430 1544 2 16 solution 22-04-2016 Mond/MP second click here (large picture)
oscil_dcop_07 430 430 1544 2 16 solution 25-04-2016 Mond/MP second click here (large picture)
oscil_dcop_08 430 430 1544 2 16 solution 25-04-2016 Mond/MP second click here (large picture)
oscil_dcop_09 430 430 1544 2 16 solution 25-04-2016 Mond/MP second click here (large picture)
oscil_dcop_10 430 430 1544 2 16 solution 28-04-2016 Mond/MP second click here (large picture)
oscil_dcop_11 430 430 1544 2 16 solution 28-04-2016 Mond/MP second click here (large picture)
oscil_dcop_12 430 430 1544 2 16 solution 29-04-2016 Mond/MP second click here (large picture)
oscil_dcop_13 430 430 1544 2 16 solution 29-04-2016 Mond/MP second click here (large picture)
oscil_dcop_14 430 430 1544 2 16 solution 29-04-2016 Mond/MP second click here (large picture)
oscil_dcop_15 430 430 1544 2 16 solution 04-05-2016 Mond/MP second click here (large picture)
oscil_dcop_16 430 430 1544 2 16 solution 04-05-2016 Mond/MP second click here (large picture)
oscil_dcop_17 430 430 1544 2 16 solution 04-05-2016 Mond/MP second click here (large picture)
oscil_dcop_18 430 430 1544 2 16 solution 09-05-2016 Mond/MP second click here (large picture)
oscil_dcop_19 430 430 1544 2 16 solution 09-05-2016 Mond/MP second click here (large picture)
oscil_dcop_20 430 430 1544 2 16 solution 10-05-2016 Mond/MP second click here (large picture)
oscil_dcop_21 430 430 1544 2 16 solution 10-05-2016 Mond/MP second click here (large picture)
oscil_dcop_22 430 430 1544 2 16 solution 10-05-2016 Mond/MP second click here (large picture)
oscil_dcop_23 430 430 1544 2 16 solution 11-05-2016 Mond/MP second click here (large picture)
oscil_dcop_24 430 430 1544 2 16 solution 11-05-2016 Mond/MP second click here (large picture)
oscil_dcop_25 430 430 1544 2 16 solution 11-05-2016 Mond/MP second click here (large picture)
oscil_dcop_26 430 430 1544 2 16 solution 12-05-2016 Mond/MP second click here (large picture)
oscil_dcop_27 430 430 1544 2 16 solution 12-05-2016 Mond/MP second click here (large picture)
oscil_dcop_28 430 430 1544 2 16 solution 18-05-2016 Mond/MP second click here (large picture)
oscil_dcop_29 430 430 1544 2 16 solution 18-05-2016 Mond/MP second click here (large picture)
oscil_dcop_30 430 430 1544 2 16 solution 19-05-2016 Mond/MP second click here (large picture)
oscil_dcop_31 430 430 1544 2 16 solution 19-05-2016 Mond/MP second click here (large picture)
oscil_dcop_32 430 430 1544 2 16 solution 19-05-2016 Mond/MP second click here (large picture)
oscil_dcop_33 430 430 1544 2 16 solution 23-05-2016 Mond/MP second click here (large picture)
oscil_dcop_34 430 430 1544 2 16 solution 23-05-2016 Mond/MP second click here (large picture)
oscil_dcop_35 430 430 1544 2 16 solution 23-05-2016 Mond/MP second click here (large picture)
oscil_dcop_36 430 430 1544 2 16 solution 23-05-2016 Mond/MP second click here (large picture)
oscil_dcop_37 430 430 1544 2 16 solution 25-05-2016 Mond/MP second click here (large picture)
oscil_dcop_38 430 430 1544 2 16 solution 25-05-2016 Mond/MP second click here (large picture)
oscil_dcop_39 430 430 1544 2 16 solution 25-05-2016 Mond/MP second click here (large picture)
oscil_dcop_40 430 430 1544 2 16 solution 27-05-2016 Mond/MP second click here (large picture)
oscil_dcop_41 430 430 1544 2 16 solution 27-05-2016 Mond/MP second click here (large picture)
oscil_dcop_42 430 430 1544 2 16 solution 27-05-2016 Mond/MP second click here (large picture)
oscil_dcop_43 430 430 1544 2 16 solution 30-05-2016 Mond/MP second click here (large picture)
oscil_dcop_44 430 430 1544 2 16 solution 30-05-2016 Mond/MP second click here (large picture)
oscil_dcop_45 430 430 1544 2 16 solution 30-05-2016 Mond/MP second click here (large picture)
oscil_dcop_46 430 430 1544 2 16 solution 01-06-2016 Mond/MP second click here (large picture)
oscil_dcop_47 430 430 1544 2 16 solution 01-06-2016 Mond/MP second click here (large picture)
oscil_dcop_48 430 430 1544 2 16 solution 01-06-2016 Mond/MP second click here (large picture)
oscil_dcop_49 430 430 1544 2 16 solution 02-06-2016 Mond/MP second click here (large picture)
oscil_dcop_50 430 430 1544 2 16 solution 02-06-2016 Mond/MP second click here (large picture)
oscil_dcop_51 430 430 1544 2 16 solution 02-06-2016 Mond/MP second click here (large picture)
oscil_dcop_52 430 430 1544 2 16 solution 03-06-2016 Mond/MP second click here (large picture)
oscil_dcop_53 430 430 1544 2 16 solution 03-06-2016 Mond/MP second click here (large picture)
oscil_dcop_54 430 430 1544 2 16 solution 03-06-2016 Mond/MP second click here (large picture)
oscil_dcop_55 430 430 1544 2 16 solution 06-06-2016 Mond/MP second click here (large picture)
oscil_dcop_56 430 430 1544 2 16 solution 06-06-2016 Mond/MP second click here (large picture)
oscil_dcop_57 430 430 1544 2 16 solution 06-06-2016 Mond/MP second click here (large picture)
oscil_trans_01 430 430 1614 2 20 solution 24-09-2015 Mond/MP second click here (large picture)
GD96_a 1096 1096 1677 0 1 solution 02-05-2016 Mond/MP second click here (large picture)
lp_scagr25 471 671 1725 6 13 solution 20-05-2016 Mond/MP hour click here (large picture)
CSphd 1882 1882 1740 0 0 solution 08-02-2016 Mond/MP second click here (large picture)
p0548 176 724 1887 10 57 solution 21-06-2016 Mond/MP day click here (large picture)
bcsstm26 1922 1922 1922 0 0 solution 03-03-2016 Mond/MP second click here (large picture)
olm500 500 500 1996 2 48 solution 28-09-2015 Mond/MP second click here (large picture)
mhdb416 416 416 2312 2 66 solution 29-09-2015 Mond/MP second click here (large picture)
Chebyshev1 261 261 2319 4 5 solution 09-05-2016 Mond/MP second click here (large picture)
lp_scsd1 77 760 2388 12 20 solution 29-08-2016 Mond/MP hour click here (large picture)
gams60am 714 1071 2607 2 77 solution 29-09-2015 Mond/MP minute click here (large picture)
Harvard500 500 500 2636 10 76 solution 21-06-2016 Mond/MP hour click here (large picture)
ck400 400 400 2860 0 12 solution 03-03-2016 Mond/MP second click here (large picture)
n2c6-b9 306 1470 3060 0 0 solution 03-03-2016 Mond/MP second click here (large picture)
bcsstm23 3134 3134 3134 0 0 solution 03-03-2016 Mond/MP second click here (large picture)
dwt_492 492 492 3156 0 70 solution 02-03-2016 Mond/MP second click here (large picture)
G11 800 800 3200 0 0 solution 02-03-2016 Mond/MP second click here (large picture)
G12 800 800 3200 0 0 solution 02-03-2016 Mond/MP second click here (large picture)
bibd_81_2 3240 3240 3240 0 0 solution 10-03-2016 Mond/MP second click here (large picture)
dwt_512 512 512 3502 0 72 solution 10-03-2016 Mond/MP second click here (large picture)
tols1090 1090 1090 3546 0 54 solution 10-03-2016 Mond/MP second click here (large picture)
bcsstm24 3562 3562 3562 0 0 solution 15-03-2016 Mond/MP second click here (large picture)
bcsstm21 3600 3600 3600 0 0 solution 15-03-2016 Mond/MP second click here (large picture)
ck656 656 656 3884 0 12 solution 17-03-2016 Mond/MP second click here (large picture)
olm1000 1000 1000 3996 2 112 solution 24-09-2015 Mond/MP second click here (large picture)
tub1000 1000 1000 3996 4 116 solution 18-05-2016 Mond/MP day click here (large picture)
nos2 957 957 4137 4 123 solution 18-05-2016 Mond/MP day click here (large picture)
t2dal_e 4257 4257 4257 0 1 solution 17-03-2016 Mond/MP second click here (large picture)
ch6-6-b5 720 4320 4320 0 0 solution 18-03-2016 Mond/MP second click here (large picture)
lp_ship04s 402 1506 4400 4 100 solution 06-05-2016 Mond/MP second click here (large picture)
mk10-b4 945 4725 4725 0 45 solution 17-03-2016 Mond/MP second click here (large picture)
cage 366 366 5124 0 0 solution 16-03-2016 Mond/MP second click here (large picture)
netz4504 1961 1961 5156 0 0 solution 17-03-2016 Mond/MP second click here (large picture)
netscience 1589 1589 5484 0 0 solution 08-02-2016 Mond/MP second click here (large picture)
Pd_rhs 8081 12406 6323 0 1 solution 16-03-2016 Mond/MP second click here (large picture)
lp_ship04l 402 2166 6380 4 92 solution 06-05-2016 Mond/MP minute click here (large picture)
m3plates 11107 11107 6639 0 1 solution 17-03-2016 Mond/MP second click here (large picture)
lp_ship08s 778 2467 7194 7 174 solution 02-06-2016 Mond/MP day click here (large picture)
Chem97ZtZ 2541 2541 7361 0 1 solution 29-03-2016 Mond/MP second click here (large picture)
fpga_trans_01 1220 1220 7382 4 0 solution 05-05-2016 Mond/MP minute click here (large picture)
fpga_trans_02 1220 1220 7382 4 0 solution 05-05-2016 Mond/MP minute click here (large picture)
lung1 1650 1650 7419 4 213 solution 27-05-2016 Mond/MP day click here (large picture)
epb0 1794 1794 7764 5 184 solution 20-05-2016 Mond/MP day click here (large picture)
olm2000 2000 2000 7996 2 224 solution 28-09-2015 Mond/MP second click here (large picture)
bwm2000 2000 2000 7996 4 238 solution 17-05-2016 Mond/MP day click here (large picture)
G32 2000 2000 8000 0 0 solution 29-03-2016 Mond/MP second click here (large picture)
G34 2000 2000 8000 0 0 solution 05-04-2016 Mond/MP second click here (large picture)
rosen7 264 776 8034 8 22 solution 30-05-2016 Mond/MP second click here (large picture)
diag 2559 2559 8184 0 0 solution 30-03-2016 Mond/MP second click here (large picture)
lp_ship12s 1151 2869 8284 8 56 solution 14-06-2016 Mond/MP day click here (large picture)
iprob 3001 3001 9000 2 0 solution 02-05-2016 Mond/MP second click here (large picture)
laser 3002 3002 9000 4 270 solution 17-05-2016 Mond/MP day click here (large picture)
bcsstm38 8032 8032 10485 0 1 solution 06-04-2016 Mond/MP second click here (large picture)
G48 3000 3000 12000 0 0 solution 04-04-2016 Mond/MP second click here (large picture)
G49 3000 3000 12000 0 0 solution 04-04-2016 Mond/MP second click here (large picture)
grid2 3296 3296 12864 0 0 solution 30-03-2016 Mond/MP second click here (large picture)
lp_ship08l 778 4363 12882 7 166 solution 03-06-2016 Mond/MP day click here (large picture)
bcsstm25 15439 15439 15439 0 1 solution 05-04-2016 Mond/MP second click here (large picture)
ukerbe1 5981 5981 15704 0 0 solution 29-03-2016 Mond/MP minute click here (large picture)
rosen8 520 1544 16058 8 14 solution 30-05-2016 Mond/MP second click here (large picture)
mhd3200b 3200 3200 18316 2 542 solution 02-05-2016 Mond/MP hour click here (large picture)
p6000 2095 7967 19826 2 66 solution 02-05-2016 Mond/MP minute click here (large picture)
olm5000 5000 5000 19996 2 592 solution 28-09-2015 Mond/MP minute click here (large picture)
G57 5000 5000 20000 0 0 solution 05-04-2016 Mond/MP minute click here (large picture)
stoch_aircraft 3754 7517 20267 6 1 solution 26-08-2015 Mond/MP minute click here (large picture)
aircraft 3754 7517 20267 6 1 solution 04-08-2016 Mond/MP minute click here (large picture)
primagaz 1554 10836 21665 7 7 solution 03-06-2016 Mond/MP day click here (large picture)
rosen1 520 1544 23794 8 20 solution 18-09-2015 Mond/MP minute click here (large picture)
bcsstk21 3600 3600 26600 0 0 solution 31-03-2016 Mond/MP minute click here (large picture)
zenios 2873 2873 27191 0 1 solution 30-03-2016 Mond/MP minute click here (large picture)
mhd4800b 4800 4800 27520 2 810 solution 18-09-2015 Mond/MP hour click here (large picture)
G62 7000 7000 28000 0 0 solution 01-04-2016 Mond/MP minute click here (large picture)
plbuckle 1282 1282 30644 0 802 solution 31-03-2016 Mond/MP minute click here (large picture)
G65 8000 8000 32000 0 0 solution 01-04-2016 Mond/MP minute click here (large picture)
G66 9000 9000 36000 0 0 solution 01-04-2016 Mond/MP minute click here (large picture)
Chebyshev3 4101 4101 36879 4 5 solution 04-09-2015 Mond/MP minute click here (large picture)
G67 10000 10000 40000 0 0 solution 31-03-2016 Mond/MP minute click here (large picture)
TS 2142 2142 45262 0 48 solution 31-03-2016 Mond/MP minute click here (large picture)
rosen2 1032 3080 47536 8 1396 solution 18-09-2015 Mond/MP minute click here (large picture)
lp_fit2p 3000 13525 50284 21 340 solution 18-09-2015 Mond/MP minute click here (large picture)
rosen10 2056 6152 64192 8 456 solution 27-08-2015 Mond/MP minute click here (large picture)
c-30 5321 5321 65693 30 1 solution 03-09-2015 Mond/MP minute click here (large picture)
conf5_0-4x4-10 3072 3072 119808 0 0 solution 06-04-2016 Mond minute click here (very large picture)
conf5_0-4x4-14 3072 3072 119808 0 0 solution 06-04-2016 Mond minute click here (very large picture)
conf5_0-4x4-18 3072 3072 119808 0 0 solution 10-04-2016 Mond minute click here (very large picture)
conf5_0-4x4-22 3072 3072 119808 0 0 solution 10-04-2016 Mond minute click here (very large picture)
conf5_0-4x4-26 3072 3072 119808 0 0 solution 10-04-2016 Mond minute click here (very large picture)
conf6_0-4x4-20 3072 3072 119808 0 0 solution 04-04-2016 Mond minute click here (very large picture)
conf6_0-4x4-30 3072 3072 119808 0 0 solution 04-04-2016 Mond minute click here (very large picture)
lp_fit2d 25 10524 129042 21 3244 solution 28-08-2015 Mond minute click here (very large picture)
Muu 7102 7102 170134 0 0 solution 02-03-2016 Mond minute click here (very large picture)

Last updated November 26, 2018.