Problem class 03
Minimum Birkhoff Decomposition
Doubly Stochastic Matrix Decomposition
Minimum Birkhoff decomposition connects assignment structure, sparse representation, and quantum physics applications through a hard cardinality objective.
108
Instances
86
Model files
9
Solution files
80
Result rows
Why benchmark these instances
Birkhoff
A decomposition benchmark that tests whether a method can find sparse convex combinations of permutation matrices.
Contribute results
Submit a Birkhoff result
Have a better bound, a new feasible solution, a quantum run, or a useful negative result? QOBLIB accepts benchmark submissions by pull request using the canonical summary CSV template.
Submission sets
Top-level community submission directories for this problem class.
| Problem | Submission set | Submitter | Date key | Instances | Rows | Source |
|---|---|---|---|---|---|---|
| Minimum Birkhoff Decomposition | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 | 80 | 80 | Directory |
| Minimum Birkhoff Decomposition | 20250806_Classic_Valls | 2025-08-06 | 0 | 0 | Directory | |
| Minimum Birkhoff Decomposition | 20250130_QuantumBaseline-BlackBox_Takeori-Valls | 2025-01-30 | 0 | 0 | Directory |
Result rows
Parsed instance-level summary CSV rows for this problem class.
| Problem | Instance | Submission | Submitter | Date | Objective | Model | Algorithm | Total runtime | Source |
|---|---|---|---|---|---|---|---|---|---|
| Minimum Birkhoff Decomposition | B6_6_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:28 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:28 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:25 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:22 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:19 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:16 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:13 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:10 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:07 | 6.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B6_6_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:04 | 6.0 | Binary Linear Program | Deterministic | 0.02 | CSV |
| Minimum Birkhoff Decomposition | B5_5_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:53:01 | 5.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B5_5_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:58 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B5_5_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:58 | 5.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B5_5_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:55 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B5_5_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:52 | 5.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B5_5_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:49 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B5_5_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:46 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B5_5_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:43 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B5_5_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:40 | 5.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B5_5_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:37 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:34 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:31 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:28 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:25 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:22 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:19 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:16 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:13 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:10 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B4_4_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:07 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:04 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:52:01 | 2.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:58 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:56 | 2.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:53 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:50 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:47 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:44 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:41 | 3.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_3_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:51:38 | 2.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B6_36_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 20:39:55 | 20.0 | Binary Linear Program | Deterministic | 7200.04 | CSV |
| Minimum Birkhoff Decomposition | B6_36_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 18:48:52 | 22.0 | Binary Linear Program | Deterministic | 7200.03 | CSV |
| Minimum Birkhoff Decomposition | B6_36_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 18:38:04 | 22.0 | Binary Linear Program | Deterministic | 7200.03 | CSV |
| Minimum Birkhoff Decomposition | B6_36_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 16:46:23 | 22.0 | Binary Linear Program | Deterministic | 7200.03 | CSV |
| Minimum Birkhoff Decomposition | B6_36_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 16:36:20 | 22.0 | Binary Linear Program | Deterministic | 7200.05 | CSV |
| Minimum Birkhoff Decomposition | B6_36_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 14:43:56 | 22.0 | Binary Linear Program | Deterministic | 7200.02 | CSV |
| Minimum Birkhoff Decomposition | B6_36_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 14:34:41 | 22.0 | Binary Linear Program | Deterministic | 7200.05 | CSV |
| Minimum Birkhoff Decomposition | B6_36_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 12:42:07 | 21.0 | Binary Linear Program | Deterministic | 7200.02 | CSV |
| Minimum Birkhoff Decomposition | B6_36_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 12:32:16 | 22.0 | Binary Linear Program | Deterministic | 7200.03 | CSV |
| Minimum Birkhoff Decomposition | B6_36_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 10:38:31 | 22.0 | Binary Linear Program | Deterministic | 7200.04 | CSV |
| Minimum Birkhoff Decomposition | B5_25_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 10:27:24 | 14.0 | Binary Linear Program | Deterministic | 7200.03 | CSV |
| Minimum Birkhoff Decomposition | B5_25_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 10:24:33 | 14.0 | Binary Linear Program | Deterministic | 168.78 | CSV |
| Minimum Birkhoff Decomposition | B5_25_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 10:01:09 | 14.0 | Binary Linear Program | Deterministic | 2237.82 | CSV |
| Minimum Birkhoff Decomposition | B5_25_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 09:55:08 | 14.0 | Binary Linear Program | Deterministic | 1761.27 | CSV |
| Minimum Birkhoff Decomposition | B5_25_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 07:54:10 | 14.0 | Binary Linear Program | Deterministic | 7200.02 | CSV |
| Minimum Birkhoff Decomposition | B5_25_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 07:49:45 | 14.0 | Binary Linear Program | Deterministic | 7200.02 | CSV |
| Minimum Birkhoff Decomposition | B5_25_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 07:10:17 | 13.0 | Binary Linear Program | Deterministic | 2626.14 | CSV |
| Minimum Birkhoff Decomposition | B5_25_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 07:08:58 | 14.0 | Binary Linear Program | Deterministic | 77.02 | CSV |
| Minimum Birkhoff Decomposition | B5_25_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:46:14 | 14.0 | Binary Linear Program | Deterministic | 7200.04 | CSV |
| Minimum Birkhoff Decomposition | B5_25_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:22 | 14.0 | Binary Linear Program | Deterministic | 51.3 | CSV |
| Minimum Birkhoff Decomposition | B4_16_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:20 | 9.0 | Binary Linear Program | Deterministic | 0.01 | CSV |
| Minimum Birkhoff Decomposition | B4_16_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:17 | 10.0 | Binary Linear Program | Deterministic | 0.07 | CSV |
| Minimum Birkhoff Decomposition | B4_16_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:14 | 10.0 | Binary Linear Program | Deterministic | 0.15 | CSV |
| Minimum Birkhoff Decomposition | B4_16_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:11 | 10.0 | Binary Linear Program | Deterministic | 0.15 | CSV |
| Minimum Birkhoff Decomposition | B4_16_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:08 | 10.0 | Binary Linear Program | Deterministic | 0.12 | CSV |
| Minimum Birkhoff Decomposition | B4_16_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:04 | 10.0 | Binary Linear Program | Deterministic | 0.17 | CSV |
| Minimum Birkhoff Decomposition | B4_16_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:45:02 | 10.0 | Binary Linear Program | Deterministic | 0.06 | CSV |
| Minimum Birkhoff Decomposition | B4_16_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:58 | 8.0 | Binary Linear Program | Deterministic | 0.02 | CSV |
| Minimum Birkhoff Decomposition | B4_16_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:55 | 10.0 | Binary Linear Program | Deterministic | 0.14 | CSV |
| Minimum Birkhoff Decomposition | B4_16_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:53 | 9.0 | Binary Linear Program | Deterministic | 0.03 | CSV |
| Minimum Birkhoff Decomposition | B3_9_10 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:51 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_9 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:50 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_8 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:46 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_7 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:44 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_6 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:40 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_5 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:37 | 4.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_4 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:34 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_3 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:31 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_2 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:28 | 5.0 | Binary Linear Program | Deterministic | 0.0 | CSV |
| Minimum Birkhoff Decomposition | B3_9_1 | 20260111_Gurobi_Schicker | Maximilian Schicker | 2026-01-10 05:44:26 | 5.0 | Binary Linear Program | Deterministic | 0.01 | CSV |