Research map / Learning theory and algorithms / Combinatorial and search optimization
Parameterized Algorithms for MILPs with Small Treedepth
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Bound coefficient magnitude and the minimum of primal and dual treedepth | MILP · MILP | runtime complexity: f(a,d) poly(n) | Helped |
| Bound block size and coefficient magnitude in the 2-stage stochastic structure | MILP · 2-stage stochastic MILP | runtime complexity: 2^g · n log^3 n log ||u-l||∞ log ||c||∞ | Helped |
| Bound block size and coefficient magnitude in the n-fold structure | MILP · n-fold MILP | runtime complexity: g · n log n log ||u-l||∞ log ||c||∞ | Helped |
| Bound coefficient magnitude and primal or dual treedepth | LP · 2-stage stochastic LP | runtime complexity: 2^{2a^{O(t^3)}} · n log^3 n log ||u-l||∞ log ||c||∞ | Helped |
| Bound coefficient magnitude and primal or dual treedepth | LP · n-fold LP | runtime complexity: a^{t^{O(t^2)}} · n log n log ||u-l||∞ log ||c||∞ | Helped |
| Restrict structure only on the integer-variable columns while allowing unrestricted interaction with continuous variables | MILP · MILP feasibility | computational complexity: NP-hard | Hurt |
| Apply bounded-fractionality reasoning to matrices with constant primal, dual, and incidence treewidth | MILP · Constructed structured MILP instances | fractionality: 2^{Ω(n)} | Hurt |
| Apply bounded-fractionality reasoning to 4-block n-fold matrices | MILP · Constructed 4-block n-fold MILP instances | fractionality: Ω(n) | Hurt |
| Rely only on bounded fractionality to extend the method to separable convex objectives | MIP · Separable convex optimization examples | fractionality: fractionality n; fractionality k; unbounded fractionality | Hurt |
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