Related papers: Integer Programming and Incidence Treedepth
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Integer quantization has emerged as a critical technique to facilitate deployment on resource-constrained devices. Although they do reduce the complexity of the learning models, their inference performance is often prone to…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
Natural language (NL) interfaces to databases broaden access to heterogeneous data but often yield many ambiguous intermediate logical plans (ILPs) due to uncertain operator scope and predicate semantics. Many candidates are infeasible…
Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and…
Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…
Program behavior may depend on parameters, which are either configured before compilation time, or provided at run-time, e.g., by sensors or other input devices. Parametric program analysis explores how different parameter settings may…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
We give a fixed-parameter tractable algorithm that, given a parameter $k$ and two graphs $G_1,G_2$, either concludes that one of these graphs has treewidth at least $k$, or determines whether $G_1$ and $G_2$ are isomorphic. The running time…
Biological and machine pattern recognition systems face a common challenge: Given sensory data about an unknown object, classify the object by comparing the sensory data with a library of internal representations stored in memory. In many…
This paper studies the worst case iteration complexity of an infeasible interior point method (IPM) for seconder order cone programming (SOCP), which is more convenient for warmstarting compared with feasible IPMs. The method studied bases…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
In Constraint Programming, global constraints allow to model and solve many combinatorial problems. Among these constraints, several sortedness constraints have been defined, for which propagation algorithms are available, but for which the…
We consider ILPs, where each variable corresponds to an integral point within a polytope $\mathcal{P}$, i. e., ILPs of the form $\min\{c^{\top}x\mid \sum_{p\in\mathcal P\cap \mathbb Z^d} x_p p = b, x\in\mathbb Z^{|\mathcal P\cap \mathbb…
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in…
We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…