相关论文: Basis Reduction, and the Complexity of Branch-and-…

We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…

This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined…

We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…

A limited-memory influence diagram (LIMID) generalizes a traditional influence diagram by relaxing the assumptions of regularity and no-forgetting, allowing a wider range of decision problems to be modeled. Algorithms for solving…

Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…

Machine learning models are widely used for real-world applications, such as document analysis and vision. Constrained machine learning problems are problems where learned models have to both be accurate and respect constraints. For…

This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…

Akiba and Iwata [TCS, 2016] demonstrated that a branch and reduce (B&R) solver for the vertex cover problem can compete favorably with integer linear programming solvers (e.g., CPLEX). Our research question is are there graph…

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified…

We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches,…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…

The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of…

In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…

The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and…

This paper proposes Branch & Learn, a framework for Predict+Optimize to tackle optimization problems containing parameters that are unknown at the time of solving. Given an optimization problem solvable by a recursive algorithm satisfying…

This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…

We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…