Publications related to Opaque Sets

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For any 𝜀 > 0, we prove that 𝑘-Dimensional Matching is hard to approximate within a factor of 𝑘/(12+𝜀) for large 𝑘 unless NP ⊆ BPP. Listed in Karp’s 21 NP-complete problems, 𝑘-Dimensional Matching is a benchmark computational complexity problem which we fi ...

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

Robots outside of the fenced factories have to deal with continuously changing environment, this requires fast and flexible modes of control. Planning methods or complex learning models can find optimal paths in complex surroundings, but they are computati ...

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...

We revisit the problem max-min degree arborescence, which was introduced by Bateni et al. [STOC'09] as a central special case of the general Santa Claus problem, which constitutes a notorious open question in approximation algorithms. In the former problem ...

We address multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control pol ...

In this paper, we present a spatial branch and bound algorithm to tackle the continuous pricing problem, where demand is captured by an advanced discrete choice model (DCM). Advanced DCMs, like mixed logit or latent class models, are capable of modeling de ...

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in ...

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optim ...

Hydropower plants play a crucial role in the power system facing ambitious renewable energy targets. Due to their inherent controllability, they are well suited to provide flexibility to the grid. However, an increased flexibility provision leads to a prol ...

. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...

Finding cycles in directed graphs enables important applications in various domains such as finance, biology, chemistry, and network science. However, as the size of graph datasets continues to grow, it becomes increasingly difficult to discover cycles wit ...

Background: Although digital mobility outcomes (DMOs) can be readily calculated from real-world data collected with wearable devices and ad-hoc algorithms, technical validation is still required. The aim of this paper is to comparatively assess and validat ...

Opaque Sets

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Asymptotically Optimal Hardness for 𝑘-Set Packing and 𝑘-Matroid Intersection

A ride time-oriented scheduling algorithm for dial-a-ride problems

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

On the boundedness of n-folds with κ(X) = n - 1

Perturbed Utility Stochastic Traffic Assignment

Exact Obstacle Avoidance for Robots in Complex and Dynamic Environments Using Local Modulation

Approximation Algorithms for Allocation and Network Design

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Results on Sparse Integer Programming and Geometric Independent Sets

Fairness and Explainability in Clustering Problems

Better Trees for Santa Claus

Multi-robot task allocation for safe planning against stochastic hazard dynamics

A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

Bayesian reconstruction of memories stored in neural networks from their connectivity

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Structural impact of the start-up sequence on Pelton turbines lifetime: Analytical prediction and polynomial optimization

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Certification of Bottleneck Task Assignment With Shortest Path Criteria

Fast Parallel Algorithms for Enumeration of Simple, Temporal, and Hop-Constrained Cycles

Assessing real-world gait with digital technology? Validation, insights and recommendations from the Mobilise-D consortium