Publications related to Applications of Strong Convex Relaxations to Allocation Problems

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Vessel scheduling with pilotage and tugging considerations

Michel Bierlaire

This paper considers vessel scheduling with pilotage and tugging constraints in berthing operations with channel restrictions at seaports. To our knowledge, pilotage and tugging requirements have not been simultaneously considered in the literature. This w ...

PERGAMON-ELSEVIER SCIENCE LTD2021

Fair colorful k-center clustering

Ola Nils Anders Svensson, Xinrui Jia

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius rho such that there exist balls of radius rho aro ...

SPRINGER HEIDELBERG2021

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

A note on the integrality gap of the configuration LP for restricted Santa Claus

Klaus Jansen, Lars Rohwedder

In the restricted Santa Claus problem we are given resources R and players P. Every resource j is an element of R. has a value v(j) and every player i is an element of P desires a set of resources R(i). We are interested in distributing the resources to pl ...

ELSEVIER2020

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

Ola Nils Anders Svensson, Ashkan Norouzi Fard, Justin Dean Ward

Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for k-means in Euclidean space with a provable guarantee is a simple local ...

SIAM PUBLICATIONS2020

Fair Colorful k-Center Clustering

Ola Nils Anders Svensson, Xinrui Jia

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius ρ such that there exist balls of radius ρ around ...

Springer2020

No Small Linear Program Approximates Vertex Cover Within a Factor 2-epsilon

Ola Nils Anders Svensson, Abbas Bazzi

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev [Khot S, Regev O (2008) Vertex cover might be hard to approximate to within 2 - epsilon. J. Comput. System Sci. 74(3): 335-349 ...

INFORMS2019

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Daniel Kuhn, Napat Rujeerapaiboon, Kilian Schindler, Wolfram Wiesemann

Plain vanilla K-means clustering is prone to produce unbalanced clusters and suffers from outlier sensitivity. To mitigate both shortcomings, we formulate a joint outlier-detection and clustering problem, which assigns a prescribed number of datapoints to ...

2019

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Applications of Strong Convex Relaxations to Allocation Problems

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Vessel scheduling with pilotage and tugging considerations

Fair colorful k-center clustering

New Results in Integer and Lattice Programming

Scalable Stochastic Optimization: Scenario Reduction with Guarantees

A note on the integrality gap of the configuration LP for restricted Santa Claus

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

Fair Colorful k-Center Clustering

New Graph Algorithms via Polyhedral Techniques

No Small Linear Program Approximates Vertex Cover Within a Factor 2-epsilon

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Fair Colorful k-Center Clustering

New Results in Integer and Lattice Programming

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Scalable Stochastic Optimization: Scenario Reduction with Guarantees

A note on the integrality gap of the configuration LP for restricted Santa Claus

Fair colorful k-center clustering

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

New Graph Algorithms via Polyhedral Techniques

Vessel scheduling with pilotage and tugging considerations

No Small Linear Program Approximates Vertex Cover Within a Factor 2-epsilon