Publications associées à Oriented matroid

Streaming and Matching Problems with Submodular Functions

Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...

EPFL2022

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei, Juan Cao

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Entropic Matroids and Their Representation

Emmanuel Abbé

This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p. We draw ...

2019

An Improved Analysis of Local Search for Max-Sum Diversification

Friedrich Eisenbrand, Rico Zenklusen, Alfonso Bolívar Cevallos Manzano

We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

INFORMS2019

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

Igor Malinovic

Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...

EPFL2019

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM Publications2018

Matching fields and lattice points of simplices

Georg Peter Loho

We show that the Chow covectors of a linkage matching field define a bijection of lattice points and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels & Zelevinsky (1993) on l ...

2020

Subdeterminant Maximization via Nonconvex Relaxations and Anti-Concentration

Nisheeth Vishnoi, Javad Ebrahimi Boroojeni, Damian Mateusz Straszak

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors v(1), ..., v(m) is an element of R-d and a constraint family B subset of 2([m]), find a set S. B that maximizes the squared volume of the sim ...

Ieee2017

Clustered planarity testing revisited

Radoslav Fulek, Jan Kyncl, Igor Malinovic

The Hanani--Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generali ...

2015

Order Types of Convex Bodies

We prove a Hadwiger transversal-type result, characterizing convex position on a family of non-crossing convex bodies in the plane. This theorem suggests a definition for the order type of a family of convex bodies, generalizing the usual definition of ord ...

2011