David Avis
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View article: Parallel Redundancy Removal in lrslib with Application to Projections
Parallel Redundancy Removal in lrslib with Application to Projections Open
We describe a parallel implementation in lrslib for removing redundant halfspaces and finding a minimum representation for an $$H$$ -representation of a convex polyhedron. By a standard transformation, the same code works for $$V$$ -re…
View article: A Note on Acyclic Token Sliding Reconfiguration Graphs of Independent Sets
A Note on Acyclic Token Sliding Reconfiguration Graphs of Independent Sets Open
We continue the study of Token Sliding (reconfiguration) graphs of independent sets initiated by the authors in an earlier paper [Graphs Comb. 39.3, 59, 2023]. Two of the topics in that paper were to study which graphs \(G\) are Token Slid…
View article: HV-symmetric polyhedra and bipolarity
HV-symmetric polyhedra and bipolarity Open
A polyhedron is pointed if it contains at least one vertex. Every pointed polyhedron P in R^n can be described by an H-representation consisting of half spaces or equivalently by a V-representation consisting of the convex hull of a set of…
View article: Parallel Redundancy Removal in lrslib with Application to Projections
Parallel Redundancy Removal in lrslib with Application to Projections Open
We describe a parallel implementation in lrslib for removing redundant halfspaces and finding a minimum representation for an H-representation of a convex polyhedron. By a standard transformation, the same code works for V-representations.…
View article: A Note On Acyclic Token Sliding Reconfiguration Graphs of Independent Sets
A Note On Acyclic Token Sliding Reconfiguration Graphs of Independent Sets Open
We continue the study of token sliding reconfiguration graphs of independent sets initiated by the authors in an earlier paper (arXiv:2203.16861). Two of the topics in that paper were to study which graphs $G$ are token sliding graphs and …
View article: On Reconfiguration Graphs of Independent Sets under Token Sliding
On Reconfiguration Graphs of Independent Sets under Token Sliding Open
An independent set of a graph $G$ is a vertex subset $I$ such that there is no edge joining any two vertices in $I$. Imagine that a token is placed on each vertex of an independent set of $G$. The $\mathsf{TS}$- ($\mathsf{TS}_k$-) reconfig…
View article: On the foundations and extremal structure of the holographic entropy cone
On the foundations and extremal structure of the holographic entropy cone Open
The holographic entropy cone (HEC) is a polyhedral cone first introduced in the study of a class of quantum entropy inequalities. It admits a graph-theoretic description in terms of minimum cuts in weighted graphs, a characterization which…
View article: lrsarith: a small fixed/hybrid arithmetic C library
lrsarith: a small fixed/hybrid arithmetic C library Open
We describe lrsarith which is a small fixed precision and hybrid arithmetic C library for integers and rationals that we developed for use in the lrslib library for polyhedral computation. Using a generic set of operations, a program can b…
View article: Sparktope: linear programs from algorithms
Sparktope: linear programs from algorithms Open
In a recent paper Avis, Bremner, Tiwary and Watanabe gave a method for constructing linear programs (LPs) based on algorithms written in a simple programming language called Sparks. If an algorithm produces the solution $x$ to a problem in…
View article: Outer approximations of core points for integer programming
Outer approximations of core points for integer programming Open
For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…
View article: Sparktope example LPs
Sparktope example LPs Open
This dataset consists of the main examples from the Sparktope compiler. These examples are pre-compiled and ready to pass to a solver. The filename format is polytope-objective.lp.gz where polytope is compiled from a .spk program and objec…
View article: mts: a light framework for parallelizing tree search codes
mts: a light framework for parallelizing tree search codes Open
We describe mts, a generic framework for parallelizing certain types of tree search programs including reverse search, backtracking, branch and bound and satisfiability testing. It abstracts and generalizes the ideas used in parallelizing …
View article: Approximate Data Depth Revisited
Approximate Data Depth Revisited Open
Halfspace depth and $β$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\in \mathbb{R}^d$ with respect to $S\subset\mathbb{R}^d$ is the minimum portion of the elements …
View article: Approximate Data Depth Revisited
Approximate Data Depth Revisited Open
Halfspace depth and $\beta$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\in \mathbb{R}^d$ with respect to $S\subset\mathbb{R}^d$ is the minimum portion of the eleme…
View article: Computing the Planar $β$-skeleton Depth
Computing the Planar $β$-skeleton Depth Open
For $β\geq 1$, the \emph{$β$-skeleton depth} ($\SkD_β$) of a query point $q\in \mathbb{R}^d$ with respect to a distribution function $F$ on $\mathbb{R}^d$ is defined as the probability that $q$ is contained within the \emph{$β$-skeleton in…
View article: Computing the Planar $\beta$-skeleton Depth
Computing the Planar $\beta$-skeleton Depth Open
For $\\beta \\geq 1$, the \\emph{$\\beta$-skeleton depth} ($\\SkD_\\beta$) of a\nquery point $q\\in \\mathbb{R}^d$ with respect to a distribution function $F$ on\n$\\mathbb{R}^d$ is defined as the probability that $q$ is contained within t…
View article: Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$
Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$ Open
International audience
View article: An analysis of budgeted parallel search on conditional Galton-Watson\n trees
An analysis of budgeted parallel search on conditional Galton-Watson\n trees Open
Recently Avis and Jordan have demonstrated the efficiency of a simple\ntechnique called budgeting for the parallelization of a number of tree search\nalgorithms. The idea is to limit the amount of work that a processor performs\nbefore it …
View article: An Optimal Algorithm for Computing the Spherical Depth of Points in the Plane
An Optimal Algorithm for Computing the Spherical Depth of Points in the Plane Open
For a distribution function $F$ on $\mathbb{R}^d$ and a point $q\in \mathbb{R}^d$, the \emph{spherical depth} $\SphD(q;F)$ is defined to be the probability that a point $q$ is contained inside a random closed hyper-ball obtained from a pai…
View article: A parallel framework for reverse search using mts
A parallel framework for reverse search using mts Open
We describe mts, which is a generic framework for parallelizing certain types of tree search programs, that (a) provides a single common wrapper containing all of the parallelization, and (b) minimizes the changes needed to the existing si…
View article: Monotone Simultaneous Embeddings of Paths in R^d
Monotone Simultaneous Embeddings of Paths in R^d Open
We study the following problem: Given $k$ paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that for any dimension $d …