mplrs: A scalable parallel vertex/facet enumeration code

Avis, David; Jordan, Charles

doi:10.1007/s12532-017-0129-y

Cited by 22 publications

(28 citation statements)

References 53 publications

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“…9 https://github.com/VERIMAG-Polyhedra/VPL Parametric linear programming with the parameters in the objective function is a generalization of vertex enumeration, for which there exist parallel implementations based on reverse search [3] (vertex enumeration is the case where there are as many independent parameters as there are variables, so that the optimization direction can point to any direction). A difference of our approach with reverse search is that we store the nodes already traversed in a central location, which they do not have to do.…”

Section: Related Workmentioning

confidence: 99%

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Parallel Parametric Linear Programming Solving, and Application to Polyhedral Computations

Coti

Monniaux

2019

Lecture Notes in Computer Science

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Section: Related Workmentioning

confidence: 99%

“…Why this curse of dimensionality? There exist multiple libraries for computing over polyhedra (NewPolka, 3 Parma Polyhedra Library, 4 PolyLib, 5 CDD. .…”

Section: Introductionmentioning

confidence: 99%

Parallel Parametric Linear Programming Solving, and Application to Polyhedral Computations

Coti

Monniaux

2019

Lecture Notes in Computer Science

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“…ZRAM is a general-purpose framework that is able to handle a number of other applications, such as branch and bound and backtracking, for which there are by now a large number of competing frameworks. This is a very large area and an extensive survey of those methods relevant to the present study was given in [8]. We give a brief overview here.…”

Section: Survey Of Previous Workmentioning

confidence: 99%

“…This led us to consider building all of the parallelization into a wrapper, making only minor changes to the underlying lrs code. There followed a series of implementations resulting ultimately in the authors' mplrs code [8].…”

Section: Introductionmentioning

confidence: 99%

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mts: a light framework for parallelizing tree search codes

Avis

Jordan

2019

Optimization Methods and Software

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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 lrs, a reverse search code for vertex enumeration. mts supports sharing information between processes which is important for applications such as satisfiability testing and branch-and-bound. No parallelization is implemented in the legacy single processor programs minimizing the changes needed and simplying debugging. mts is written in C, uses MPI for parallelization and can be used on a network of computers. We give four examples of reverse search codes parallelized by using mts: topological sorts, spanning trees, triangulations and Galton-Watson trees. We also give a parallelization of two codes for satisfiability testing. We give experimental results comparing the parallel codes with other codes for the same problems.

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A task‐based approach to parallel parametric linear programming solving, and application to polyhedral computations

Coti

Monniaux

2020

Concurrency and Computation

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Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications. Here, we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems. This type of parallel applications is challenging, because several tasks might be computing the same region. In this article, we are presenting the algorithm itself with a parallel redundancy elimination algorithm, and conducting a thorough performance analysis. K E Y W O R D S parallel parametric linear programming, polyhedra 1 INTRODUCTION A convex polyhedron in dimension n is the solution set over Q n (or, equivalently, 1 R n) of a system of inequalities (with integer or rational coefficients). Since all the polyhedra we consider here are convex, we shall talk of polyhedra for short. There also exist integer polyhedra, defined over Z n , but they are very different in many respects; we shall not consider them here. 2 Computations over polyhedra arise in low dimension (n = 2 and n = 3) for modeling physical objects, but here we are interested in higher dimensions. Polyhedra in higher dimension are typically used to enclose the set of reachable states of systems whose state can be expressed, at least partially, as a vector of reals or rationals. For instance, one can study the flow of ordinary differential equations, or more generally the trajectories of hybrid systems, by enclosing the trajectories into a succession of convex polyhedra. If the internal state of a control system is expressed by a vector of n numeric variables, one may prove that this system never encounters a bad condition by exhibiting a polyhedron P such that the initial state belongs to P, no bad condition belongs to P, and all possible time steps of the control system leave P stable (i.e., it is not possible to execute a step starting in P and ending outside of P). One generally proves the correctness of programs by exhibiting inductive invariants-an inductive invariant for a loop is a set containing the precondition of the loop, stable by moving to the next loop iteration, and implying the desired postcondition. Since providing inductive invariants by hand is tedious, it is desirable to automate that process. One approach for doing so is abstract interpretation, where an ascending sequence of sets of states is computed until reaching a fixed point. One may, for instance, search such sets as products of intervals, an approach known as interval analysis, but the lack of relationships between the dimensions tends to severely limit the kind of properties that can be proved (e.g., one cannot have an invariant i < n where n is a parameter: this is neither an interval on i nor on n nor a combination thereof). Cousot and Halbwachs proposed searching for polyhedral inductive invariants. 1,2 The operations needed there are projection, more generally image by an affine transformation, convex hull, and inclusion (or equality) test, together with an extrapolation operator known as widening. 1 Whether emptiness tests, inclusio...

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mplrs: A scalable parallel vertex/facet enumeration code

Cited by 22 publications

References 53 publications

Parallel Parametric Linear Programming Solving, and Application to Polyhedral Computations

Parallel Parametric Linear Programming Solving, and Application to Polyhedral Computations

mts: a light framework for parallelizing tree search codes

A task‐based approach to parallel parametric linear programming solving, and application to polyhedral computations

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