Leon Eifler
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View article: Certified Constraint Propagation and Dual Proof Analysis in a Numerically Exact MIP Solver
Certified Constraint Propagation and Dual Proof Analysis in a Numerically Exact MIP Solver Open
This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while sacrifici…
View article: Branch and Cut for Partitioning a Graph into a Cycle of Clusters
Branch and Cut for Partitioning a Graph into a Cycle of Clusters Open
In this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data ge…
View article: PACE Solver Description: Crossy - An Exact Solver for One-Sided Crossing Minimization
PACE Solver Description: Crossy - An Exact Solver for One-Sided Crossing Minimization Open
We describe Crossy, an exact solver for One-sided Crossing Minimization (OSCM) that ranked 5th in the Parameterized Algorithms and Computational Experiments (PACE) Challenge 2024 (Exact and Parameterized Track). Crossy applies a series of …
View article: Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization
Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization Open
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of pr…
View article: A proof system for certifying symmetry and optimality reasoning in integer programming
A proof system for certifying symmetry and optimality reasoning in integer programming Open
We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and Nordström…
View article: Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework
Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework Open
This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible…
View article: Enabling Research through the SCIP Optimization Suite 8.0
Enabling Research through the SCIP Optimization Suite 8.0 Open
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP . The focus of this article is on the role of the SCIP Optimization Suit…
View article: A Safe Computational Framework for Integer Programming Applied to Chvátal’s Conjecture
A Safe Computational Framework for Integer Programming Applied to Chvátal’s Conjecture Open
We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a rat…
View article: A computational status update for exact rational mixed integer programming
A computational status update for exact rational mixed integer programming Open
The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We descr…
View article: The SCIP Optimization Suite 8.0
The SCIP Optimization Suite 8.0 Open
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8…
View article: A Computational Status Update for Exact Rational Mixed Integer Programming
A Computational Status Update for Exact Rational Mixed Integer Programming Open
The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We descr…
View article: Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes
Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes Open
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations …