Related papers: On Integer Programs with Irrational Data
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…
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…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…
We give two elementary proofs, at a level understandable by students with only pre-calculus knowledge of Algebra, of the well known fact that an irreducible irrational n-th root of a positive rational number cannot be solution of a…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control…
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
Let X be the set of integer points in some polyhedron. We investigate the smallest number of facets of any polyhedron whose set of integer points is X. This quantity, which we call the relaxation complexity of X, corresponds to the smallest…
The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and…