Related papers: Binary Extended Formulations
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Much work on argument systems has focussed on preferred extensions which define the maximal collectively defensible subsets. Identification and enumeration of these subsets is (under the usual assumptions) computationally demanding. We…
We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…
Lookup tables (finite maps) are a ubiquitous data structure. In pure functional languages they are best represented using trees instead of hash tables. In pure functional languages within constructive logic, without a primitive integer…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Extended resolution shows that auxiliary variables are very powerful in theory. However, attempts to exploit this potential in practice have had limited success. One reasonably effective method in this regard is bounded variable addition…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
We study the reformulation of integer linear programs by means of a mixed integer linear program with fewer integer variables. Such reformulations can be solved efficiently with mixed integer linear programming techniques. We exhibit…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
The secure domination problem, a variation of the domination problem with some important real-world applications, is considered. Very few algorithmic attempts to solve this problem have been presented in literature, and the most successful…
The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…