Related papers: An extension of disjunctive programming and its im…

Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…

A binary code is said to be a disjunctive list-decoding $s_L$-code, $s\ge1$, $L\ge1$, (briefly, LD $s_L$-code) if the code is identified by the incidence matrix of a family of finite sets in which the union of any $s$ sets can cover not…

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…

We describe constructions of extended formulations that establish a certain relaxed version of the Hirsch conjecture and prove that if there is a pivot rule for the simplex algorithm for which one can bound the number of steps by a…

A recurring theme in the least squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least squares estimates of edge lengths. These formulas have proved useful for the development of efficient…

We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…

Generalized Disjunctive Programming (GDP) provides a powerful framework for combining algebraic constraints with logical disjunctions. To solve these problems, mixed-integer reformulations are required, but traditional reformulation…

The minimum graph cut and minimum $s$-$t$-cut problems are important primitives in the modeling of combinatorial problems in computer science, including in computer vision and machine learning. Some of the most efficient algorithms for…

This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length $L$ of the…

We prove complex contraction for zero-free regions of counting weighted set cover problem in which an element can appear in an unbounded number of sets, thus obtaining fully polynomial-time approximation schemes(FPTAS) via Barvinok's…

In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motzkin (1936) made a transition from the polyhedron to a polyhedral cone. Based on his excellent idea, we represent a set by a characteristic…

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…

A celebrated theorem of Balas gives a linear mixed-integer formulation for the union of two nonempty polytopes whose relaxation gives the convex hull of this union. The number of inequalities in Balas formulation is linear in the number of…

When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…

Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…

Dissections of polytopes are a well-studied subject by geometers as well as recreational mathematicians. A recent application in coding theory arises from the problem of parameterizing binary vectors of constant Hamming weight which has…

Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…

Branch and cut is the dominant paradigm for solving a wide range of mathematical programming problems -- linear or nonlinear -- combining efficient search (via branch and bound) and relaxation-tightening procedures (via cutting planes, or…

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…