Related papers: On Integer Programs with Irrational Data
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
We consider the ILP Feasibility problem: given an integer linear program $\{Ax = b, x\geq 0\}$, where $A$ is an integer matrix with $k$ rows and $\ell$ columns and $b$ is a vector of $k$ integers, we ask whether there exists…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming (MIP) relaxations.…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
There has been significant work recently on integer programs (IPs) $\min\{c^\top x \colon Ax\leq b,\,x\in \mathbb{Z}^n\}$ with a constraint marix $A$ with bounded subdeterminants. This is motivated by a well-known conjecture claiming that,…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Let $k$ be an algebraically closed field of characteristic zero and $P(x,y)\in k[x,y]$ be a polynomial which depends on all its variables. $P$ has an algebraic constraint if the set $\{(P(a,b),(P(a',b'),P(a',b),P(a,b')\,|\,a,a',b,b'\in k\}$…
Solving integer programs of the form $\min \{\mathbf{x} \mid A\mathbf{x} = \mathbf{b}, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \mathbf{x} \in \mathbb{Z}^n \}$ is, in general, $\mathsf{NP}$-hard. Hence, great effort has been put into…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
The existing software requirement selection methods have mainly focused on optimizing the economic value of a software product while ignoring its social values and their long-term impacts on the society. Social values however, are also…
In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem $\Pi$, a bound $n$ and a pattern -- defined as an arbitrary sequence of actions -- we encode…
In this work, an integer linear programming (ILP) based model is proposed for the computation of a minimal cost addition sequence for a given set of integers. Since exponents are additive under multiplication, the minimal length addition…
We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this we use the two different mathematical tools of Propositional Logic and…
This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…