Search · four archives
Search · four archives
11 papers · ranked by Valyu relevance
Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
Approximate integer programming is the following: For a given convex body $K \subseteq{\mathbb{R}}^n$, either determine whether $K \cap{\mathbb{Z}}^n$ is empty, or find an integer point in the convex body $2\cdot K - c +c$ which is K, scaled by 2 from its center of gravity c. Approximate integer programming can be…
Nikhil Bansal, Tim Oosterwijk, Tjark Vredeveld, Ruben van der Zwaan
We consider the Vector Scheduling problem, a natural generalization of the classical makespan minimization problem to multiple resources. Here, we are given n jobs, represented as d-dimensional vectors in $[0,1]^d$, and m identical machines, and the goal is to assign the jobs to machines such that the maximum load of…
Hendrik Schawe, Roman Bleim, Alexander K. Hartmann, Andrea Gambassi
Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or…
Ritchie Lee, Susmit Jha, Anastasia Mavridou, Dimitra Giannakopoulou + 4 more
'Ralph Bottesch' 'Max W. Haslbeck' 'Alban Reynaud' 'René Thiemann'] We implement a decision procedure for linear mixed integer arithmetic and formally verify its soundness in Isabelle/HOL. We further integrate this procedure into one application, namely into CeTA, a formally verified certifier to check untrusted…
Markus Leitner
In this article, we introduce the Generalized ${0,1,2}$-Survivable Network Design Problem ( ${0,1,2}$-GSNDP) which has applications in the design of backbone networks. Different mixed integer linear programming formulations are derived by combining previous results obtained for the related ${0,1,2}$-GSNDP and…
Ahmad Abdi, Gérard Cornuéjols, Bertrand Guenin, Levent Tunçel
A rational number is dyadic if it has a finite binary representation $p/2^k$, where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in floating-point arithmetic on a computer. A vector is dyadic if all its entries are…
Gennadiy Averkov, Matthias Schymura
For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity ${{\,\mathrm{rc}\,}}X$. This parameter, introduced by Kaibel & Weltge (2015), captures the complexity of linear descriptions of X without using…
Ahmed Ibrahim, Attahiru Alfa
This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool…
Kim-Manuel Klein
We consider so called 2-stage stochastic integer programs (IPs) and their generalized form, so called multi-stage stochastic IPs. A 2-stage stochastic IP is an integer program of the form $\max{c^T x \mid{\mathcal{A}}x = b, \,l \le x \le u,\, x \in{\mathbb{Z}}^{s + nt}}$ where the constraint matrix…
Peiping Shen, Tongli Zhang, Chunfeng Wang
This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an…
Syed Inayatullah, Nasir Touheed, Muhammad Imtiaz, Cheng-Yi Xia
This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method. For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP. This method follows the same pivoting…