Related papers: Extended formulations from communication protocols…
Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended…
An extended formulation of a polyhedron $P$ is a linear description of a polyhedron $Q$ together with a linear map $\pi$ such that $\pi(Q)=P$. These objects are of fundamental importance in polyhedral combinatorics and optimization theory,…
An extended formulation of a polytope P is a polytope Q which can be projected onto P. Extended formulations of small size (i.e., number of facets) are of interest, as they allow to model corresponding optimization problems as linear…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
We describe a technique to obtain linear descriptions for polytopes from extended formulations. The simple idea is to first define a suitable lifting function and then to find linear constraints that are valid for the polytope and guarantee…
Extended regular expressions with counting and interleaving are widely used in practice. However the related theoretical studies for this kind of expressions currently cannot meet the need of practical work. This paper develops syntax…
This paper investigates the extension complexity of polytopes by exploiting the correspondence between non-negative factorizations of slack matrices and randomized communication protocols. We introduce a geometric characterization of…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
Synthesizing specifications for real time applications that involve distributed communication protocol entities from a service specification, which is modeled in the UML state machine with composite states, is a time-consuming and…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
In distributed learning, the goal is to perform a learning task over data distributed across multiple nodes with minimal (expensive) communication. Prior work (Daume III et al., 2012) proposes a general model that bounds the communication…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
Synthesis of distributed protocols is a hard, often undecidable, problem. Completion techniques provide partial remedy by turning the problem into a search problem. However, the space of candidate completions is still massive. In this…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} for the cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in [n]. First, we find an extended formulation of size log(n) for d= 2. Then, we use…
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy.…