相关论文: Representative Families: A Unified Tradeoff-Based …
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
In this paper we study the relation of two fundamental problems in scheduling and fair allocation: makespan minimization on unrelated parallel machines and max-min fair allocation, also known as the Santa Claus problem. For both of these…
Let K be a field and G a split connected reductive affine algebraic K-group. Let T be a split maximal torus of G, W its finite Weyl group, and R its root system. After fixing a realization of R in G and choosing a simple system for R, one…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
In this paper we propose a new methodology to represent the results of the robust ordinal regression approach by means of a family of representative value functions for which, taken two alternatives $a$ and $b$, the following two conditions…
In this paper, we study several generalizations of multiway cut where the terminals can be chosen as \emph{representatives} from sets of \emph{candidates} $T_1,\ldots,T_q$. In this setting, one is allowed to choose these representatives so…
Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
Graphs are widely used for representing pairwise interactions in complex systems. Since such real-world graphs are large and often evergrowing, sampling a small representative subgraph is indispensable for various purposes: simulation,…
In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the…
The connection between the commutativity of a family of $n\times n$ matrices and the generalized joint numerical ranges is studied. For instance, it is shown that ${\cal F}$ is a family of mutually commuting normal matrices if and only if…
This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…
We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…
This paper considers the problem of solving a symmetric positive definite system of linear equations over a network of agents with arbitrary asynchronous interactions and membership dynamics. The latter implies that each agent is allowed to…
A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix…
A set family ${\cal F}$ is $uncrossable$ if $A \cap B,A \cup B \in {\cal F}$ or $A \setminus B,B \setminus A \in {\cal F}$ for any $A,B \in {\cal F}$. A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993:708-717] states…
Given two matroids $\mathcal{M}_{1} = (E, \mathcal{B}_{1})$ and $\mathcal{M}_{2} = (E, \mathcal{B}_{2})$ on a common ground set $E$ with base sets $\mathcal{B}_{1}$ and $\mathcal{B}_{2}$, some integer $k \in \mathbb{N}$, and two cost…
The problem of scheduling conflicting jobs on parallel machines consists in assigning a set of jobs to a set of machines so that no two conflicting jobs are allocated to the same machine, and the maximum processing time among all machines…
Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…