Work

Sparse Solutions of Linear Diophantine Equations

Year: 2017

Type: article

Abstract: We present structural results on solutions to the Diophantine system $Ay = b$, $ y \in \mathbb{Z}^t_{\ge 0}$ that have the smallest number of nonzero entries. Our tools are algebraic and number theoretic in nature and include Siegel's lemma, generating functions, and commutative algebra. These results have some interesting consequences in discrete optimization.

Source: SIAM Journal on Applied Algebra and Geometry

DOI: 10.1137/16m1083876

Authors: Iskander Aliev, Jesús A. De Loera, Timm Oertel, Christopher O'Neill

Institutions: Cardiff University, University of California, Davis

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Collaborative Research: Randomized and Structure-Based Algorithms in Commutative Algebra