Year: 2019
Type: article
Abstract: In this work we study the problem of integer programming in fixed \ndimension, with a particular focus on the problem in dimension 2. Integer \nprogramming in dimension 2 is linked to elementary algorithmic number \ntheory. \nIn particular, the problem of computing the greatest common divisor of 2 \nintegers is a 2-dimensional IP (that clearly can be solved by the Euclidean \nAlgorithm). Many results in IP in dimension 2 have their foundation in the \ntheory of lattices and continued fractions. \nIP in dimension 2 has been extensively studied and today many algorithms \nare known to solve an integer problem in dimension 2 in polynomial \ntime. \nSpecifically, in this work we study the currently fastest algorithm which \nsolves an integer problem in dimension 2, due to Eisenbrand, Rote and Laue. The algorithm takes O(m + k) arithmetic operations, where m is \nthe number of constraints and k is the maximum binary encoding length of \nthe coefficients involved. This algorithm is believed to be optimal.
Author: Martina Gallato
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2956214188