Year: 2015
Type: preprint
Abstract: In the Integer Quadratic Programming problem input is an n*n integer matrix Q, an m*n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x in Z^n, minimizing x^TQx, subject to Ax <= b. We give a fixed parameter tractable algorithm for Integer Quadratic Programming parameterized by n+a. Here a is the largest absolute value of an entry of Q and A. As an application of our main result we show that Optimal Linear Arrangement is fixed parameter tractable parameterized by the size of the smallest vertex cover of the input graph. This resolves an open problem from the recent monograph by Downey and Fellows.
Source: arXiv (Cornell University)
Author: Lokshtanov, Daniel
Institution: University of Bergen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2239770983