An Improved Approximation Algorithm for the s-t Path Movement Problem

Abstract

This paper considers a movement problem that minimizes the maximum movement of pebbles on a graph to form a path from source vertex to destination vertex . The best known algorithm for this problem is a 7-approximation algorithm developed by Berman, Demaine, and Zadimoghaddam in 2011. We refine the analysis of Berman et al. to obtain an -approximation algorithm for any constant . This problem is a subroutine used by Berman et al. for finding a solution to the connectivity movement problem. Using our improved algorithm as a subroutine, the approximation ratio for the connectivity movement problem improves from 136 to .