Coordinating Pebble Motion on Graphs, The Diameter of Permutation Groups, and Applications

Abstract

The problem of memory management in totally distributed computing systems leads to the following movers' problem on graphics: Let G be a graph with n vertices with k < n pebbles number 1...,k on distinct vertices. A move consists of transferring a pebble to an adjacent unoccupied vertex. The problem is to decide whether one arrangement of the pebbles is reachable from another, and to find the shortest sequence of moves to find the rearrangement when it is possible.