 
Summary: ELSEVIER Theoretical Computer Science 178 (1997) 103l 18
Theoretical
Computer Science
Permutations generated by token passing in graphs
M.D. Atkinson*, M.J. Livesey, D. Tulley
School of Mathematical and Computational Sciences, North Haugh, St. Andrews KY16 9SS, UK
Received May 1995; revised February 1996
Communicated by MS. Paterson
Abstract
A transportation graph is a directed graph with a designated input node and a designated
output node. Initially, the input node contains an ordered set of tokens 1,2,3, .. The tokens
are removed from the input node in this order and transferred through the graph to the output
node in a series of moves; each move transfers a token from a node to an adjacent node. Two or
more tokens cannot reside on an internal node simultaneously. When the tokens arrive at the
output node they will appear in a permutation of their original order. The main result is
a description of the possible arrival permutations in terms of regular sets. This description
allows the number of arrival permutations of each length to be computed. The theory is then
applied to packetswitching networks and has implications for the resequencing problem. It is
also applied to some complex data structures and extends previously known results to the case
that the data structures are of bounded capacity. A byproduct of this investigation is a new
