Reachability in Restricted Walk on Integers

: We prove that two conditions are sufficient, and with three exceptions also necessary, for reachability of any position in restricted walk on integers in which the sizes of the moves to the left and to the right are constant but need not be equal. A method to compute the length of the shortest path between any two positions, as well as a shortest path algorithm when the reachability conditions are true are given. Also the necessary and sufficient conditions for Hamiltonian restricted walk between absorbing boundaries, and the method to construct such walks are given. ACM Categories: G.2.2, C.3.

• Type: Journal
• Year: 2010
• Where: JUCS
• Authors: Philip Ginzboorg, Valtteri Niemi
• Keywords: Conditions, JUCS 2010, Reachability, Shortest Path