Generating trees on multisets

Abstract

Given a multiset M = V1 ∪ V2 ∪ ⋯ ∪ VC of n elements and a capacity function Δ: [1,C]→[2,n - 1], we consider the problem of enumerating all unrooted trees T on M such that the degree of each vertex υ ∈ Vi is bounded from above by Δ(i). The problem has a direct application of enumerating isomers of tree-like chemical graphs. We give an algorithm that generates all such trees without duplication in O(1)-time delay per output in the worst case using O(n) space, with O(n) initial preprocessing time. © 2010 Springer-Verlag.