On Assigning Prefix Free Codes to the Vertices of a Graph

• Authors: N. S. Narayanaswamy;C. E. Veni Madhavan
• Venue: COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
• Year: 2001

For a graph G on n vertices, with positive integer weights w1, . . ., wn assigned to the n vertices such that, for every clique K of G, Σ1/2wt ≤ 1, the problem we are interested in is to assign binary codes C1, . . ., Cn to the vertices such that Ci has wi (or a function of wi) bits in it and, for every edge {i, j}, Ci and Cj are not prefixes of each other.We call this the Graph Prefix Free Code Assignment Problem. We relate this new problem to the problem of designing adversaries for comparison based sorting algorithms. We show that the decision version of this problem is as hard as graph colouring and then present results on the existence of these codes for prefect graphs and its subclasses.