Graph Inference from a Walk for TRees of Bounded Degree 3 is NP-Complete

The graph inference from a walk for a class C of undirected edge-colored graphs is, given a string x of colors, nding the smallest graph G in C that allows a traverse of all edges in G whose sequence of edge-colors is x, called a walk for x. We prove that the graph inference from a walk for trees of bounded degree k is NP-complete for any k  3, while the problem for trees without any degree bound constraint is known to be solvable in O(n) time, where n is the length of the string. Furthermore, the problem for a special class of trees of bounded degree 3, called (1,1)-caterpillars, is shown NPcomplete. This contrast with the case that the problem for linear chains is known to be solvable in O(nlog n) time since a (1,1)-caterpillar is obtained by attaching at most one edge to each node of a linear chain. We also show the MAXSNP-hardness of these problems.

• Type: Conference
• Year: 1995
• Where: MFCS
• Authors: Osamu Maruyama, Satoru Miyano
• Keywords: Graph Inference, MFCS 1995, Smallest Graph, Theoretical Computer Science, Undirected Edge-colored Graphs