Testing Convexity Properties of Tree Colorings

A coloring of a graph is convex if it induces a partition of the vertices into connected subgraphs. Besides being an interesting property from a theoretical point of view, tests for convexity have applications in various areas involving large graphs. We study the important subcase of testing for convexity in trees. This problem is linked, among other possible applications, with the study of phylogenetic trees, which are central in genetic research, and are used in linguistics and other areas. We give a 1-sided, non-adaptive, distribution-free -test for the convexity of tree colorings. The query complexity of our test is O (k/ ), where k is the number of colors, and the additional computational complexity is O(n). On the other hand, we prove a lower bound of Ω( k/ ) on the query complexity of tests for convexity in the standard model, which applies even for (unweighted) paths. We also consider whether the dependency on k can be reduced in some cases, and provide an alternative testin...

• Type: Conference
• Year: 2007
• Where: STACS
• Authors: Eldar Fischer, Orly Yahalom
• Keywords: Additional Computational Complexity, Connected Subgraphs, Query Complexity, STACS 2007, Theoretical Computer Science