Abstract:
Graph coloring is a well known problem with wide-ranging applications. The vertex
and edge coloring problems have been studied in various models of computation.
Rainbow coloring is a type of edge coloring that also acts as a connectivity measure
for graphs. A graph is said to be rainbow colored or rainbow connected if there exists
an edge coloring such that every pair of vertices, if connected, is connected by a
path having distinct colors for all edges contained in it. The veri cation of rainbow
coloring is an NP-Complete problem whereas the problems of verifying vertex and
edge coloring admit easy solutions in the RAM model. Veri cation of graph coloring
in the streaming model of computation is a problem that has not been studied before.
We focus on the vertex coloring problem in the streaming model and give algorithms
that verify if a given vertex coloring is valid with a high probability. We also give
lower bounds for verifying vertex coloring in a few streaming models.
