 
Summary: A Parallel Maximal Independent Set Algorithm \Lambda
Mark Adams y
Abstract
The parallel construction of maximal independent sets is a useful building block for many algorithms in
the computational sciences, including graph coloring and multigrid coarse grid creation on unstructured
meshes. We present an efficient asynchronous maximal independent set algorithm for use on parallel
computers, for ``well partitioned'' graphs, that arise from finite element models. For appropriately par
titioned bounded degree graphs, it is shown that the running time of our algorithm under the PRAM
computational model is O(1), which is an improvement over the previous best PRAM complexity for this
class of graphs. We present numerical experiments on an IBM SP, that confirm our PRAM complexity
model is indicative of the performance one can expect with practical partitions on graphs from finite
element problems.
Key words: maximal independent sets, multigrid, parallel algorithms, graph coloring
AMS(MOS) subject classification: 65F10, 65F50, 65Y05, 68Q22, 68R10, 05C85
1 Introduction
An independent set is a set of vertices I ` V in a graph G = (V; E), in which no two members of I are
adjacent (i.e. 8v; w 2 I; (v; w) =
2 E); a maximal independent set (MIS) is an independent set for which no
proper superset is also an independent set. The parallel construction of an MIS is useful in many computing
applications, such as graph coloring and coarse grid creation for multigrid algorithms on unstructured finite
