Summary: A Sublinear­Time Randomized Parallel Algorithm for
the Maximum Clique Problem in Perfect Graphs \Lambda
Farid Alizadeh y
Abstract
We will show that Lovasz number of graphs may be com­
puted using interior­point methods. This technique will
require O(
p jV j) iterations, each consisting of matrix
operations which have polylog parallel time complexity.
In case of perfect graphs Lovasz number equals the size
of maximum clique in the graph and thus may be ob­
tained in sublinear parallel time. By using the isolating
lemma, we get a Las Vegas randomized parallel algo­
rithm for constructing the maximum clique in perfect
graphs.
1 Introduction.
In this work, we will be studying algorithms for compu­
tation of maximum cliques and maximum independent
sets in perfect graphs. A graph G = (V; E) is perfect
when, for all of its induced subgraphs G 0 , the size of

Source: Alizadeh, Farid - Rutgers Center for Operations Research, Rutgers University

Collections: Mathematics