A parallel algorithm for computing the critical independence number and related sets

Ermelinda DeLaViña, Craig Eric Larson
2012 Ars Mathematica Contemporanea  
An independent set I c is a critical independent set if |I c | − |N (I c )| ≥ |J| − |N (J)|, for any independent set J. The critical independence number of a graph is the cardinality of a maximum critical independent set. This number is a lower bound for the independence number and can be computed in polynomial-time. The existing algorithm runs in O(n 2.5 m/ log n) time for a graph G with n = |V (G)| vertices and m edges. It is demonstrated here that there is a parallel algorithm using n
more » ... ors that runs in O(n 1.5 m/ log n) time. The new algorithm returns the union of all maximum critical independent sets. The graph induced on this set is a König-Egerváry graph whose components are either isolated vertices or which have perfect matchings.
doi:10.26493/1855-3974.165.b8b fatcat:tzvoqqkbcnckzlaogb2wwqwhfu