Linear-time certifying algorithms for the path cover and Hamiltonian cycle problems on interval graphs

✍ Scribed by Ruo-Wei Hung; Maw-Shang Chang

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 252 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.11.030

✦ Synopsis

A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is an evidence that can be used to authenticate the correctness of the answer. A Hamiltonian cycle in a graph is a simple cycle in which each vertex of the graph appears exactly once. The Hamiltonian cycle problem is to test whether a graph has a Hamiltonian cycle. A path cover of a graph is a family of vertex-disjoint paths that covers all vertices of the graph. The path cover problem is to find a path cover of a graph with minimum cardinality. This paper presents O(n)-time certifying algorithms for the above two problems on interval graphs given a set of n intervals with endpoints sorted. The certificates provided by our algorithms can be authenticated in O(n) time.