Hard Problems on Layered Graphs: Parallel Algorithms and Improvements

Abstract

Layered graph G = (V, E) is defined as a graph containing several subgraphs also called as layers: G1 = (V1, E1), G2 = (V2, E2), …Gq = (Vq, Eq) where the edges incident on the Vi are restricted to the vertices from Vi−1∪ Vi ∪ Vi+1. Layered graphs have applications in computational molecular biology and social networks. Several hard graph theoretic problems such as Maximum Independent Set (MIS), Minimum Vertex Cover (MVC) and Minimum Dominating Set (MDS) are shown to be computationally tractable on layered graphs when the corresponding upper bound is imposed on the number of vertices that a layer can have. We present algorithmic improvements and design parallel algorithms for the computing these measures.