Optimizing IPOG's Vertical Growth with Constraints Based on Hypergraph Coloring

Abstract

In this paper, we present an optimization of IPOG's vertical growth phase in the presence of constraints. The vertical growth problem is modeled as a classical NP-hard graph problem called "Minimum Vertex Coloring". In the graph model, vertices are either missing tuples that are waiting to be colored or existing tests that are already colored in different colors at the initial state, edges/hyperedges are conflicts among vertices that cannot be put in a same test. After coloring, a group of vertices in same color can be transformed to exactly a valid test. Since the original IPOG algorithm uses an arbitrary order to cover missing tuples during vertical growth, in order to reduce the number of tests, we compute the Degree of Conflicts (DOC) for each tuple, and cover the tuples in the non-increasing order of DOC. We implement a new IPOG algorithm incorporating this optimization. The experimental results show that the new IPOG algorithm reduces the number of tests for many real-life systems with constraints.