Balanced Queries: Divide and Conquer

Abstract

We define a new hypergraph decomposition method called Balanced Decomposition and associate Balanced Width to hypergraphs and queries. We compare this new method to other well known decomposition methods, and analyze the complexity of finding balanced decompositions of bounded width and the complexity of answering queries of bounded width. To this purpose we define a new complexity class, allowing recursive divide and conquer type algorithms, as a resource-bounded class in the nondeterministic auxiliary stack automaton computation model, and show that finding decompositions of bounded balanced width is feasible in this new class, whereas answering queries of bounded balanced width is complete for it.