Abstract—Coverage problem is a fundamental issue in wireless ad hoc and sensor networks. Previous techniques for coverage scheduling often require accurate location information or range measurements, which cannot be easily obtained in resource-limited ad hoc and sensor networks. Recently, a method based on algebraic topology has been proposed to achieve coverage verification using only connectivity information. The topological method sheds some light on the issue of location-free coverage. Unfortunately, the needs of centralized computation and rigorous restriction on sensing and communication ranges greatly limit the applicability in practical large-scale distributed sensor networks. In this work, we make the first attempt towards establishing a graph theoretical framework for connectivity-based coverage with configurable coverage granularity. We propose a novel coverage criterion and scheduling method based on cycle partition. Our method is able to construct a sparse coverage se...