On the Theoretical Link between Optimized Geospatial Conflation Models for Linear Features

Geospatial data conflation involves matching and combining two maps to create a new map. It has received increased research attention in recent years due to its wide range of applications in GIS (Geographic Information System) data production and analysis. The map assignment problem (conceptualized in the 1980s) is one of the earliest conflation methods, in which GIS features from two maps are matched by minimizing their total discrepancy or distance. Recently, more flexible optimization models have been proposed. This includes conflation models based on the network flow problem and new models based on Mixed Integer Linear Programming (MILP). A natural question is: how are these models related or different, and how do they compare? In this study, an analytic review of major optimized conflation models in the literature is conducted and the structural linkages between them are identified. Moreover, a MILP model (the base-matching problem) and its bi-matching version are presented as a common basis. Our analysis shows that the assignment problem and all other optimized conflation models in the literature can be viewed or reformulated as variants of the base models. For network-flow based models, proof is presented that the base-matching problem is equivalent to the network-flow based fixed-charge-matching model. The equivalence of the MILP reformulation is also verified experimentally. For the existing MILP-based models, common notation is established and used to demonstrate that they are extensions of the base models in straight-forward ways. The contributions of this study are threefold. Firstly, it helps the analyst to understand the structural commonalities and differences of current conflation models and to choose different models. Secondly, by reformulating the network-flow models (and therefore, all current models) using MILP, the presented work eases the practical application of conflation by leveraging the many off-the-shelf MILP solvers. Thirdly, the base models can serve as a common ground for studying and writing new conflation models by allowing a modular and incremental way of model development.