The Generalized Steiner Cable-Trench Problem with Application to Error Correction in Vascular Image Analysis

The Cable-Trench Problem (CTP) is the problem of minimizing the cost to connect buildings on a campus to a central server so that each building is connected directly to the server via a dedicated underground cable. The CTP is odeled by a weighted graph in which the vertices represent buildings and the edges represent the possible routes for digging trenches and laying cables between two buildings. In this paper, we define the Generalized Steiner CTP (GSCTP), which considers the situation in which a subset of the buildings is connected to the server and also the possibility that trench costs vary because of vegetation or physical obstacles, for example. The GSCTP has several natural applications, but we will focus on its nontrivial and novel application to the problem of digitally connecting icroCT scan data of a vascular network with fully automated error correction. The CTP and its variants are NP-hard. However, we show that modifications to Prim's algorithm find nearly optimal solutions to the GSCTP efficiently.