Routing multi-class traffic flows in the plane

We study a class of multi-commodity flow problems in geometric domains: For a given planar domain P populated with obstacles (holes) of K ≥ 2 types, compute a set of thick paths from a “source” edge of P to a “sink” edge of P for vehicles of K distinct classes. Each class k of vehicle has a given set, Ok, of obstacles it must avoid and a certain width, wk, of path it requires. The problem is to determine if it is possible to route Nk width-wk paths for class k vehicles from source to sink, with each path avoiding the requisite set Ok of obstacles, and no two paths overlapping. This form of multi-commodity flow in two-dimensional domains arises in computing throughput capacity for multiple classes of aircraft in an airspace impacted by different types of constraints, such as those arising from weather hazards. We give both algorithmic theory results and experimental results. We show hardness of many versions of the problem by proving that two simple variants are NP-hard ev...

• Type: Journal
• Year: 2012
• Where: COMGEO
• Authors: Joondong Kim, Joseph S. B. Mitchell, Valentin Polishchuk, Shang Yang, Jingyu Zou
• Keywords: Applied Computing, Approximation Algorithms, COMGEO 2012, Criteria Optimization, Polynomial Time Algorithm