Homotopy and alternative routes in indoor navigation scenarios

There are lots of innovative use cases possible that build on a shortest route between two locations together with a set of alternatives that are highly different yet short. Imagine, for example, a complicated building like an airport, where passengers can consult a computer terminal to get navigation advices to a desired goal. By scanning the boarding card the calculation of alternatives can be made context-sensitive. Based on gender, amount of time, or shopping preferences, for example, the terminal can display different routes regarding floors traversed, or shops and restaurants passed. Furthermore, the building operator can control the presentation of alternatives in order to influence visitor flows in real time. Therefore, we propose to use the topological concept of homotopy in order to decide if two routes should be considered equivalent or alternative. Basically, the homotopy relation identifies equivalence classes. We propose that a representative of an equivalence class is an alternative regarding another equivalence class. We concatenate the two routes in question and thus, create a polygon. If there is an obstacle inside, the routes are non-homotopic and we consider them as proper alternatives. For this situation, we propose two fundamentally different approaches that are able to find alternative routes with respect to homotopy. The input is a building plan in form of an occupancy grid. Bitmaps allow for fast calculation of the homotopy relation and can be generated from almost any type of environmental model. The first approach aims for enumerating routes that have to visit a special supporting point. This concatenation of two shortest paths leads to alternatives very fast. The second approach is orthogonal to that in the sense that it generates alternatives roughly ordered by their length. Finally, we evaluate and discuss the approaches' feasibility based on different metrics in several scenarios.