Fast travel-distance estimation using overhead graph

Abstract

Shortest path can be computed in real-time for single navigational instructions. However, in complex optimisation tasks, lots of travel-distances (lengths of shortest paths) are needed and the total workload becomes a burden. We present a fast method for estimating the travel-distance from one location to another by using an overhead graph that stores the ratio between the bird-distance and the travel-distance for few representative locations. The travel-distance is then estimated for any two locations using the corresponding value between their nearest nodes in the graph. We test the method within an optimization setting where the goal is to relocate health services so that the travel-distance of patients is minimised. We build the overhead graph using road network information from Open Street Map and experiment with real-world data in the region of North Karelia, Finland as a part of the ongoing IMPRO project. The results show that the average estimation error is 0.5 km with a graph of 512 nodes, and the total processing time reduces from 1.2 hours to 2.9 seconds per iteration in the optimisation process. The error in the estimated travel-distances is 2%, on average, which is significantly smaller than 8% of the second best estimation method.

Can we optimize locations of hospitals by minimizing the number of patients at risk?

“…However, we use travel distance calculated using road network because simple Euclidean (Bird’s) distance can cause major inaccuracies. It may work well in flat areas with extensive road network [ 14 ] but large errors were reported in [ 15 ] of about 30% with SiunSote data in North Karelia, Finland, in the region of many lakes and rivers. Travel time is then estimated from the travel distance.…”

“…To keep the optimization efficient, we therefore use the overhead graph method in [ 15 ] to provide rapid estimation for both travel-distance and travel-time. This method has two stages.…”

“…The effect of the graph is that the processing time of the optimization is reduced from 1.2 h to only 2.9 s per iteration (up to 10,000) in case of SiunSote data in North Karelia using a graph with 512 nodes. The huge speed-up is achieved at the cost of 2% inaccuracy in the distance estimation using memory for 512 × 512 = 0.25 MB look-up for the graph [ 15 ]. The process and two sample graphs are shown in Fig.…”

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Fig. 6 Fast travel time estimation using overhead graph [ 15 ]. The two-stage process is shown (left), and two example graphs (right) optimized for Finland (1024 nodes) and for North Karelia region (256 nodes)

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