Online Strategies for Evacuating from a Convex Region in the Plane
This paper studies an evacuation problem that evacuees inside an affected convex region in the plane try to escape to a boundary of the region as quickly as possible. The boundary information of the region is usually unknown to the evacuees at the beginning during an emergency. But with the help of helicopters or even satellite remote sensing technology, outside rescuers can easily get complete boundary information, and rescuers can share the information with evacuees once getting in touch with the evacuee who firstly reaches a boundary. For the scenario that people evacuate from several different positions, we first show that 3 is a lower bound on the competitive ratio, and present an online strategy with its competitive ratio proved to be no more than \( 2 + \sqrt 5 \). For the scenario that people evacuate from a single initial position, we present a strategy with its competitive ratio very close to the lower bound.
KeywordsEvacuation strategy Competitive analysis Convex region
This research is partially supported by the NSFC (Grant No. 71601152), and by the China Postdoctoral Science Foundation (Grant No. 2016M592811).
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