Geodesic
Carrying Umbrellas: an Online Relocation Game on a Graph
Journal of Graph Algorithms and Applications, Selected Papers from the 1998 Dagstuhl Seminar on Graph Algorithms and Applications , Tome 5 (2001) no. 5, pp. 3-16.

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We introduce an online relocation problem on a graph, in which a player that walks around the vertices makes decisions on whether to relocate mobile resources, while not knowing the future requests. We call it Carrying Umbrellas. This paper gives a necessary and sufficient condition under which a competitive algorithm exists. We also describe an online algorithm and analyze its competitive ratio. 
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Jae-Ha Lee; Chong-Dae Park; Kyung-Yong Chwa. Carrying Umbrellas: an Online Relocation Game on a Graph. Journal of Graph Algorithms and Applications, 
							Selected Papers from the 1998 Dagstuhl Seminar on Graph Algorithms and Applications
					, Tome 5 (2001) no. 5, pp. 3-16. doi : 10.7155/jgaa.00037. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00037/

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