Interleaved Caching with Access Graphs

We consider a semi-online model for caching in which request sequences are generated by walks on a directed graph, called the access graph. The caching algorithm knows the access graph but not the actual request sequences. We then extend this model to multiple access graphs, where request sequences from the access graphs are interleaved arbitrarily and presented to the caching algorithm. For both these problems, we obtain tight upper and lower bounds on the competitive ratio; our bounds depend on a structural property of the access graph. Our work is motivated by multitasking systems with shared cache, where each task can be abstracted as a directed graph with nodes corresponding to data access and directed edges corresponding to the control flow of the task.