On the Competitive Complexity of Navigation Tasks

A strategy S solving a navigation task T is called competitive with ratio r if the cost of solving any instance t of T does not exceed r times the cost of solving t optimally. The competitive complexity of task T is the smallest possible value r any strategy S can achieve. We discuss this notion, and survey some tasks whose competitive complexities are known. Then we report on new results and ongoing work on the competitive complexity of exploring an unknown cellular environment.

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