We introduce tool auctions, a novel market mechanism for constructing a cost-efficient assembly line for producing a desired set of products from a given set of goods and tools. Such tools can be used to transform one type of good into a different one. We then study the computational complexity of tool auctions in detail, using methods from both classical and parameterized complexity theory. While solving such auctions is intractable in general, just as for the related frameworks of combinatorial and mixed auctions, we are able to identify several special cases of practical interest where designing efficient algorithms is possible.

Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is a heuristic approach where one tries to reuse previous experience when solving similar problems in order to avoid some of the planning effort. Plan reuse may offer an interesting alternative to plan generation in some settings. We provide theoretical results that identify situations in which plan reuse is provably tractable. We perform our analysis in the framework of parameterized complexity, which supports a rigorous worst-case complexity analysis that takes structural properties of the input into account in terms of parameters. A central notion of parameterized complexity is fixed-parameter tractability which extends the classical notion of polynomial-time tractability by utilizing the effect of parameters. We draw a detailed map of the parameterized complexity landscape of several variants of problems that arise in the context of case-based planning. In particular, we consider the problem of reusing an existing plan, imposing various restrictions in terms of parameters, such as the number of steps that can be added to the existing plan to turn it into a solution of the planning instance at hand.