Martin Olsen

Martin Olsen

We consider the stacking problem where items are temporarily stored in stacks in a stacking area. The stacks are working as Last In First Out (LIFO) data structures. The objective is to avoid {\em shifts} or {\em restows} that occur when an item has to leave the stacking area earlier than an item above it. We present a simple online algorithm for the problem where we pick a stack for an incoming item without any information on future items. We present a sufficient condition for the algorithm to avoid shifts expressed as an inequality involving the dimension of the stacking area, the number of load/unload points and the maximum number of items present at the same time. The condition is relatively tight in the sense that we can find instances requiring shifts for {\em any} algorithm (including offline algorithms) with small modifications of the condition. Our results indicate that our algorithm is useful if the number of load/unload points is relatively small compared to the number of items.

André Artelt, Martin Olsen, Kevin Tierney

Providing clear explanations to the choices of machine learning models is essential for these models to be deployed in crucial applications. Counterfactual and semi-factual explanations have emerged as two mechanisms for providing users with insights into the outputs of their models. We provide an overview of the computational complexity results in the literature for generating these explanations, finding that in many cases, generating explanations is computationally hard. We strengthen the argument for this considerably by further contributing our own inapproximability results showing that not only are explanations often hard to generate, but under certain assumptions, they are also hard to approximate. We discuss the implications of these complexity results for the XAI community and for policymakers seeking to regulate explanations in AI.