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We propose a framework of individual problem-solving and communicative demands (IproCo) that bridges the gap between models from cognitive psychology and communication pragmatics. Furthermore, we present two experiments conducted to identify factors influencing the demands and to test possibilities for support. The experiments employed a remote collaborative picture-sorting task with concrete and abstract pictures and applied non-interactive conditions compared to interactive conditions. In a first experiment, the influence of the postulated demands on collaboration process and outcome was analysed, and the impact of shared applications was tested. In a second experiment, we evaluated instructional support measures consisting of model collaboration and a collaboration script. The collaboration process showed benefits of the support but the outcome did not. However, the support measures fostered the collaboration process even in the particularly difficult conditions with non-interactive communication. We discuss the impact of the IproCo framework and apply it to other tasks.
Integer point sets minimizing average pairwise L1 distance: What is the optimal shape of a town?
(2010)
An n-town, n[is an element of]N , is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form solution is known. We show that optimal n-towns can be computed in O(n[superscript 7.5]) time. This is also practically useful, as it allows us to compute optimal solutions up to n=80.