Finding the sub-vector with the largest sum in a sequence of n numbers is known as the maximum sum problem. Finding the k sub-vectors with the largest sums is a natural extension of this, and is known as the k maximal sums problem. In this paper we design an optimal O(n+k) time algorithm for the k maximal sums problem. We use this algorithm to obtain algorithms solving the two-dimensional k max...

Computational models, such as simulations, are central to a wide range of fields in science and industry. Those models take input parameters produce some output. To fully exploit their utility, relations between outputs must be understood. These include, for example, which parameter setting produces the best result (optimization) or ranges settings variety results (sensitivity). Such tasks ofte...

The continuous nature of space and time is a fundamental tenet many scientific endeavors. That digital representation imposes granularity well recognized, but whether it possible to address completely remains unanswered. This paper argues Hales’ proof Kepler’s conjecture on the packing hard spheres suggests answer be “no”, providing examples why this matters in GIS generally considering implica...

The well-known distinction between field-based and object-based approaches to spatial information is generalised to arbitrary locational frameworks, including in particular space, time and space-time. We systematically explore the different ways in which these approaches can be combined, and address the relative merits of a fully four-dimensional approach as against a more conventional ‘three-p...