Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional Euclidean space, describes restricted-orientation analogs of lines, hyperplanes, flats, and halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. We then introduce the notion of strong restricted-orientation convexity, which is an...
Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion ge...
The purpose of our research is to enhance the efficiency of AI problem solvers by automating representation changes. We have developed a system that improves the description of input problems and selects an appropriate search algorithm for each given problem. Motivation. Researchers have accumulated much evidence on the impor- tance of appropriate representations for the efficiency of AI systems. The same problem may be easy or difficult, depending on the way we describe it and on the search algorithm we use. Previous work on the automatic im- provement of problem descriptions has mostly been...
The purpose of our research is to enhance the efficiency of AI problem solvers by automating representation changes. We have developed a system that i...
Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional Euclidean space, describes restricted-orientation analogs of lines, hyperplanes, flats, and halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. We then introduce the notion of strong restricted-orientation convexity, which is an...
Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion ge...
