A Global Method for Reducing Multidimensional Size Graphs

This paper introduces the concept of discrete multidimensionalsize function, a mathematical tool studying the so-called sizegraphs. These graphs constitutes an ingredient of Size Theory, a geometrical/topological approach to shape analysis and comparison. A globalmethod for reducing size graphs is presented, together with a theoremstating that size graphs reduced in such a way preserve all the informationin terms of multidimensional size functions. This approach can leadto simplify the effective computation of discrete multidimensional sizefunctions, as shown by examples.