Simultaneous edge flips for convex subdivisions

It hasbeenshown that onetriangulation of a setof points canbeconvertedto any othertriangulationof thesamesetof pointsby asequenc eof edgeflip operations.In thispaperwe considera tesselationof a setof pointsconsistingof convex cells,aconvex subdivision, andexplorethenotionof flipping edgesfrom oneconvex subdi vision of thepoints to another, wherebothsubdi visions usethesamenumber of edges.It is easyto construct examplesof aconvex subdi visionwhereno singleedgecanbe flipped so that the convexity of all cells of thesubdi vision is maintained. At theCCCG in 2003 FerranHurtadoaskedwhetherthereexistsaconvex subdivision for which the sizeof the minimal simultaneous edgeflip is linearwith respectto thenumberof edges.In thepaperwe construct sucha subdivision.