@InProceedings{CLR82,
  replaced-by =  { CLRS86 },                  
  author = 	 { Benny Chor and Charles E. Leiserson and Ronald L. Rivest },
  title = 	 { An Application of Number Theory to the Organization of Raster-Graphics Memory },
  pages = 	 { 92--99 },
  doi =          { 10.1109/SFCS.1982.10 },                  
  booktitle =    { Proceedings 23rd Annual Symposium on Foundations of Computer Science },
  publisher =    { IEEE },
  editor = 	 { Nicholas Pippenger },
  issn =         { 0272-5428 },                  
  date =         { 1982 },                  
  OPTyear = 	 { 1982 },
  OPTmonth =     { November 3--5 },                  
  eventdate =    { 1982-11-03/1982-11-05 },                  
  eventtitle = 	 { FOCS '82 },
  venue =        { Chicago, Illinois },                  
  OPTorganization = { IEEE },
  abstract =     {
         A high-resolution raster-graphics display is usually combined with processing power
         and a memory organization that facilitates basic graphics operations.  For many
         applications, including interactive text processing, the ability to quickly move or
         copy small rectangles of pixels is essential.  This paper proposes a novel
         organization of raster-graphics memory that permits all small rectangles to be 
         moved efficiently.  The memory organization is based on a doubly periodic
         assignment of pixels to $M$ memory chips according to a ``Fibonacci'' lattice.
         The memory organization guarantees that if a rectilinearly oriented rectangle 
         contains fewer than $M/\sqrt{5}$ pixels, then all pixels will reside in different
         memory chips, and thus can be accessed simultaneously.
         \par
         We also define a continuous analogue of the problem which can be posed as,
         ``What is the maximum density of a set of points in the plane such that
         no two points are contained in the interior of a rectilinearly oriented 
         rectangle of area $N$.''  We give a lower bound of $1/2N$ on the density of
         such a set, and show that $1/\sqrt{5}N$ can be achieved.
                 },
}