Abstract. We consider the problem of drawing Venn diagrams for which each region's area is proportional to some weight (e.g., population or percentage) assigned to that region. These area-proportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing area-proportional Venn diagrams for any population distribution over two characteristics using circles and over three characteristics using rectangles and near-rectangular polygons; modifications of these algorithms are then presented for drawing the more general Euler diagrams. We present results concerning which population distributions can be drawn using specific shapes. A program to aid further investigation of area-proportional Venn diagrams is also described.

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We describe novel methods for embedding 2-dimensional grid graphs into cylinders (one way wrap-around grids), toruses and hypercubes where the guest grid G is larger than the host graph H, implying a many to one embedding. We call dj G j = j H je the optimal load, denoted l. We consider only optimal This work has been submitted to Academic Press for possible publication. Copyright may be transferred without notice, after which this version may no longer be available y This work was supported by the Natural Sciences and Engineering Research Council of Canada 1 any load, and is applicable to the simpler classes of host. The simplicity of the method suggests it may be of practical value. The many re nements that we exhibit yielding embiddings for critical instances cause us to conjecture that optimal embeddings exist for all critical instances, at least for a hypercube hosts.

We introduce the problem of polyomino Gray codes, which is the listing of all members of certain classes of polyominoes such 4 that successive polyominoes differ by some well-defined closeness condition (e.g., the movement of one cell). We discuss various 5 closeness conditions and provide several Gray codes for the class of column-convex polyominoes with a fixed number of cells 6 in each column. For one of our closeness conditions, a natural new class of distributive lattice arises: the partial order is defined 7 on the set of m-tuples [S 1 ] × [S 2 ] × • • • × [S m ], where each S i > 1 and [S i ] = {0, 1,. .. , S i − 1}, and the cover relations are 8