  A framework with two scalar parameters is introduced for various problems of
finding a prefix code minimizing a coding penalty function. The framework
encompasses problems previously proposed by Huffman, Campbell, Nath, and Drmota
and Szpankowski, shedding light on the relationships among these problems. In
particular, Nath's range of problems can be seen as bridging the minimum
average redundancy problem of Huffman with the minimum maximum pointwise
redundancy problem of Drmota and Szpankowski. Using this framework, two
linear-time Huffman-like algorithms are devised for the minimum maximum
pointwise redundancy problem, the only one in the framework not previously
solved with a Huffman-like algorithm. Both algorithms provide solutions common
to this problem and a subrange of Nath's problems, the second algorithm being
distinguished by its ability to find the minimum variance solution among all
solutions common to the minimum maximum pointwise redundancy and Nath problems.
Simple redundancy bounds are also presented.
