Derandomizing Non-uniform Color-Coding I
Joachim Kneis, Alexander Langer, Peter Rossmanith
Color-coding, as introduced by Alon, Yuster, and Zwick, is a well-known
tool for algorithm design and can often be efficiently derandomized using
universal hash functions. In the special case of only two colors, one
can use (n,k)-universal sets for the derandomization. In this paper,
we introduce (n,k,l)-universal sets that are typically smaller and can
be constructed faster. Nevertheless, for some problems they are still
sufficient for derandomization and faster deterministic algorithms can
be obtained. This particularly works well when the color-coding does
not use a uniform probability distribution. To exemplify the concept,
we present an algorithm for the Unique Coverage problem introduced by
Demaine, Feige, Hajiaghayi, and Salavatipour. The example also shows
how to extend the concept to multiple colors.