Ten algorithms for Egyptian fractions.
D. Eppstein.
Mathematica in Education and Research 4 (2): 5–15, 1995.
Number theory. I survey and implement in Mathematica several methods for representing rational numbers as sums of distinct unit fractions. One of the methods involves searching for paths in a certain graph using a k shortest paths heuristic.
Also available in HTML and Mathematica notebook formats. See also "Egyptian fractions with denominators from sequences closed under doubling".