  For a graph G with real weights assigned to the vertices (edges), the MAX
H-SUBGRAPH problem is to find an H-subgraph of G with maximum total weight, if
one exists. The all-pairs MAX H-SUBGRAPH problem is to find for every pair of
vertices u,v, a maximum H-subgraph containing both u and v, if one exists. Our
main results are new strongly polynomial algorithms for the all-pairs MAX
H-SUBGRAPH problem for vertex weighted graphs. We also give improved algorithms
for the MAX-H SUBGRAPH problem for edge weighted graphs, and various related
problems, including computing the first k most significant bits of the distance
product of two matrices. Some of our algorithms are based, in part, on fast
matrix multiplication.
