Method and apparatus for propagating cost functions

A computer readable medium that stores a computer program having executable code, the computer program for expanding a path in a space, said space having a plurality of states, the computer program comprising sets of instructions for:

• a) identifying a first expansion for the path from a start state to a first destination state, said first destination state having at least one dimension;
• b) specifying a first cost function that specifies the cost of the first expansion, wherein the first cost function is defined over the first destination state;
• c) identifying a second expansion for the path from a first portion of the first destination state to a second destination state, wherein said first portion is less than the entirely of said first destination state;
• and
• d) from a particular portion of the first cost function that is defined over the first portion of the first destination state, computing a second cost function that specifies the cost of the second expansion, wherein said particular portion of the first cost function does not represent the entirety of said first cost function.