Method and apparatus for identifying a path between source and target states in a space with more than two dimensions

A method of identifying a path between a set of source states and a set of target states in a space with more than two dimensions, the method comprising:

• specifying at least one path that starts from one state;
• after specifying the at least one path, iteratively specifying new paths by expanding previously specified paths to other states in the space until a path is identified that connects a source and target state, wherein expanding previously specified paths includes expanding paths in more than two dimensions of the space, wherein at least some of the states are non-zero dimensional states;
• and
• for at least one specified path that includes an expansion to a particular non-zero dimensional state, computing a particular cost function that is defined over the particular non-zero dimensional state, wherein the particular cost function is a piecewise linear function.

A computer readable medium storing a computer program for identifying a path between a set of source states and a set of target states in a space with more than two dimensions, the computer program comprising instructions for:

• specifying at least one path that starts from one state;
• after specifying the at least one path, iteratively specifying new paths by expanding previously specified paths to other states in the space until a path is identified that connects a source and target state, wherein the instructions for expanding previously specified paths includes instructions for expanding paths in more than two dimensions of the space, wherein at least some of the states are non-zero dimensional states;
• and
• for at least one specified path that includes an expansion to a particular non-zero dimensional state, computing a particular cost function that is defined over the particular non-zero dimensional state, wherein the particular cost function comprises at least two different values associated with at least two different locations on the particular non-zero dimensional state.

A computer readable medium storing a computer program for identifying a path between a set of source states and a set of target states in a space with more than two dimensions, the computer program comprising instructions for:

• specifying at least one path that starts from one state;
• after specifying the at least one path, iteratively specifying new paths by expanding previously specified paths to other states in the space until a path is identified that connects a source and target state, wherein the instructions for expanding previously specified paths includes instructions for expanding paths in more than two dimensions of the space, wherein at least some of the states are non-zero dimensional states;
• and
• for at least one specified path that includes an expansion to a particular non-zero dimensional state, computing a particular cost function that is defined over the particular non-zero dimensional state, wherein the particular cost function is a piecewise linear function.