  We report on a detailed analysis of generalization of the local adiabatic
search algorithm. Instead of evolving directly from an initial ground state
Hamiltonian to a solution Hamiltonian a different evolution path is introduced
and is shown that the time required to find an item in a database of size $N$
can be made to be independent of the size of the database by modifying the
Hamiltonian used to evolve the system.
