VLSI (Very Large Scale Integration) physical design automation has been an area ofrngreat interest for the researchers in integrated circuit design. In earlier times physicalrndesign was done manually. The manual generation of layout designs has proved to bernbackbreaking, time consuming and error prone. In this thesis a rigorous study of VLSIrnswitchbox routing algorithms and their implementation is done to evaluate thernperformance of these algorithms and to propose an algorithm which provides a betterrnsolution for some of the benchmark problems. A java implementation provides arngraphical display of the result of execution of an algorithm under investigation and it alsornprovides the number of tracks and vias a given problem requires to complete the routing.