The Internet is growing at an astonishing rate, nearly doubling its enormous size every year. There is an increasing demand for using real time multimedia applications over the Internet. One of the challenging issues in exchanging multimedia information over a network is how to determine a feasible path that satisfies all the requirements of multimedia applications. Thus there is a need for routing mechanism which are able to satisfy requirement of both real time traffic and efficient management of network resources. Quality of service routing is one of these components. QoS (Quality of service) routing provides guarantee of service to the receiver. The main problem to be solved by QoS routing algorithm is multi constrained path problem. In general, The multi constrained path problem is NP-complete that cannot be exactly solved in polynomial time. So various types of heuristic and approximate algorithms have been presented in literature to solve this problem. This paper discusses main approaches used to reduce QoS routing algorithms complexity and to improve overall network performance.