with the recent advancements in multi-core era, workstation clusters have emerged as a cost-effective approach to build a network of workstations (NOWs). NOWs connect the small groups of processors to a network of switching elements that form irregular topologies. Designing an efficient routing and a deadlock avoidance algorithm for irregular networks is quite complicated in terms of latency and area of the routing tables, thus impractical for scalability of On Chip Networks. Many deadlock free routing mechanisms have been proposed for regular networks, but they cannot be employed in irregular networks. In this paper a new methodology has been proposed for efficient routing scheme, called LBDR-UD, which save the average 64.59% routing tables in the switch for irregular networks as compare to up*/down* routing. The Basic concept of routing scheme is combination of up*/down* and Logic Based Distributed Routing. By simulation, it has been shown that the LBDR-UD is deadlock free and adaptive to all dynamic network traffic conditions.