Recently an approach to the problem of robot navigation in an unexplored terrain was develped by Iyengar, et al, which involves concepts of learning. The method proposed involves representing the terrain as a spatial graph which is updated as the robot undertakes a number of goal-directed traversals. The current paper focuses on the implementation of the spatial graph data structure and Parallel Algorithms needed to maintain the data structure. A modified adjacency list data structure is proposed for representing the spatial graph of the terrain. The model of computation being used is the multiple instruction stream multiple data stream shared memory model MIMD-SMM. The parallel algorithms required to implement the navigation technique (described in the previously mentioned paper) using the modified adjacency list data structure are presented and the time and space complexities of the various algorithms are discussed. The algorithms presented provide the basis for an efficient navigation sytem for an autonomous robot working in an unexplored terrain.