In this Master Thesis the possibility to efficiently divide a graph into spanner islands is examined. Spanner islands are islands of the graph that fulfill the spanner condition, that the distance between two nodes via the edges in the graph cannot be too far, regulated by the stretch constant, compared to the Euclidian distance between them. In the resulting division the least number of nodes connecting to other islands is sought-after. Different heuristics are evaluated with the conclusion that for dense graphs a heuristic using MAX-FLOW to divide problematic nodes gives the best result whereas for sparse graphs a heuristic using the single-link clustering method performs best. The problem of finding a spanner path, a path fulfilling the spanner condition, between two nodes is also investigated. The problem is proven to be NP-complete for a graph of size n if the spanner constant is greater than n^(1+1/k)*k^0.5 for some integer k. An algorithm with complexity O(2^(0.822n)) is given. A special type of graph where all the nodes are located on integer locations along the real line is investigated. An algorithm to solve this problem is presented with a complexity of O(2^((c*log n)^2))), where c is a constant depending only on the spanner constant. For instance, the complexity O(2^((5.32*log n)^2))) can be reached for stretch 1.5.