Two Block Partitioned Dijkstra Algorithms

The Dijkstra algorithm (DA) is a kind of tree search algorithm. The biggest advantage is that it has the smallest number of visited nodes among all optimal tree search algorithms. But stack sizes required by the DA are always too large to achieve. By partitioning the searching tree into blocks, two modified algorithms are proposed in this article to shrink stack sizes. One, serial block partitioned DA, searches blocks one by one. Another, parallel block partitioned DA, searches blocks at the same time. Radii, which are updated when one block search is finished, are set to cut nodes with metrics larger than them in both algorithms. Simulation results show that the visited nodes number of serial block partitioned DA increase is very limited while the stack size is reduced exponentially. It also shows that stack sizes of the parallel block partitioned DA are reduced exponentially and the processing time is reduced efficiently. The performance of proposed algorithms is kept optimal in both proposed algorithms.