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Computing Shortest Paths in Series-Parallel Graphs in Logarithmic Space

Series-parallel graphs, which are built by repeatedly applying series or parallel composition operations to paths, play an 
 important role in computer science as they model the flow of 
 information in many types of programs. For directed series-parallel 
 graphs, we study the problem of finding a shortest path between two 
 given vertices. Our main result is that we can find such a path in 
 logarithmic space, which shows that the distance problem for 
 series-parallel graphs is L-complete. Previously, it was known 
 that one can compute some path in logarithmic space; but for 
 other graph types, like undirected graphs or tournament graphs, 
 constructing some path between given vertices is possible in 
 logarithmic space while constructing a shortest path is 
 NL-complete.