TR02-021 Authors: Andreas Jakoby, Maciej Liskiewicz, RĂ¼diger Reischuk

Publication: 15th April 2002 16:08

Downloads: 2079

Keywords:

The subclass of directed series-parallel graphs plays an important role in

computer science. Whether a given graph is series-parallel is a

well studied problem in algorithmic graph theory, for which fast sequential and

parallel algorithms have been developed in a sequence of papers.

Also methods are known to solve the reachability and the decomposition

problem for series-parallel graphs time efficiently.

However, no dedicated results have been obtained for

the space complexity of these problems when restricted to series-parallel

graphs -- the topic of this paper.

Deterministic algorithms are presented for the recognition, reachability,

decomposition and the path counting problem for series-parallel graphs that use only

logarithmic space. Since for arbitrary directed graphs reachability and path

counting are believed not to be solvable in Logspace the main contribution of

this work are novel deterministic path finding routines that work

correctly in series-parallel graphs, and a characterization of

series-parallel graphs by forbidden subgraphs that can be tested

space-efficiently. The space bounds are best possible,

i.e. the decision problem is shown to be L-complete with respect to

AC^0-reductions. They have also implications for the parallel time complexity

of these problems when restricted to series-parallel graphs.

Finally, we sketch how these results can be generalised to extension of the

series-parallel graph family: to graphs with multiple sources or multiple sinks

and to the class of minimal vertex series-parallel graphs.