Problems complete for deterministic logarithmic space
Journal of Algorithms
Parallel recognition and decomposition of two terminal series parallel graphs
Information and Computation
Parallel transitive closure and point location in planar structures
SIAM Journal on Computing
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Computing algebraic formulas using a constant number of registers
SIAM Journal on Computing
An optimal parallel algorithm for formula evaluation
SIAM Journal on Computing
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
Parallel recognition of series-parallel graphs
Information and Computation
Graph classes: a survey
Paths Problems in Symmetric Logarithmic Space
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Parallel Algorithms for Series Parallel Graphs
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Logspace Reduction of Directed Reachability for Bounded Genus Graphs to the Planar Case
ACM Transactions on Computation Theory (TOCT)
Logspace algorithms for computing shortest and longest paths in series-parallel graphs
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Algorithms for core stability, core largeness, exactness, and extendability of flow games
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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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 AC0-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 generalized to extension of the series-parallel graph family: to graph with multiple sources or multiple sinks and to the minimal vertex series-parallel graphs.