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COCO
2010
Springer

A Log-Space Algorithm for Reachability in Planar Acyclic Digraphs with Few Sources

14 years 3 months ago
A Log-Space Algorithm for Reachability in Planar Acyclic Digraphs with Few Sources
Designing algorithms that use logarithmic space for graph reachability problems is fundamental to complexity theory. It is well known that for general directed graphs this problem is equivalent to the NL vs L problem. This paper focuses on the reachability problem over planar graphs where the complexity is unknown. Showing that the planar reachability problem is NLcomplete would show that nondeterministic log-space computations can be made unambiguous. On the other hand, very little is known about classes of planar graphs that admit log-space algorithms. We present a new ‘source-based’ structural decomposition method for planar DAGs. Based on this decomposition, we show that reachability for planar DAGs with m sources can be decided deterministically in O(m + log n) space. This leads to a log-space algorithm for reachability in planar DAGs with O(log n) sources. Our result drastically improves the class of planar graphs for which we know how to decide reachability in deterministic...
Derrick Stolee, Chris Bourke, N. V. Vinodchandran
Added 15 Aug 2010
Updated 15 Aug 2010
Type Conference
Year 2010
Where COCO
Authors Derrick Stolee, Chris Bourke, N. V. Vinodchandran
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