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 comple...

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Bibliographic Details
Published in:2010 IEEE 25th Annual Conference on Computational Complexity pp. 131 - 138
Main Authors: Stolee, Derrick, Bourke, Chris, Vinodchandran, N V
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2010
Subjects:
acyclic digraph
Algorithm design and analysis
Complexity theory
Computational complexity
Computer science
Concurrent computing
Jacobian matrices
logspace algorithm
Mathematics
Parallel processing
Particle separators
planar graph
reachability
USA Councils
ISBN:9781424472147, 1424472148
ISSN:1093-0159
Online Access:Get full text
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Summary: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 NL-complete 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 log-space. Specifically, the class extends from planar DAGs with at most two sources to at most O(log n) sources.
ISBN:9781424472147
1424472148
ISSN:1093-0159
DOI:10.1109/CCC.2010.36