The method of forced enumeration for nondeterministic automata
Acta Informatica
Nondeterministic space is closed under complementation
SIAM Journal on Computing
Proceedings of the 30th IEEE symposium on Foundations of computer science
Journal of the ACM (JACM)
Journal of the ACM (JACM)
The Complexity of Planarity Testing
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
The complexity of planarity testing
Information and Computation
Undirected connectivity in log-space
Journal of the ACM (JACM)
Directed Planar Reachability Is in Unambiguous Log-Space
ACM Transactions on Computation Theory (TOCT)
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Planar Graph Isomorphism is in Log-Space
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs
Theory of Computing Systems - Special Title: Symposium on Theoretical Aspects of Computer Science; Guest Editors: Susanne Albers, Pascal Weil
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Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly deterministic logarithmic space by Allender and Mahajan [AM00] with the aid of Reingold's result [Rei08]. Unfortunately, the algorithm is quite daunting and generalizing it to, say the bounded genus case, seems a tall order. We present a simple planar embedding algorithm running in logspace. The algorithm uses the unique embedding of 3-connected planar graphs, a variant of Tutte's criterion on the conflict graphs of cycles and an explicit change of basis for the cycle space. We also present a logspace algorithm to find an obstacle to planarity, viz. a Kuratowski minor, for non-planar graphs. To the best of our knowledge this is the first logspace algorithm for this problem.