NP is as easy as detecting unique solutions
Theoretical Computer Science
Matching is as easy as matrix inversion
Combinatorica
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Boolean complexity classes vs. their arithmetic analogs
Proceedings of the seventh international conference on Random structures and algorithms
Isolation, matching and counting uniform and nonuniform upper bounds
Journal of Computer and System Sciences
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Grid Graph Reachability Problems
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Directed Planar Reachability Is in Unambiguous Log-Space
ACM Transactions on Computation Theory (TOCT)
Planarity, Determinants, Permanents, and (Unique) Matchings
ACM Transactions on Computation Theory (TOCT)
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
The directed planar reachability problem
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
| Hi-index | 0.00 |
We study (deterministic) isolation for certain structures in directed and undirected planar graphs. The motivation for undertaking such a study comes from recent positive results on this topic. For example: Bourke et al. [2009] isolate a directed path in planar graphs and subsequently Datta et al. [2010b] isolate a perfect matching in bipartite planar graphs. Our first observation is that sufficiently strong (and plausible) isolations for certain structures in planar graphs would have strong consequences such as: NL ⊆ ⊕L, Bipartite-Matching ∈ NC, and NP ⊆ ⊕P. Our second observation is that although we do not yet have such strong isolations for arbitrary planar graphs, we do have them for bipartite planar graphs, that is, non-bipartiteness is the main bottleneck.