Journal of Algorithms
Problems complete for deterministic logarithmic space
Journal of Algorithms
Languages that capture complexity classes
SIAM Journal on Computing
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
NC algorithms for computing the number of perfect matchings in K3,3-free graph and related problems
Information and Computation
An $\cal NC$ Algorithm for Evaluating Monotone Planar Circuits
SIAM Journal on Computing
The Complexity of Planar Counting Problems
SIAM Journal on Computing
The complexity of matrix rank and feasible systems of linear equations
Computational Complexity
Isolation, matching and counting uniform and nonuniform upper bounds
Journal of Computer and System Sciences
Making Nondeterminism Unambiguous
SIAM Journal on Computing
A note on closure properties of logspace MOD classes
Information Processing Letters
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Uniform constant-depth threshold circuits for division and iterated multiplication
Journal of Computer and System Sciences - Complexity 2001
The complexity of planarity testing
Information and Computation
The combinatorial approach yields an NC algorithm for computing Pfaffians
Discrete Applied Mathematics
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Directed Planar Reachability is in Unambiguous Log-Space
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
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 and Grid Graph Reachability Problems
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
Upper Bounds for Monotone Planar Circuit Value and Variants
Computational Complexity
One-input-face MPCVP is hard for l, but in LogDCFL
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
#3-Regular bipartite planar vertex cover is #p-complete
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
The directed planar reachability problem
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
On the bipartite unique perfect matching problem
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Planarity, determinants, permanents, and (unique) matchings
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
On the Power of Isolation in Planar Graphs
ACM Transactions on Computation Theory (TOCT)
Planarizing gadgets for perfect matching do not exist
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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Viewing the computation of the determinant and the permanent of integer matrices as combinatorial problems on associated graphs, we explore the restrictiveness of planarity on their complexities and show that both problems remain as hard as in the general case, that is, GapL- and P- complete. On the other hand, both bipartite planarity and bimodal planarity bring the complexity of permanents down (but no further) to that of determinants. The permanent or the determinant modulo 2 is complete for ⊕L, and we show that parity of paths in a layered grid graph (which is bimodal planar) is also complete for this class. We also relate the complexity of grid graph reachability to that of testing existence/uniqueness of a perfect matching in a planar bipartite graph.