Matching is as easy as matrix inversion
Combinatorica
The graph genus problem is NP-complete
Journal of Algorithms
Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
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
Making Nondeterminism Unambiguous
SIAM Journal on Computing
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Undirected connectivity in log-space
Journal of the ACM (JACM)
Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
Logspace Reduction of Directed Reachability for Bounded Genus Graphs to the Planar Case
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
On the Matching Problem for Special Graph Classes
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
| Hi-index | 0.00 |
We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a perfect matching or not and (2) a unique perfect matching or not, are in the log-space complexity class Stoic Probabilistic Log-space (SPL). Since SPL is contained in the log-space counting classes @?L (in fact in Mod"kL for all k=2), C"=L, and PL, our upper bound places the above-mentioned matching problems in these counting classes as well. We also show that the search version, computing a perfect matching, for this class of graphs can be performed by a log-space transducer with an SPL oracle. Our results extend the same upper bounds for these problems over bipartite planar graphs known earlier. As our main technical result, we design a log-space computable and polynomially bounded weight function which isolates a minimum weight perfect matching in bipartite graphs embedded on surfaces of constant genus. We use results from algebraic topology for proving the correctness of the weight function.