Matching is as easy as matrix inversion
Combinatorica
On threshold circuits and polynomial computation
SIAM Journal on Computing
Boolean complexity classes vs. their arithmetic analogs
Proceedings of the seventh international conference on Random structures and algorithms
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Isolation, matching and counting uniform and nonuniform upper bounds
Journal of Computer and System Sciences
Making Nondeterminism Unambiguous
SIAM Journal on Computing
Uniform constant-depth threshold circuits for division and iterated multiplication
Journal of Computer and System Sciences - Complexity 2001
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)
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
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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We show a simple application of Green@?s theorem from multivariable calculus to the isolation problem in planar graphs. In particular, we give a log-space construction of a skew-symmetric, polynomially-bounded edge weight function for directed planar graphs, such that the weight of any simple cycle in the graph is non-zero with respect to this weight function. As a direct consequence of the above weight function, we are able to isolate a directed path between two fixed vertices, in a directed planar graph. We also show that given a bipartite planar graph, we can obtain an edge weight function (using the above function) in log-space, which isolates a perfect matching in the given graph. Earlier this was known to be true only for grid graphs - which is a proper subclass of planar graphs. We also look at the problem of obtaining a straight line embedding of a planar graph in log-space. Although we do not quite achieve this goal, we give a piecewise straight line embedding of the given planar graph in log-space.