We study depth lower bounds against non-monotone circuits, parametrized by a new measure of non-monotonicity: the orientation of a function $f$ is the characteristic vector of the minimum sized set of negated variables needed in any DeMorgan circuit computing $f$. We prove trade-off results between the depth and the weight/structure ... more >>>

We show an O(sqrt(n))-space and polynomial-time algorithm for solving the planar directed graph reachability problem. Imai et al. showed in CCC 2013 that the problem is solvable in O(n^{1/2+eps})-space and polynomial-time by using separators for planar graphs, and it has been open whether the space bound can be improved to ... more >>>

We study the complexity of Geometric Graph Isomorphism, in
$l_2$ and other $l_p$ metrics: given two sets of $n$ points $A,
B\subset \mathbb{Q}^k$ in
$k$-dimensional euclidean space the problem is to
decide if there is a bijection $\pi:A \rightarrow B$ such that for
... more >>>