Let $\tau(n)$ denote the minimum number of arithmetic operations sufficient to build the integer $n$ from the constant~$1$. We prove that if there are arithmetic circuits for computing the permanent of $n$ by $n$ matrices having size polynomial in $n$, then $\tau(n!)$ is polynomially bounded in $\log n$. Under the ... more >>>

In this paper
we establish a general algorithmic framework between bin packing
and strip packing, with which we achieve the same asymptotic
bounds by applying bin packing algorithms to strip packing. More
precisely we obtain the following results: (1) Any offline bin
packing algorithm can be applied to strip packing ... more >>>

We present two new methods for finding a lowest common ancestor (LCA)
for each pair of vertices of a directed acyclic graph (dag) on
n vertices and m edges.

The first method is a natural approach that solves the all-pairs LCA
problem for the input dag in time O(nm).

The ... more >>>