Artur Czumaj, Miroslaw Kowaluk, Andrzej Lingas

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 >>>

Artur Czumaj, Andrzej Lingas

We show that for any $\epsilon > 0$, a maximum-weight triangle in an

undirected graph with $n$ vertices and real weights assigned to

vertices can be found in time $\O(n^{\omega} + n^{2 + \epsilon})$,

where $\omega $ is the exponent of fastest matrix multiplication

algorithm. By the currently best bound ...
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Ryan Williams

We prove a model-independent non-linear time lower bound for a slight generalization of the quantified Boolean formula problem (QBF). In particular, we give a reduction from arbitrary languages in alternating time t(n) to QBFs describable in O(t(n)) bits by a reasonable (polynomially) succinct encoding. The reduction works for many reasonable ... more >>>