We study languages with bounded communication complexity in the multiparty "input on the forehead" model with worst-case partition. In the two party case, it is known that such languages are exactly those that are recognized by programs over commutative monoids. This can be used to show that these languages can ... more >>>

We study the use of spectral techniques for graph partitioning. Let G=(V,E) be a graph whose vertex set has a ``latent'' partition V_1,...,V_k. Moreover, consider a ``density matrix'' E=(E_vw)_{v,w in V} such that for v in V_i and w in V_j the entry E_{vw} is the fraction of all possible ... more >>>

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 ... more >>>