The graph partition problem (GPP) aims at clustering the vertex set of a graph into a fixed
number of disjoint subsets of given sizes such that the sum of weights of edges joining …

Computing the edge expansion of a graph is a famously hard combinatorial problem for
which there have been many approximation studies. We present two versions of an exact …

Recently, numerous graph partitioning approaches have been proposed to distribute a big
graph to machines in a cluster for distributed computing. Due to heavy communication …

提出一种递归的二分算法, 用于求解带顶点权重约束的图划分问题. 首先利用内点法求解不加
顶点权重约束的半定规划松弛模型, 然后利用超平面舍入算法得到满足顶点权重约束的初始可行 …

The Lov\'asz theta function $\theta (G) $ provides a very good upper bound on the stability
number of a graph $ G $. It can be computed in polynomial time by solving a semidefinite …

The singularity degree plays a crucial role in understanding linear and semidefinite
programming, providing a theoretical framework for analyzing these problems. It is defined …

提出一种改进的近似最优梯度法, 求解图划分问题中的无约束目标函数. 先用修正的BFGS
更新公式及选取BB 类步长的线性组合作为标量矩阵得到近似最优步长, 再引入参数对经典的 …

Computing the edge expansion of a graph is a famously hard combinatorial problem for
which there have been many approximation studies. We present two versions of an exact …

The Lovász theta function θ (G) provides a very good upper bound on the stability number of
a graph G. It can be computed in polynomial time by solving a semidefinite program (SDP) …

1 results demonstrate that with our algorithms one can compute the edge expansion on
graphs up to 400 vertices in a routine way, including instances where standard branch-and …