Deterministic fully dynamic graph algorithms are presented for connectivity, minimum
spanning tree, 2-edge connectivity, and biconnectivity. Assuming that we start with no edges …

Sparse matrixlization, an innovative programming style for MATLAB, is introduced and used
to develop an efficient software package, iFEM, on adaptive finite element methods. In this …

In the most general sense, a factor of a graph G is just a spanning subgraph of G and a
graph factorization of G is a partition of the edges of G into factors. However, as we shall see …

We introduce a simple initialization of the Maubach bisection routine for adaptive mesh
refinement which applies to any conforming initial triangulation. Using Maubach's routine …

In this paper, we study lower bounds on the size of maximal and maximum matchings in 3-
connected planar graphs and graphs with bounded maximum degree. For each class, we …

We show that we can maintain up to polylogarithmic edge connectivity for a fully-dynamic
graph in\ifmmode\expandafter ̃\else\expandafter\~ O\left (\sqrt n\right) worst-case time per …

We give an overview of multilevel methods, such as V-cycle multigrid and BPX
preconditioner, for solving various partial differential equations (including H (grad), H (curl) …

We design and analyze optimal additive and multiplicative multilevel methods for solving H
1 problems on graded grids obtained by bisection. We deal with economical local …

The SQuad data structure represents the connectivity of a triangle mesh by its “S table” of
about 2 rpt (integer references per triangle). Yet it allows for a simple implementation of …

We consider the problem of testing the uniqueness of maximum matchings, both in the
unweighted and in the weighted case. For the unweighted case, we have two results. Given …