In this thesis, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixed d > 3, all sufficiently large n and all b = o(ni-1/d2lJ), the algorithm finds...

In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixed d 2 3, all suffciently large n and all b = o(nl l / lT j ) , the algorithm find...

The bisection method is the consecutive bisection of a triangle by the median of the longest side. This paper introduces a taxonomy of triangles that precisely captures the behavior of the bisection method. Our main result is an asymptotic upper bound for the number of similarity classes of triangles generated on a mesh obtained by iterative bisection, which previously was known only to be fini...

A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection cost is the number of edges connecting the two sets. Finding the bisection of minimum cost is NP-hard. We present an algorithm that finds a bisection whose cost is within ratio of O(log2 n) from the optimal. For graphs excluding any fixed graph as a minor (e.g. planar graphs) we ...

It is still unclear whether the contralateral line bisection error in unilateral homonymous hemianopia is caused by the visual field defect, strategic oculomotor adaptation or by additional extrastriate brain injury. We therefore simulated hemianopia in healthy participants using a gaze-contingent display paradigm and investigated its effects on manual and ocular line bisection performance and ...

OBJECTIVES To clarify the mechanisms of left unilateral spatial neglect found in the bisection of lines after cueing to the left end point and to determine whether neglect occurs for the mental representation of a line. METHODS A new representational bisection task was developed to eliminate the influence of the right segment of the physical line that would attract attention. Eight patients w...

The communication overhead is a major bottleneck for the execution of a process graph on a parallel computer system. In the case of two processors, the minimization of the communication can be modeled by the graph bisection problem. The spectral lower bound of 2jV j 4 for the bisection width of a graph is well-known. The bisection width is equal to 2jV j 4 iff all vertices are incident to 2 2 c...

An exhaustive qualitative (vote-counting) review is conducted of the literature concerning visual and non-visual line bisection in neurologically normal subject populations. Although most of these studies report a leftward bisection error (i.e., pseudoneglect), considerable between-study variability and inconsistency characterize this literature. A meta-analysis of this same literature is perfo...

We present an n-dimensional marked bisection method for unstructured conformal meshes. devise the local refinement in adaptive applications. To this end, we propose a mesh marking pre-process and three stages. The marks initial conformingly. Then, first n−1 bisections, accumulates reverse order list of new vertices. In second stage, n-th bisection, uses reversed to cast bisected simplices as re...