In the problem (Unweighted) Max-Cut we are given a graph $$G = (V,E)$$ and asked for set $$S \subseteq V$$ such that number of edges from S to $$V \setminus S$$ is maximal. this paper consider an even harder problem: (Weighted) Max-Bisection. Here undirected weight function $$w :E \rightarrow \mathbb {Q}_{>0}$$ task find (i) sum weights maximal; (ii) contains $$\lceil * \rceil {\frac{n}{2}}$$ v...

We discuss algorithms for graph bisection which are relevant to the distribution of tasks, such as the elements and nodes of an unstructured mesh to the processors of a parallel computer. Starting with a cost function consisting of a part to ensure equal numbers of tasks for each processor, and a part to minimize communication time between processors, we derive the spectral bisection method, wh...

Crossover refers to a pattern of performance on the line bisection test in which short lines are bisected on the side opposite the true center of long lines. Although most patients with spatial neglect demonstrate crossover, contemporary theories of neglect cannot explain it. In contrast, we show that blending the psychophysical construct of magnitude estimation with neglect theory not only exp...

We investigate an algorithm derived based on the belief propagation method of Pearl [11] applied to the (Min-)Bisection problem under the standard planted solution model (or more precisely the Most Likely Partition problem under the same planted solution model). We first point out that the algorithm (without thresholding) is nothing but the standard power method for computing an eigenvector wit...

The Satisfactory Bisection problem means to decide whether a given graph has a partition of its vertex set into two parts of the same cardinality such that each vertex has at least as many neighbors in its part as in the other part. A related variant of this problem, called Co-Satisfactory Bisection, requires that each vertex has at most as many neighbors in its part as in the other part. A ver...

K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms...

Continuous subjective bisection of a right angle rotating through 360° in a frontal plane was performed by 10 Ss using the Be'ke'sy technique. The largest and most consistent constant errors in bisection, ranging up to 10°, occurred in upper-right and upper-left quadrants. Interindividual and interquadrant differences indicate that the constant errors cannot be attributed solely to the effect o...

We investigate a new method for partitioning a graph into two equal-sized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applies to graphs that are meshes in Euclidean space). The new method does not require geometric coordi...

Given a random graph G = G n;1=2 , we give almost sure bounds for the value of the minimum bisection of G. The lower bound is obtained by applying the rst moment method, while the upper bound is given by the analysis of a simple algorithm. Moreover, these results enable us to derive upper bounds for the maximum bisection and the maxcut of G.

The effect of the presentation of two different auditory pitches (high and low) on manual line-bisection performance was studied to investigate the relationship between space and magnitude representations underlying motor acts. Participants were asked to mark the midpoint of a given line with a pen while they were listening a pitch via headphones. In healthy participants, the effect of the pres...