For Erdős-Rényi random graphs with average degree γ, and uniformly random γ-regular graph on n vertices, we prove that with high probability the size of both the Max-Cut and maximum bisection are n( γ 4 + P∗ √ γ 4 + o( √ γ)) + o(n) while the size of the minimum bisection is n( γ 4 − P∗ √ γ 4 + o( √ γ)) + o(n). Our derivation relates the free energy of the anti-ferromagnetic Ising model on such ...

A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NP-hard. We present an algorithm that nds a bisection that is within O(p n log n) of optimal. No sublinear approximation ratio for bisection was previously known.

In recent decades, various graph partitioning heuristic algorithms have been developed by researchers, which are widely used in “realworld” applications. As a starting point of graph partition problem, graph bisection algorithms provide basic approaches and solutions for other graph partition instances. This work implemented part of contemporary graph bisection algorithms which produce high-qua...

The token distribution problem is an important data distribution problem akin to the problems of sorting and routing, in which data elements, or tokens-must be evenly distributed amongst the processors of a parallel network. To date, all algorithms to solve this problem on the mesh and reconngurable mesh architectures have lagged (in terms of the time required to obtain a solution) the state-of...

BACKGROUND AND OBJECTIVES The line bisection error to the left of the true center has been interpreted as a relative right hemisphere activation, which might relate to the subject's emotional state. Considering that patients with generalized anxiety disorder (GAD) or treatment-resistant depression (TRD) often have negative emotions, we hypothesized that these patients would bisect lines signifi...

In this paper, we present a new hypergraph partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hyper...

In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hyperg...