We prove lower and upper bounds on bisection widths of the transposition graphs. This class of graphs contains several frequently studied interconnection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order (n:n!) which solves the open problem (R) 3.356 of the Leighton's book 11] and determine nearly exac...

Abstmct-VLSI communication networks are wire-limited. The cost of a network is not a function of the number of switches required, but rather a function of the wiring density required to construct the network. This paper analyzes communication networks of varying dimension under the assumption of constant wire bisection. Expressions for the latency, average case throughput, and hot-spot throughp...

We settle an open problem mentioned in Diaz, Petit, and Serna: A survey of graph layout problems (ACM Computing Surveys 34:313–356, 2002). Of eight objectives considered in that survey, only the complexity status of minimum vertex bisection is listed as unknown. We show that both minimum and maximum vertex bisection are NP-hard, but polynomially solvable on special graph classes such as hypercu...

In this paper we provide an explicit way to compute asymptotically almost sure upper bounds on the bisection width of random d-regular graphs, for any value of d. The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to find bisections of d-regular graphs. We provide bounds for 5 ≤ d ≤ 12. We also give empirical values of the size of the bisection f...

Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a “cardinality constraint”, as in, say, the Min-Bisection problem. Second, while the pseudoexpectation of the objective function was shown to have some value β, it did not necessarily actually “satisfy” the constraint “objective = β”. In this paper we...

Two experiments examined identification and bisection of tones varying in temporal duration (Experiment 1) or frequency (Experiment 2). Absolute identification of both durations and frequencies was influenced by prior stimuli and by stimulus distribution. Stimulus distribution influenced bisection for both stimulus types consistently, with more positively skewed distributions producing lower bi...

Perceptual learning can occur when stimuli are only imagined, i.e., without proper stimulus presentation. For example, perceptual learning improved bisection discrimination when only the two outer lines of the bisection stimulus were presented and the central line had to be imagined. Performance improved also with other static stimuli. In non-learning imagery experiments, imagining static stimu...

In this paper we study the different approaches used so far to apply the bisection method for solving the symmetric tridiagonal eigenproblem. We review the sequential methods used to perform the final extraction of the eigenvalues and compare two new techniques that offer very good results. The sequential version of the bisection method we have implemented even surpasses the results of the QR i...

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class of graphs, we prove that the standard spectral graph bisection can produce bisections that are far from optimal. In particular, we show that the maximum error...