An efficient algorithm for partitioning parameterized polygons into rectangles

In this paper, we propose an algorithm for partitioning parameterized orthogonal polygons into rectangles. The algorithm is based on the plane-sweep technique and can be used for partitioning polygons which contain holes. The input to the algorithm consists of the contour of a parameterized polygon to be partitioned and the constraints for those parameters which reside in the contour. The algorithm uses horizontal cuts only and generates a minimum number of rectangles whose union is the original orthogonal polygon. The proposed algorithm can be used as the basis to build corner stitching data structure for parameterized VLSI layouts and has been implemented in Java programming language. Copyright © 2010 ACM, Inc.

Random graph coloring:Statistical physics approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. ©2002 The American Physical Society.

On the use of likert-type scales in multilevel data:Influence on aggregate variables

In multilevel analyses, problems may arise when using Likert-type scales at the lowest level of analysis. Specifically, increases in variance should lead to greater censoring for the groups whose true scores fall at either end of the distribution. The current study used simulation methods to examine the influence of single-item Likert-type scale usage on ICC(1), ICC(2), and group-level correlations. Results revealed substantial underestimation of ICC(1) when using Likert-type scales with common response formats (e.g., 5 points). ICC(2) and group-level correlations were also underestimated, but to a lesser extent. Finally, the magnitude of underestimation was driven in large part to an interaction between Likert-type scale usage and the amounts of within- and between-group variance. © Sage Publications.