An approximation algorithm for a generalized assignment problem with small resource requirements.

We investigate a generalized assignment problem where the resource requirements are either 1 or 2. This problem is motivated by a question that arises when data blocks are to be retrieved from parallel disks as efficiently as possible. The resulting problem is to assign jobs to machines with a given capacity, where each job takes either one or two units of machine capacity, and must satisfy certain assignment restrictions, such that total weight of the assigned jobs is maximized. We derive a 2/3-approximation result for this problem based on relaxing a formulation of the problem so that the resulting constraint matrix is totally unimodular. Further, we prove that the LP-relaxation of a special case of the problem is half-integral, and we derive a weak persistency property.Assignment; Constraint; Data; Matrix; Requirements;

PRINCIPALS’ PERCEPTION OF TEACHER PERFORMANCE GIVEN SELECTED BARRIERS TO ACCURATE EVALUATIONS

This quantitative, non-experimental study explored the differences between principals’ perceived level of influence evaluation barriers have on the accuracy of teacher evaluations. A self-administered questionnaire was used to collect data from Montana principals regarding their perceptions of: (a) teacher performance combinations (b) the strength of influence selected barriers have on the accuracy of teacher evaluations principals provide teachers, and (c) demographic information. Participating Montana principals were asked to categorize the teachers they supervise into four performance combinations: (1) Good Teacher/Good Employee or (GT/GE), (2) Good Teacher/Marginal Employee or (GT/ME), (3) Marginal Teacher/Good Employee or (MT/GE), and (4) Marginal Teacher/Marginal Employee or (MT/ME). Principals then used an 11-point Thurstone scale to estimate the influence eleven evaluation barriers (Board, Community, Conflict, Expectations, Process, Staff, Standards, Superiors, Time, and Training, Union) had on the accuracy of teacher evaluations. A 4 X 11 factorial design was used to explore differences between principals’ perceived influence of selected evaluation barriers for different teacher performance categories, and a 10 X 11 factorial design to explore the differences between barriers. A one-way between groups ANOVA was used to identify any statistically significant mean differences and a post-hoc Tukey HSD test was used to determine the magnitude of the mean differences. The results this study identified the percentages of performance combination distribution as: 6% MT/ME, 11% MT/GE, 11% GT/ME, and 72% GT/GE. The evaluation barriers were found to have hierarchical levels of influence on the accuracy of teacher evaluations principals provide teachers: (1) Dominant Barriers (Expectations, Time, Process, Union) have higher levels of influence, (2) Mixed Moderate Barriers (Standards, Staff, Training) have indeterminate levels of influence, and (3) Subordinate Barriers (Conflict, Community, Superiors, Board) have lower levels of influence. Three performance combinations were identified as challenging when differentiating performance: (1) (GT/GE & MT/GE) influenced by the evaluation barrier Conflict, (2) (GT/GE & GT/ME) influenced by the evaluation barrier Conflict, and (3) (GT/GE & MT/ME) influenced by the evaluation barriers Conflict, Union, Time, and Staff

Metaheuristic approaches for the quartet method of hierarchical clustering

Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several metaheuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times

Random redundant storage in disk arrays: Complexity of retrieval problems

Random redundant data storage strategies have proven to be a good choice for efficient data storage in multimedia servers. These strategies lead to a retrieval problem in which it is decided for each requested data block which disk to use for its retrieval. In this paper, we give a complexity classification of retrieval problems for random redundant storage