Using Patterns to Form Homogeneous Teams

Abstract

Homogeneous team formation is the task of grouping individuals into teams, each of which consists of members who fulfill the same set of prespecified properties. In this theoretical work, we propose, motivate, and analyze a combinatorial model where, given a matrix over a finite alphabet whose rows correspond to individuals and columns correspond to attributes of individuals, the user specifies lower and upper bounds on team sizes as well as combinations of attributes that have to be homogeneous (that is, identical) for all members of the corresponding teams. Furthermore, the user can define a cost for assigning any individual to a certain team. We show that some special cases of our new model lead to NP-hard problems while others allow for (fixed-parameter) tractability results. For example, the problem is already That version concentrates on the anonymization aspects of the model. In our new version we slightly extend our model and show how it applies to (homogeneous) clustering of individuals, that is, to homogeneous team formation. Indeed, we now claim that the models and ideas better fit with these applications than with the previous data anonymization motivation. Apart from full proofs omitted in the extended abstract and also adapting our old ideas to the new extended model, the current article also contains a new and easier proof of NP-hardness, a new proof for showing that polynomial-time data reduction in term of so-called polynomial-size problem kernels is unlikely to exist with respect to certain parameterizations, and a new algorithm for the (still NP-hard) special case ignoring costs. Many of the new findings are part of the diploma thesis [18] NP-hard even if (i) there are no lower and upper bounds on the team sizes, (ii) all costs are zero, and (iii) the matrix has only two columns. In contrast, the problem becomes fixed-parameter tractable for the combined parameter "number of possible teams" and "number of different individuals", the latter being upper-bounded by the number of rows.

Separating sets of strings by finding matching patterns is almost always hard

“…They also present an ILP based implementation and computational results. Bredereck et al [3] examine forming teams, i.e., mapping the set of strings to the set of patterns in a consistent manner. They use a similar basis, excepting that the special symbol in a pattern now matches any symbol in a string and that the symbol requires homogeneity of the matched strings (i.e.…”

Decision Making Method to Select Team Members Applying Personnel Behavior Based Lean Model

“…Hayano et al (2014) propose the use of multi-agent systems in task-oriented situations with no prior knowledge of the resources or abilities of other agents. Another quantitative approach is proposed by Bredereck et al (2015) who mention a theoretical and mathematical approach using as constraints an attribute matrix, the cost to design each team, and team sizes.…”

“…Their results indicate that some factors must be taken into account during the team design, and those factors are often not considered because they cannot be controlled. Following this idea, various models to select team members have been proposed, the majority conceptual and some quantitative (Childs and Wolfe, 1972;Hackman, 1987;Bredereck et al, 2015). The Personnel Behavior Based Lean Model (PBBL) proposed by Sawhney and Chason (2005), is one of these models.…”

Pattern-Guided k-Anonymity

“…Notably, the previous model is more suitable for homogeneous team formation instead of data anonymization [14].…”