International Journal of Innovative Computing, Information ... · cohesive subgroups can be found...

International Journal of InnovativeComputing, Information and Control ICIC International c°2006 ISSN 1349-4198Volume 2, Number 4, August 2006 pp. 885—896

REDESIGNING SUBGROUPS IN A PERSONNEL NETWORK BASEDON DNA COMPUTING

Ikno Kim, Don Jyh-Fu Jeng and Junzo Watada

Graduate School of Information, Production and SystemsWaseda University

2-7 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka 808-0135, [email protected]; [email protected]; [email protected]

Received July 2005; revised November 2005

Abstract. Employees’ tasks have been changing according to the current times by tech-nical development and reform in complicated human relationships, and their capabilitiesand abilities are also continuing to improve. Therefore, the necessity for a competentrating to qualitatively understand relations between employees arises. In this paper, weselect a model of a workplace where employees are sharing information from a variety ofworkplaces, and we suppose a personnel network which contains their relations in termsof mutual understanding. Some subgroups are sure to exist in this employee personnelnetwork, and the personnel network can be improved by redesigning all the cliques of sub-group networks. However, with a huge number of employees it becomes extremely hard tofind the maximum clique in the personnel network, meaning this problem is NP-hard. Allcohesive subgroups can be found by making the best use of DNA-based computing, alsoknown as molecular computation, which is a new approach to massively parallel compu-tation. DNA computing is drawing attention from many researchers around the world.The goal of this paper is to propose a way to apply DNA computing, one of the newbiotechnologies, to human resource management that is a part of the management engi-neering field, and to measure the efficiency of DNA computing in redesigning subgroupsto support work rotation.Keywords: Subgroup, Personnel network, Work rotation, Clique, DNA computing

1. Introduction. Routine tasks that are very specialized, such as assembly-line posi-tions, hold limited appeal in advanced industrial societies. Rarely do these routine tasksoffer opportunities for achievement, recognition, psychological growth, or other sourcesof satisfaction. To enhance the quality of work life for those who hold such responsibili-ties, human resource managers can use a variety of methods to improve tasks. The mostwidely practiced technique includes work rotation [1,2]. Work rotation moves employeesfrom task to task. Tasks themselves are not actually changed a lot, only the employ-ees are rotated. Rotation breaks the monotony of highly specialized work by calling ondifferent skills and abilities. The organization benefits because employees become com-petent in several tasks rather than only one. Knowing a variety of tasks improves theemployee’s self-image, provides personal growth, and makes the employee more valuableto the organization.The most important point is to note all the subgroups [3] in the personnel network to

execute work rotation. The most important reason is that the personnel network might

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886 I. KIM, D. J. JENG AND J. WATADA

become a huge number of employees composed of all the connected subgroups, and thosesubgroups are also composed of subgroups, both small and large. Another importantreason is that human resource managers hope to find the maximal number of employeeswho mutually exchange and share their information by close interpersonal relationships atwork. However, even if employees’ close interpersonal relationships in the huge personnelnetwork are known, it would be quite difficult to redesign all the subgroups efficiently,because the maximum cliques [4] from all the subgroups in the huge personnel networkmust be extremely hard to discern exactly. Furthermore, finding the maximum cliqueof employees becomes NP-hard, and cannot be solved using present electronic computersin polynomial time unless P=NP, which is widely believed to be false. Ordinarily, themajority of human resource managers redesign subgroups statistically based on eitherthe frequency of employees’ relationships or managers’ experiences. To address this, weuse DNA computing to solve these redesign problems of the subgroups in the personnelnetwork.DNA computing has drawn attention in various fields [5,6] since it was proposed to be

able to solve a Hamiltonian path with molecular computation by L. Adleman in 1994 [7].Until now, there are no cases that apply to management problems. The attention is almostentirely from either the computer science fields or the biotechnology fields. However, weargue that DNA computing should be a very useful tool for a variety of managementproblems. Thus, we have shown that efficient solutions are obtained by DNA computing,and the efficiency of DNA computing is examined by redesigning subgroups in a personnelnetwork to solve one of the management problems.

2. Analysis of Subgroups. A personnel network is composed of various types of sub-groups. It is necessary to analyze all the subgroups to accurately understand the personnelnetwork. Therefore, in this section, we describe and analyze subgroups in more detail toprovide a better understanding of this personnel network problem.

2.1. Cohesive subgroups. Cohesion is closely related to concepts of strong ties amongmembers of embedded social groups or closed social circles. Cohesive subgroups [3] aresubsets of actors among whom there are relatively strong, dense, direct, frequent, intense,or positive ties. These are relations that enable employees to share or exchange theirinformation, create solidarity, or act collectively. Numerous direct contacts among allcohesive subgroup employees, combined with few or null ties to outsiders, dispose a grouptoward a close interpersonal relationship in business, homogeneity of thought, behavior,and identity. Examples of formal cohesive groups include the personnel department,production department, quality control department, and finance department, whereasinformal cohesive groups include religious cults and hobby clubs.Structural variables are measured on a single set of actors, such as relationships among

employees give rise to one-mode networks, whereas there are types of structural variablesthat are measured on two sets of entities, such as actors of employees from different sets,one set consisting of corporations and a second set consisting of non-profit organizations.It could be measured the flows of financial support flows from corporations to non-profitemployees. These two sets of employees are referred to as a two-mode network. A one-mode network is the most common type of personnel network since all actors of employeescome from only one set. Cohesive subgroups in one-mode networks focus on properties of

REDESIGNING SUBGROUPS IN A PERSONNEL NETWORK 887

pair-wise ties, whereas cohesive subgroups in two-mode affiliation networks focus on tiesexisting among employees through their joint relationships in organizations.

Figure 1. Presonnel network and nodal degrees for employees’ relations

2.2. Cliques. A cohesive subgroup should have a clique that is a useful starting pointfor specifying the formal properties. The clique also has well-specified mathematicalproperties, and captures much of the intuitive notion of cohesive subgroups. In a graph,the clique is a maximal complete subgraph of three or more nodes, and it consists of asubset of nodes, all of which are adjacent to each other, and there are no other nodes thatare also adjacent to the employees of the clique.The most common concept for real personnel networks is the n-clique, which is much

closer to people’ everyday understanding of the word ‘clique’. In this concept, n is themaximum path length at which employees of the clique will be regarded as connected.Thus, a 1-clique should be the maximal complete subgraph itself, and the subset in whichall pairs of points are directly connected at distance only 1. On the other hand, a 2-clique should be one in which the employees are either directly connected at distance 1or indirectly connected at distance 2 through a common neighbor.

2.3. Maximum clique. A complete graph is a simple graph where an edge connectsevery pair of nodes in graph theories. A graph G = (N , E) is complete if all its nodes arepair-wise adjacent. A clique C in a graph G is a subset of nodes N such that the inducedgraph G(C) is complete. That is, there is an edge between every pair of distinct nodesin N . Clique problem takes a graph G and an integer k as input and asks whether there


is a clique in G of size at least k. The cardinality of C is the number of nodes containedin C, denoted by |C|. Thus, the objective of the maximum clique is to find a cliqueof maximum cardinality in G. Furthermore, the maximum clique can be represented inthe maximum number of employees who mutually exchange and share their informationby close interpersonal business relationships, also the inclusiveness and the density of acomplete relational graph should be 1 in the maximum clique.

2.4. Model graph of personnel networks. We select actors of employees in the samefirm to create their own personnel network based on employees’ records and descriptions.This personnel network is a highly skilled group in a consulting firm that was first orga-nized by the human resource manager, and was made for providing thoughtful leadershipand specialized support to the firm’s knowledge management consultants; the group wascomposed of employees who had advanced degrees or extensive industry experience intechnical fields.The network for this model is given in Figure 1. In the graph, there are N = 20

nodes, and E = 32 edges between the pairs of nodes. Even with as few as twenty ac-tors of employees and thirty-two ties, the graph looks very complicated. There are alsothe four circles that represent present subgroups which do not really look like cohesivesubgroups, and the connected lines that represent the relationships among the employeeswho mutually exchange and share their business information through a close interpersonalrelationship in business. Although this personnel network is very intricately connectedwith four subgroups, it is important for the human resource manager to redesign bettersubgroups by finding a subgroup of all the cliques including the maximum clique, in orderto satisfy work rotation requirements with a new personnel network.

3. DNA Computing Approach. DNA computing is recently drawing attention froma number of scientists, engineers and other researchers [8-10]. The attention is almostalways focused on solving NP-completeness problems, combinational problems and diffi-cult mathematical problems. However, we propose a way to solve one of the managementproblems using DNA computing. Therefore, in this section, we describe how to relateemployees to DNA sequences, and how to approach redesigning subgroups based on aDNA experiment.

Figure 2. Watson-crick complementarity


3.1. DNA computing. DNA computing is that using bio-molecules as a support fordevising computers and computations, a new approach to massively parallel computation.In 1994, L. Adleman discovered a way to solve the Hamiltonian path problem, which isone of the NP-complete problems, using only biochemical techniques. He used DNA tosolve a 7-node, a special case of an NP-complete problem that attempts to visit everynode in a graph exactly once.Deoxyribonucleic acid consists of polymer chains, call DNA strands, that are composed

of nucleotides adenine (A), guanine (G), cytosine (C) and thymine (T). Adenine alwaysbonds with only thymine, while guanine always bonds with only cytosine. This phenom-enon is called Watson-Crick complementarity.

3.2. Algorithm to find cliques. Basically, the ideas of analyzing and designing cohesivesubgroups can define specific graph theoretic properties that should be satisfied in orderto identify a subset of employees. For these kinds of approaches to cohesion in personnelnetworks, examining a set of personnel network data is to find collections of employees whohave relatively strong ties, and it becomes visible by displaying functions or rearrangementof these networks. We note one of the approaches to cohesive subgroup analysis that is asocio-matrix [11], because this is the most important analyzing procedure to find all thecliques of the subgroups using DNA computing.A systematic way for ordering rows and columns of the socio-matrix reveals the sub-

group structure of the personnel network. Figure 3 shows a socio-matrix of the modelgraph with the rows and columns, employees who have ties and close interpersonal busi-ness relationships to each other in the socio-matrix. The socio-matrix of size m × mbecomes 20 rows and 20 columns for the model graph. There is a row and column foreach node, and the rows and columns are labeled 1, 2, 3,. . . , 20. xij denotes the value ofthe tie from employee i to employee j, and xij records which pairs of nodes are adjacent.If nodes Ni and Nj are adjacent, then xij = 1, and if nodes Ni and Nj are not adjacent,then xij = 0. In addition, an edge between two nodes is either present or absent. If anedge is present, it goes both from Ni to Nj and from Nj to Ni, thus, xij = 1, and xji = 1.The total sum of rows and columns represents the level of the connections between edges,which is divided by 2, becomes

L =

mPi=1

mPj=1

xij

2for i 6= j (1)

where the number of edges corresponds to L. As shown in Figure 3, the total sum of rowsand columns is 64, which means the number of edges should be 32. The number of edgesshould be equal to the number of all the independent lines in a 2-node. Furthermore,the connectivity matrix for 20 employees shown in Figure 1 is the 20 × 20 socio-matrixin Figure 3. This socio-matrix makes the best use of this DNA application because it issimple, and easy to understand how many DNA fragments and sequences we will need forthe DNA experiment.We designed a new algorithm based on the socio-matrix in Figure 3 and the algorithm

of the maximal clique problem solution that was proposed by Q. Ouyang [8], the methodto find the maximum clique. However, the new algorithm that finds all the 1-cliques, as


Figure 3. Socio-matrix for the personnel network of 20 employees

well as the maximum clique, because we would like to design more cohesive and efficientsubgroups in the personnel network based on the DNA results.Step 1: For a graph with N nodes, each possible clique is represented by a binary

number, which 1 is in the clique, and 0 is vise versa. Also, if the total is 1, 1 is in theindependent line.Step 2: Create all the possible combinations from 2N ; in this case, it becomes 220=1048576

where N=20.Step 3: The graph containing all edges missing in the original graph is called the

complementary graph. Any two nodes connected in the complementary are illegally con-nected in the original graph. Remove those cliques and independent lines that containillegal connections, corresponding to xij = 0 in Figure 3.Step 4: Sort the remaining data pool to select the DNA-sequence from 2 bits of value

1 to 20 bits of the value 1 in existence.


Step 5: Find the nodes that connected between the possible cliques, and distinguishthose connected cliques from other cliques.

3.3. Experiment. In this experiment, the DNA-sequence is designed in the form ofdouble-stranded DNA, and it corresponds to 20 nodes while satisfying the given algorithmabove. Each node of the DNA-sequence in a binary number is composed of two sequencesthat are a position sequence Ei and a value sequence Ni. The position sequences areused for connecting each node of the DNA-sequence, and the value sequence is usedfor distinguishing whether those position sequences contain that node or not. For atwenty-digit binary number in the graph, twenty value sections (N1 to N20) are preparedsandwiched sequentially between twenty-one position sections (E1 to E21). To amplifythe DNA sequence using polymerase chain reaction (PCR), the last section E21 is needed.We set Ei with the length of 10 base pairs (bp), Ni with the length of 0 bp if the value of1, and 6 bp if the value of 0. In this case, the longest DNA has 330 bp, and the shortestDNA has 210 bp. As Table 1 shows, we created 40 oligonucleotides for the experiment.Each oligonucleotide consists of two different position motifs, EiNiEi+1 for odd i, and

Ei+1NiEi for even i, where the boxed represents the complementary sequence, and the

value of Ni can be 1 or 0. The 40 fragment oligonucleotides were mixed together forthermal cycling.We need to remove the complementary sequences that contained illegal connections.

Therefore, as Table 2 shows, we selected the 20 restriction enzyme sites through on tech-nical references that are provided from New England BioLabs.Finally, we repeat selecting the shortest DNA strands, which correspond to all the

possible cliques using a gel electrophoresis apparatus.

3.4. Experiment results. The experiment in repetition was able to find all the possiblecliques including the maximum clique in the test tube. We decide the size of the clique byseeing the length of DNA strands. The clique of largest size is represented by the shortestlength of DNA. As Table 3 shows, the maximum clique is {N2, N7, N9, N18, N20}, whichis connected at distance 300 bp by five nodes. The second largest clique is {N3, N8, N10,N19}, which is connected at distance 306 bp by four nodes. There are also six possiblecliques that are all connected by three nodes, and the two independent lines with a 2-nodewerefound as well. In addition, there are some nodes that represent empty black boxes which

are vertically arranged in Table 3, so we can understand the possible cliques which aremutually connected together and find out all the nodes are divided into three componentsthat also can be a component and two subgroups.

4. Redesign of Subgroups. Although there are many different kinds of cliques in ahuge and complicated network, we hope to find all the cliques, and we hope to arrangethem in the large order of cohesion. Moreover, even though we do not know exactlywhich cliques connect with which others or how connected subgroups are in the network,we hope to redesign subgroups efficiently.

4.1. Personnel network analysis. All these problems have been known from the resultsof the DNA experiment results. The personnel network is redesigned based on all theDNA experiment results, as shown in Figure 4. To prove the efficiency of the redesigned


Table 1. Restriction enzyme sites are indicated by underlining and valuesequences N j

i , where j indicates the value of Ni. The value sequences arewritten with outlined letters.


Table 2. 20 restriction enzyme sites c°New England BioLabs Inc.

Table 3. Experiment results of the DNA-sequences for 8 cliques and 2 lines

personnel network using DNA computing, we show the differences between the redesignedpersonnel network and the previous personnel network. Therefore, we calculated theinclusiveness and the density of the both personnel networks [12].Recall that a complete graph is one in which all the nodes are adjacent to one another.

The concept of density is an attempt to summarize the overall distribution of edges inorder to measure how far from this state of completion the graph is.First, inclusiveness defines the number of nodes that are included within the various

connected parts of the graph. The inclusiveness of a graph is the total number of nodesminus the number of isolated nodes. The most useful measure of inclusiveness forcomparing various types of graphs is the number of connected nodes expressed as a

proportion of the total number of nodes. Thus, the proportion of the inclusiveness is


Figure 4. Redesigned personnel network and nodal degrees for employees’ relations

denoted by Π, and the inclusiveness is calculated as follows:

Π = C/

nXi=1

Ni for 0 ≤ Π ≤ 1 (2)

where C is the number of connected nodes.Secondly, the density of a graph is defined as the number of edges in a graph. The

density also expressed as a proportion of the maximum possible number of edges. Thedensity is denoted by ∆, and the density is calculated as follows:

∆ =L

n(n− 1)/2 for 0 ≤ ∆ ≤ 1 (3)

where there are n(n−1)/2 possible unordered pairs of nodes, and thus n(n−1)/2 possibleedges that could be presented in the graph. Table 4 shows the results of the inclusiveness,the density, and others for the both personnel networks.

4.2. Analysis results. As Figure 4 shows, it is known that the new subgroup 1 andsubgroup 2 are connected by the relations between the two employees, N3 (Yoshiro) andN20 (Seiji). These two employees are appropriate to be information communicators, toexchange their information between subgroups 1 and 2. In addition, subgroups 3 and4 show that, if the number of degrees is considered, N16 (Yasuo) could be a leader forsubgroup 3, and N13 (Gohei) could be a leader for subgroup 4. Furthermore, it can besaid that, if the four employees who are N20 (Seiji), N3 (Yoshiro), N16 (Yasuo), and N13(Gohei) are connected, the network could be an integrated personnel network.


Table 4. Inclusiveness and density comparisons

Finally, following the results in Figure 4 and Table 4 we can measure the efficiencyof DNA computing in redesigning subgroups. Thus, it is better to use DNA computingrather than Figure 1 when human resource managers redesign subgroups in any kinds ofpersonnel networks or other social networks to support work rotation in efforts to improvethe quality of work life.

5. Concluding Remarks. In this paper, the subgroups were redesigned more efficientlyand effectively as shown in the new personnel network. A massively parallel computationcorresponds to DNA computing that was able to be done to make a new personnel networkfor an efficient work rotation. In addition, we show various ideas on human resourcemanagement based on the results of DNA computing. On the other hand, there weresome problems, mainly that mistakes often happen in cutting DNA strands, and thenumber of nodes is limited to processes with picomole operations.Further research includes investigating DNA computing for nodes in signed or valued

graphs to develop a proactive systematic approach to solving a real personnel networkproblem, and expanding the different kinds of applications for managerial problems from avariety of industrial and management fields in order to support optimal decision-making.

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