Module Management Tool in Software Development Organizations
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1 Journal of Computer Scence (5): 8-, 7 ISSN Scence Publcatons Management Tool n Software Development Organzatons Ahmad A. Al-Rababah and Mohammad A. Al-Rababah Faculty of IT, Al-Ahlyyah Amman Unversty, P.O.Box 5,98, Amman, Jordan Faculty of Scence, Jerash Prvate Unversty, Jordan Abstract: management s an mportant task at developers level n software development organzatons. So we consder n ths paper software as collecton of several modules. Also we study a method of clusterng of modules of a large software system. The need of dong such clusterng s ustfed to be an mportant part of software management n the software development organzatons. An algorthm of mantenance and modfcatons s presented for dong the clusterng by the developers n the respectve development organzatons, whose complexty s calculated. The method wll be very much helpful, as an essental tool, at the developer level n software development organzatons for module management. Key words: Lnk graphs, lnk matrx, MC, updated lnk matrx, couplng matrx INTRODUCTION The software archtect devotes best effort for dervng an overall structural model of the system as a collecton of several modules [], as far as possble by retanng loose lnks. Ths helps the developers to modfy the modules almost ndependently, rrespectve of the codes of other modules. But n realty, t s not always feasble to develop any system as a collecton of only mutually ndependent modules. management [-] s a very mportant ob at the developers surface to mprove the process vsblty and the overall cost effectveness. In obect orented model, modules are obects wth prvate state and defned operatons on that states. In the data flow models, modules are functonal transformatons. In both cases, module may be mplemented as sequental components or as processes. An obect-orented model of a system archtecture structures the system nto a set of loosely coupled obects wth well-defned nterface [5,6]. s and lnk graphs: Among these modules, a par of modules may be mutually ndependent (deal stuaton), or may have lnk. If a flow of data (or a flow of control) exsts between these two modules, we say that they are lnked, they are not ndependent. Thus, there are three types of lnk possble to be exstng between a par of modules: * mo lnk, (f the modules are mutually ndependent) * one lnk, (f there exsts a flow of data or control from any one module to other, but not both ways). * two lnks (f there exsts a flow of data or control both ways). Fg. : Software We gnore the trval case of the exstence of lnk of one module wth tself. Thus, between a par of modules, there could be at most two lnks (accordng to our concept of lnk as stated above). Consder a system S consttuted of n modules developed under obect orented paradgm. Suppose that the modules are numbered from to n. Consder two modules module- and module-. Correspondng Author: Ahmad A. Al-Rababah, Faculty of IT, Al-Ahlyyah Amman Unversty, P.O. Box 5,98, Amman, Jordan 8 Fg. : No lnk graph between two modules
2 J. Computer Sc., (5): 8-, 7 For n= W Fg. : and W W W W Fg.: One-lnk graphs (drected) W Fg. 9: and so on. Fg. 5: Two-lnk graph (drected) Let us assume that any two modules are lnked wth some weght W (number of lnks) such that W = weght of the lnk between module- and module- Then, W =, f no lnk =, f one lnk =, f two lnks. Clearly, W s commutatve wth respect to ts ndces and..e. W = W. Then the lnk graph of the system S wll be an undrected graph as shown bellow: For n= Fg. 6: S For n= One W Fg. 7: Lnk matrx and the nteger set Zr: Now, let us dvde each element W nto two parts such that * W = l + l, * l =, f module- has to send a delverable to module- =, f module- wll not have to send any delverable to module-. (and same type of defnton s also true for every l, ). We assume that l = D (don t care symbol), (or the number ) gnorng the or cases of delverables whch are nternal only. Obvously, m and m are not necessarly equal. They are one way lnk values only. Then the Lnk matrx of the system S s defned as the square matrx L = [l ] In the lnk matrx L, each row could be vewed as the modules to perform the role of supplers and each column could be vewed as modules to perform the role of consumers. Example of a lnk matrx: Consder a system S wth modules,, and L = For n= Fg. 8: W W W W 9 In ths lnk matrx, the data l = means that the module- wll send a delverable to module-, whereas the data l = means that module- wll not. The data l = and l = combned sgnfes that module- and module- are mutually ndependent, because W wll be zero n ths case. If numbers of s are more n the matrx L, t mples that there are many modules lnked wth each other. The deal stuaton under obect orented paradgm s that the number of s n nondagonal postons of L should be more and more.
3 J. Computer Sc., (5): 8-, Fg. : Lnk-graph of S (Undrected) Fg. : Lnk-graph of S (Drected) + Integer-Set Z r: Let r I. We defne nteger-set Z r as the set of all non negatve nteger less than or equal to r. Thus, Z = {,, }, Z 5 = {,,,,, 5} etc. ng of modules: By groupng together the modules whch nteract wth each other very closely, t s certanly possble to reduce the efforts n the software mantenance [,7]. Two or more closely related modules, f grouped as one obect, forms a modulecluster (MC). MC Fg. : Software system Now, we study how to group two modules to form a cluster and then how to update the lnk-matrx of the system after completng each clusterng. Consder the system S as chosen n example earler. Suppose that we lke to group module- and module- to form a new cluster MC. Fg. : One C For ths we consder the sub matrx L of L correspondng to row-, row- and column-, column- gven by L = Now ths new cluster C s to be treated as good as one bgger module, say module- (specfed by bold one). Thus, at present the system S conssts of one cluster (the new created module-), module- and module-. The total number of delverables from ths cluster to module-, (for =, ) s clearly equal to the sum of the numbers of delverables from module- and module- to module-. The lnk values wll now be changed accordngly, and thus our updated lnk-matrx for the system S wll be as below: L = It s to be notced that n ths updated lnk matrx L, l s not zero but, whch s clear from the submatrx L, and the updated lnk matrx L s stll a square matrx. Also n the ntal lnk matrx L of the system S, the matrx-elements Z. In the frst updated lnk matrx L, the elements Z. We wll see next that n the p th updated lnk matrx L of the system S, the elements Z p+k where k. Thus, after ths clusterng, the software system S wll be apparently as shown n Fg. to the developers eyes. The method could be generalzed to group together two clusters to form a bgger cluster of clusters. For example, the followng two fgures can be seen: * New cluster (by groupng one cluster and one module) Fg. :
4 * New cluster (by groupng two clusters) J. Computer Sc., (5): 8-, 7 - Fg. 5: Couplngmatrx M: Each module could be vewed as a trval cluster ntally. However, f we consder two clusters C r and C s, then these are two parameters whch we shall consder now. The parameters are: * maxmum number (m) of possble lnks between C r and C s * actual number (a) of lnks exstng between C r and C s a Clearly, the rato wll be a member n the m closed nterval [, ]. Ths number (collectvely for every par of clusters) consttutes the couplng matrx M of a system S. For example, at the ntal stage of the system S when each cluster contans exactly one module, the number a Z and m =. Thus, a {, ½, }. The elements of the m couplng matrx MC= [m ] are defned now as below. (There are three dfferent cases): Case : Suppose that both of the clusters contans sngle module only. - MC C Fg. 6: MC C In ths case, a = w = l +l and m = where l, l are elements of the current lnk matrx L of the system S. w l + l Thus, m = = Clearly, m [, ]. Case : Suppose that a cluster C contans n number of modules and another cluster C contans only one module module-. l + l n In ths case, m =, Clearly m [,]. - because m = n here. MC C Fg. 7: s MC C Case : Suppose that a cluster C contans n number of modules and another cluster C contans n number of modules. MC C Fg. 8: MCC MC C l + l In ths case, m = n n, and m =, nn Where l and l are the elements of the last updated lnk matrx of the software system S. In ths case also, m [, ]. Clearly, the couplng matrx M s a square and a symmetrc matrx. If m =, t ndcates that the two clusters C and C are mutually ndependent. If m s a low value, t ndcates that the two clusters C and C are loosely coupled and f t s a hgh value (close to ) then t ndcates that the two clusters are strongly couplng. At every stage we shall look at the couplng matrx M to watch whch par of clusters s most strongly couplng and n the next step we wll group these two clusters to form a new cluster. Ths s the man paradgm of clusterng n our work here. Such par of clusters s called Strongly Coupled s (SCC). The task of clusterng by ths method s contnued untl we reach at a sngle cluster (whch s equvalent to the complete software system S). But t s most preferable to stop once a small number of meanngful and low-couplng clusters have been reached upon.the fnal number of clusters should be optmal n the context of mantenance and modfcatons to be done by the developers n the respectve development organzatons. We shall not cluster C and C nto one cluster f m =, or very close to zero. For ths the Developers (or the Software Development
5 Organzaton) choose a threshold value µ whch s very close to zero. Now, we present an algorthm for the above task of clusterng. Algorthm for module clusterng: Here, we present an algorthm for module clusterng whch s an mproved verson of the exstng algorthms [7]. At each teraton n ths algorthm, two clusters wth strongest couplngvalue are merged to form a new cluster and the lnk matrx s updated mmedately. Snce the couplng matrx M s a symmetrc matrx, the elements of ts uppers trangular regon are suffcent for us to consder. The algorthm uses an mportant data structure whch s an array N = < N, N,, N n > of n elements, where N s number of modules present n the th cluster. Clearly, at the ntal stage, N =, =,,,,n. -clusterng Algorthm Step : Calculate the ntal lnk matrx L and the upper trangular porton of the couplng matrx M, (.e. and where n) Step : Repeat step- through step-6, (n-) tmes. Step : Fnd the par of SCC wth couplng value more than µ. (f more than one par exsts, chose any one arbtrarly) whch are C and C where n (ths nequalty whch can be assumed wth no loss of generalty). Calculate m = max {m }, n Step : Merge C and C to form a new cluster C. Step.: N N + N Step.: Update th column ( th row ) of the lnk matrx such that k=,, n where, k, l k l k + l k l k Step 5: Ignore now the cluster, and set N. Step 6: Update the couplng matrx M. Step 6.: Update the th row of M by dong: k=,, n where k m k m k Step 6.: Update th column of M by dong: k=,, n where k m k m k Step 7: Stop. Complexty of the algorthm: To calculate the complexty T(n) of the module clusterng algorthm we see that: J. Computer Sc., (5): 8-, 7 In step-, there wll be computaton of n C elements of the couplng matrx M. The complexty of ths step s O(n ) Step- nvolves a sortng algorthm, n worst-case whch wll consume O(n ) amount of tme (n case the developers seeks alternatve SCC from the sorted clusters). All other steps from to 6 have the complexty O(n) respectvely. Thus, the porton from step- through step-6 has the complexty = O(n ) + O(n) = O(n ). But, due to the repetton of ths computaton for (n-) tmes ( because of step ), we have the total complexty of the algorthm gven by T(n) = O(n ) + (n-) * O(n ) = O(n ) Thus, we see that the algorthm s a P-class algorthm. CONCLUSION We have studed here a methodology for module clusterng n a huge type of software system whch has been developed wth a large number of modules. The need of dong such clusterng s ustfed to be an mportant part of software management n the software development organzatons. We present a polynomal tme algorthm for module clusterng and the method can be well applcable especally for the large software systems developed wth obect orented approach. The fnal number of clusters should be optmal n the context of mantenance and modfcatons to be done by the developers n the respectve development organzatons. REFERENCES. Gao, J.Z. and H.S.J. Tsao, 6. Testng and Qualty Assurance for Component-Based Software. Artech House Publshers.. Berczuk, S. and B. Appleton,. Software Confguraton Management Patterns: Effectve Teamwork. Addson-Wesley.. Pullum, L.L.,. Software Fault Tolerance Technques and Implementaton, Norwood, MA: Artech House.. Summervlle, I.,. Software Engneerng, Pearson Educaton Asa. New Delh. 5. Kartashev, S., 99. Supercomputng Systems: Archtectures, Desgn and Performance. New York. 6. Zedan, H.S.M. and A. Cau, 999. Obect-Orented Technology and Computng Systems Re- Engneerng. Horwood Publshng Lmted. 7. Councll, W. and G.T. Heneman,. Defnton of a Software Component and ts Elements. Addson-Wesley.
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