DETERMINING INTUITIONISTIC FUZZY DEGREE OF OVERLAPPING OF COMPUTATION AND COMMUNICATION IN PARALLEL APPLICATIONS USING GENERALIZED NETS

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1 DETERMINING INTUITIONISTIC FUZZY DEGREE OF OVERLAPPING OF COMPUTATION AND COMMUNICATION IN PARALLEL APPLICATIONS USING GENERALIZED NETS Pave Tchesmedjiev, Peter Vassiev Centre for Biomedica Engineering, Bugarian Academy of Sciences Acad. G. Bonchev Str., B. 05, Sofia-3, Bugaria E-mais: Abstract Overapping of computation and communication can reduce overa appication execution time and a parae appications coud benefit to a certain degree. In order to achieve this we present a new approach for determining the degree of overapping. Keywords: Communication, Computation, Generaized net, Intuitionistic fuzzy sets, Modeing, MPI, Overapping, Parae process INTRODUCTION Overapping is a high performance software mechanism that enabes concurrent execution of independent communication and computation activities. The major objective of overapping is to reduce the overa appication time by utiizing hardware and software architectures that offer concurrent progress of communication and computation. Overapping is one of the fundamenta agorithmic approaches for improving parae performance. A parae appications coud benefit from overapping to a certain degree. This paper focuses on a new approach for determining degree of overapping. This approach incudes evauating the intuitionistic fuzzy vaue of the degree, using a generaized net mode (GN, see []). 2 COMMON GENERALIZED NET MODEL FOR MPI PARALLEL FUNCTIONS In order to determine the vaue of overapping we wi introduce a common generaized net for modeing and simuating parae appications. The foowing MPI functions (definitions are given in the C programming anguage; see [3]) are commony used in parae programs: 50

2 int MPI_Bcast(void *buf, int count, MPI_Datatype datatype, int root, MPI_Comm comm) the vaue of the data, pointed by *buf, of type datatype and containing count eements, is sent to a other processes(associated to the communicator comm). So afer caing the function every process ends with a copy of the data. int MPI_Reduce(void *sendbuf, void *recvbuf, int count, MPI_Datatype datatype, MPI_Op op, int root, MPI_Comm comm) the vaue of the data, pointed by *sendbuf, of type datatype and containing count eements from each process are sent to the process with rank root and paced in the *recvbuf, as operation op is committed before that. int MPI_Send(void *buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm comm) the vaue of the data, pointed by *buf, of type datatype and containing count eements is sent to the destination process from the communicator comm - dest, using additiona information tag. int MPI_Recv(void *buf, int count, MPI_Datatype datatype, int source, int tag, MPI_Comm comm, MPI_Status *status) the master process requests for information from another process source from the communicator comm and bocks unti the an answer is returned. The information is represented by the vaue, pointed by *buf, of type datatype and containing count eements with additiona information tag. Status is returned by the variabe *status. The described parae routines can be represented in the common GN mode for n parae processes and one master process that activates them see Fig.. For the master process, represented by transition Z 0 : Z 0 = <{ 0 },{, 3,... 2i+,... 2n+ }, r 0 > r 0 = 0 W 0, W 3 0,3 L L W 2i+ 0,2i+ L L W 2n+ 0,2n+ For one of the parae processes, represented by transition Z i+, i = {0,n}: Z i+ = <{ 2i+ },{ 2i+2 }, r i+ > r = 2i+ 2 i+ true The transitions represent parae processes. When the master process sends a message to other parae processes a token is created and the 2i+ 5

3 respective transition is activated. The tokens have the foowing properties data, count and datatype. The conditions W 0,, W 0,3, W 0,2i+, W 0,2n+ for the case of MPI_Bcast, MPI_Reduce and MPI_Send functions are aways TRUE. Figure. 52

4 When the used function is MPI_Recv, W 0,, W 0,3, W 0,2i+, W 0,2n+ are initiay FALSE and become TRUE when the master process is ready with the requested token (data). 3 DEFINITION OF OVERLAPPING If the tota execution time (see [2]) of a parae appication is T p the computation time is T comp and the communication time is T c, the objective of overapping can be expressed as foows: T p = T comp + T c T o, Where T o is the time saving achieved through overapping. Traditiona approaches for parae performance improvement emphasize minimization of T comp and T c and typicay rey on increasing raw processor speed and network speeds. Ceary, overapping presents aternative approach for improving performance. Overapping depends primariy on efficient software and hardware architectures rather than on top speed components. Overapping utiizes software techniques such as asynchronous message-competion notification, ow processor overhead, independent message progress. Major hardware features of the parae system needed for effective overapping are avaiabiity of excess bandwidth of the memory subsystem and inteigent network interface controers capabe of accessing host memory. The introduced common GN mode provides the needed abstraction of a hardware and software ayers of a rea parae system. The reation between the communication and computation activities pays an important roe in achieving effective overapping. To iustrate this importance, a computation activity X and a communication activity Y are reviewed. The durations of these activities are, respectivey, t x and t y. For simpicity we can assume that there are no preparation times and the entire communication and computation times can be represented as s sum of N individua activities, such as T comp (estimated) = t x and T c (estimated) = t y or if we want to be more precise T comp (actua) = ( + π(t comp )).T comp (estimated) and T c (actua) = ( + π(t c )).T c (estimated), where π(t comp ), π(t c ) are numbers between 0 and that refect the deays of the tasks (in the idea case the vaue woud be 0). We aso assume that X and Y shoud be agorithmicay independent they can be executed concurrenty without vioating the correct semantics of the agorithm. 53

5 If the reviewed computation and communication activities are not overapped, the seria time for their competion is t s = t x + t y. If the two activities are ideay overapped, the tota time t o wi be the arger of t x and t y and t o = max(t x, t y ). The overa time reduction is S = (t x + t y ) / max(t x, t y ) In order to quantify the speedup because of overapping, the reationship between X and Y is represented as t y = q.t x, where q > 0 is a factor that represents how much Y is onger or shorter than X. Then speedup is as foows: S = (t x + q.t x ) / max(t x, q.t x ) = ( + q)t x / max(t x, q.t x ) In the first case et q >, that is, communication is onger than computation, then S = ( + q).t x / (q.t x ) = ( + q) / q. This expression shows that if q approaches, then S approaches 2, and when q approaches positive infinity, S approaches. In the second case when 0 < q, meaning that the communication time is shorter than the computation time, then S = + q. So when q approaches 0, S approaches whie for q approaches, S approaches 2. So S 2, the maximum achieved when t x = t y. 4 DETERMINING INTUITIONISTIC FUZZY DEGREE OF OVERLAPPING We wi introduce a new metric, used for accurate modeing of overapping degree of overapping, denoted by µ(d 0 ) and degree of indeterminacy (uncertainty) π(d 0 ). As in a Intuitionistic Fuzzy Set (IFS, see [4]) we wi impose the restrictions µ+π. The degree of overapping is used as a quantitive description of the capabiities of a system in order to perform effective overapping of communication and computation. This quantification is necessary for devising a reaistic mode of parae execution time. Overapping is now expressed in the form: T p = T comp + T pc (( π(t o )).T o (µ(d 0 ))), for 0 µ(d 0 ), where measures π(t o ) the uncertainty of the time of the executed agorithm. Degree µ(d 0 ) is chosen so that the maximum impact of overapping on the overa performance is achieved as the vaue of µ(d 0 ) approaches. As we assumed earier, π(d 0 ) wi approach 0 and that s why 0 µ(d 0 ). There are severa reasons for introducing degree-of-overapping metric. First it can be 54

6 used to distinguish between hardware patforms and software systems that have specific optimizations for achieving effective overapping and those that do not provide such optimizations. Second, this new metric heps to provide more reaistic mode of overapping that accuratey quantifies the performance benefits to appications. And third it can be used for a guideine for improving parae patform architectures and appication agorithms impementation. Using the proposed common GN mode and IF vaues wi hep even more for achieving this tasks. Degree µ(d 0 ) = means that the system can achieve idea overapping and µ(d 0 ) = 0 means that no overapping is possibe. Idea overapping is impossibe because the communication activities require certain processor overhead and the message transfers compete to some degree with the centra processor to access to the main memory. As a resut of CPU anaysis, the communication activity Y, introduced earier, can be presented as a sum of two sub-activities Y h and Y c, where Y h denotes a activity that cause processor overhead and resource contention, and Y c is the component that can be overapped with computation. During Y h no overapping is possibe, because CPU is busy with communication-reated work. The time of activity Y can be represented as sum of two components t y = t yh + t yc then the seria time of X and Y is: t s = t x + t yh + t yc and the overapped time is: t o = t xh + max(t yc, t x ) Ceary the onger the overhead time t xh is, the smaer the effect of overapping wi be. So we can formay define the degree of overapping as: µ(d 0 ) = t y / t xy = t yc / t yh + t yc and finay t o = t x + ( µ(d 0 )).t y, when t x > t xc and t o = t y, when t x t yc We wi consider the case when when t x > t y since this condition can be easiy identified by a singe experiment. In summary the vaues of the degree of overapping are in the range 0 µ(d 0 ). Degree µ(d 0 ) can be determined using the GN mode s execution times as foows: µ(d 0 ) = + (t x t o ) /t y = (t s t o ) /t y Common generaized net for executing parae appication and determining the degree of overapping is shown on Fig. 2. The transitions from Z to Z n+ represent the n parae processes that are executing computation and communication activities. Each token keeps the needed time vaues. The degree of overapping µ(d 0 ) is cacuated by the token in pace 3n+4. 55

7 Figure 2. 56

8 5 CONCLUSION By determining the IF vaue of the degree of overapping capabiities of a system we can perform effective overapping of communication and computation. By using common generaized net mode we can evauate this vaue and use it for further enhancements of the parae system and software. ACKNOWLEDGEMENTS This work was supported by Grant BIn-2/09 Design and deveopment of intuitionistic fuzzy ogic toos in information technoogies of the Nationa Science Fund of Bugaria. REFERENCES [] Atanassov, K., Generaized Nets, Word Scientific, Singapore, 99 [2] Dimitrov, Rossen, Overapping of communication and computation and eary binding, University of Mississipi, 200 [3] Gropp, Wiiam, Lusk, Ewing, Skjeum, Anthony, Using MPI Portabe Parae Programming with the Message-Passing Interface, The Mit Press, 997 [4] Atanassov, K, Intuitionsitic Fuzzy Sets. Springer Physica-Verag, Heideberg,