Effects of communication characteristics on task mapping quality on a 2-D mesh with wormhole routing

Given that computational load is well balanced, task mapping is mainly concerned with reducing communication overhead. How much communication time can be reduced by optimizing allocation of tasks on a multiprocessor system would be dependent on several factors. In this study, dependency of improvement by task mapping on communication pattern is investigated on a mesh with wormhole routing. Communication pat tern may be described by a set of parameters such as the total number of messages, the number of sources, the number of destinations, and distribution of message size. Through extensive simulation, it has been shown that the communication pattern has a significant effect on reduction in communication overhead that can be achieved by task mapping. Effects of individual communication parameters have been analyzed. 1. I N T R O D U C T I O N As more parallel computing systems, tightly-coupled multiprocessors or networks of workstations, are made commercially available, how those systems can be efficiently used for various applications has become an important issue. A specific issue of task mapping concerns with assigning partitioned tasks onto processing elements (PE's). Task mapping has been extensively studied by many researchers for a long time [1][2][3][4][5]. However, as a whole, it is still an open problem. The term, task mapping, is to be distinguished from task scheduling which determines the order in which a given set of tasks are to be executed on a single or multiple PE's. Task mapping (as used in this paper) allocates tasks, which are communicating concurrently and are to be executed at the same time, onto multiple PE's. With task partitioning fixed, task mapping mainly affects communication overhead. As the ratio of communication time to computation time in parallel or distributed computing increases, it is required that a mapping scheme take communication overPermission to make digital or hard copies o f all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and or fee. SAC'00 March 19-21 Como, Italy (e) 2000 ACM 1-58113-239-5/00/003>...>$5.00 head into account. This increased ratio is due to a larger number of PE's now available for an application, a larger size of shared data involved in many recently-emerging applications, the ever-increasing processor speed, etc. One may attempt to reduce communication overhead by optimizing "when PE's send out messages", i.e., scheduling communication with a given (spatial) mapping. However, the achievable improvement can be limited since a spatial assignment (mapping) of communicating tasks is fixed. That is, mapping would help scheduling to achieve a better result (a smaller communication overhead). Also, this approach would require more information to deal with such as timing information. Furthermore, it can be more sensitive to dynamic variation of communication. Communication pattern among PE's in a multiprocessor system depends on where communicating tasks are assigned and shared data are allocated. Depending on the relative positions of communicating tasks, the resulting communication overhead may vary significantly. In some cases, random mapping may work just as well as any elaborated mapping. Therefore, whether one should concern about mapping at all and what should be optimized in mapping are to be addressed. There have been significant research efforts in optimizing communication in order to minimize communication overhead including [7][8]. Various communication patterns such as multicasting, broadcasting, all-to-all broadcasting, etc. were investigated. Hambrusch et. al. [9] considered "S-toP" broadcasting problem on meshes, where S is the number of source PE's and P is the total number of PE's in a mesh, 1 < S < P. A set of particular source distribution patterns were examined. In this paper, how much communication overhead can be reduced by optimizing locations of communicating tasks (task mapping) on a 2-D mesh with wormhole routing depending on the characteristics of communication pattern is analyzed for general (or random) communication patterns. It is well known that communication time for a pair of PE's is almost independent of the distance between them in a wormhole routing network while it is proportional to the distance in a packet switching or message switching network [10][11]. Nevertheless, it should not be "extrapolated" to: communication overhead in a wormhole routing multiprocessor system does not depend on what PE's communicating tasks axe mapped onto. Conflict among messages is dependent on locations of communicating tasks while communication