Abstract
The author advances a new model termed Geometric Representation of Programs (GRP) that is useful for programming sequential, parallel, distributed or web-based computers. GRP has three main domains: computational, data and awareness. In typical programming, computational and data domains are often mixed together while there is little or no representation of awareness (conceptual information representation often accomplished via code indentation, commenting or other documentation techniques). The integration of these domains provides for a complete program representation. This talk focuses on computational spaces as part of the computational domain. (It is noted that there is much similarity between the three domains.)

A computation space is a group of computations such that each element computation in the group is assigned to a Cartesian coordinate. An iteration space defined by a (perfect) loop nest is therefore a specific (simple) example of a computation space. The computation spaces allowed in the GRP model are complicated by a number of factors. Briefly, groups of computations are enclosed by geometric objects termed polytopes; such polytopes provide abstractions of the group. Inter- and intra-relationships are subsequently formed and are represented as graphs internal to a polytope or between polytopes. Some of these relationships include data dependences, spatial, temporal and hierarchal. An additional important relationship that is considered for the first time is that of communication requirements within and between polytopes.

It is desirable to model a group of computations as requiring fast and possibly simultaneous point-to-point, point-to-all, all-to-point or all-to-all communication. Hence a model of an interconnection network can be embedded into the polytope to accommodate for the necessary communication. However, there is the significant problem of selecting the type (e.g. static, multi-stage, shared, hybrid, etc.) of interconnection network and in parameterizing the selected network for optimal performance given the wide structural variability inherent in GRP. Optical interconnection networks offer the potential of high speed and high bandwidth communication and is proposed to address some of these issues. In particular the Linear Array with a Reconfigurable Pipelined Bus System (LARPBS) optical bus model is currently under study for its use and impact in GRP.

This talk presents an overview of the GRP model in terms of computational spaces. Some current work regarding scientific visualization research will also be discussed. The focus of the talk will be to consider the integration of optical-based communication, specifically the LARPBS model, and its impact on the GRP model.

All faculty and students are welcome. In particular, students interested in taking the `Advanced Interconnection Network' course offered in the Winter session, 2001, are highly encouraged to attend. Students currently taking the Program Visualization course or those interested in working with the author in the future are also encouraged to attend.