Application sharing is an important aspect of collaborative computing. One mechanism for sharing applications is a multiplexor, a tool that broadcasts input/output messages from a single client to multiple displays. We describe the design and implementation of a multiplexor for X windows that supports a heterogeneous environment and works effectively across both local and wide area networks. This X-multiplexor is composed of two distinct components, the Collaborative Computing Frameworks X-Multiplexor (CCFX) which acts as a pseudo server for the client, and the Collaborative Computing Session Manager (CCSM) which renders the client images and supplies the user interface to the system. In effect, CCSM acts as a distributed window manager, ensuring that all participants have the same view of the shared clients. This two headed approach offers significant gains in flexibility and resource usage. CCFX and CCSM can communicate using any reliable transport protocol. This can result in significant reduction of bandwidth, decreased latency, and avoids some TCP/IP communication required by the X protocol. In addition, this architecture facilitates the creation of a virtual X environment. Using this virtual environment, instead of an actual X server's environment, and then translating the virtual properties to a specific server's properties, allows for more robust support of heterogeneous systems.

CCF (Collaborative Computing Frameworks) is a suite of software systems, communications protocols, and tools that enable collaborative, computer-based cooperative work. CCF constructs a virtual work environment on multiple computer systems connected over the Internet, to form a Collaboratory. In this setting, participants interact with each other, simultaneously access and operate computer applications, refer to global data repositories or archives, collectively create and manipulate documents or other artifacts, perform computational transformations, and conduct a number of other activities via telepresence. Research issues addressed in this project include problem solving environments and methodologies for laboratory and instrument-based scientific disciplines, and computer science issues in heterogeneous distributed systems. New approaches are being investigated and developed for fast multiway communication, robust geographically distributed data management methodologies, high-performance computational transforms inlined within collaboration sessions, and related auxiliary issues such as active documents, security, archival storage, and experiment management and control. In this paper, we discuss the design philosophy and systems rationale behind CCF, describe the major subsystems of the collaborative computing environment, and discuss the salient features of the system.

The Brouwer fixed point theorem has become a major tool for modeling economic systems during the 20th century. It was intractable to use the theorem in a computational manner until 1965 when Scarf provided the first practical algorithm for finding a fixed point of a Brouwer map. Scarf's work left open the question of worstcase complexity, although he hypothesized that his algorithm had "typical" behavior of polynomial time in the number of variables of the problem. Here we show that any algorithm for fixed points based on function evaluation (which includes all general purpose fixed-point algorithrna) must in the worst case take a number of steps which is exponential both in the number of digits of accuracy and in the number of variables.