Conceptual and algorithmic tools are developed as a foundation for a theory of scheduling complex computation-dags for Internet-based computing. The goal of the schedules produced is to render tasks eligible for allocation to remote clients (hence, for execution) at the maximum possible rate. This allows one to utilize remote clients well, as well as to lessen the likelihood of the "gridlock" that ensues when a computation stalls for lack of eligible tasks. Earlier work has introduced a formalism for studying this optimization problem and has identified optimal schedules for several significant families of structurally uniform dags. The current paper extends this work via a methodology for devising optimal schedules for a much broader class of complex dags, which are obtained via composition from a prespecified collection of simple building-block dags. The paper provides a suite of algorithms that decompose a given dag /spl Gscr/ to expose its building blocks and an execution-priority relation /spl utri/ on building blocks. When the building blocks are appropriately interrelated under /spl utri/ the algorithms specify an optimal schedule for /spl Gscr/.

We present a game-theoretic model of the interactions between server and clients in a constrained family of commercial P2P computations (where clients are financially compensated for work). We study the cost of implementing redundant task allocation (redundancy, for short) as a means of preventing cheating. Under the assumption that clients are motivated solely by the desire to maximize expected profit, we prove that, within this framework, redundancy is cost effective only when collusion among clients, including the Sybil attack, can be prevented. We show that in situations where this condition cannot be met, non-redundant task allocation is much less costly than redundancy.

A "pebble game" is developed to model the process of scheduling computation-dags for Internet-based computing (IC, for short). Strategies are derived for scheduling three common, significant families of such dags for IC: reduction-meshes, which represent (the intertask dependencies of) computations that can be performed by "up-sweeps" of meshes; reduction-trees, which represent "accumulative" computations that can be performed by "up-sweeps" of trees; and FFT (fast fourier transform) dags, which represent a large variety of convolutional computations. Two criteria are used to assess the quality of a schedule: its memory requirements and its rate of producing tasks that are eligible for allocation to remote clients. These criteria are important because of, respectively, the typically enormous sizes of IC computations and the typical temporal unpredictability of remote clients in IC. In particular, a high production rate of eligible tasks decreases a computation's vulnerability to the gridlock that can occur when a computation stalls pending the return of intermediate results by remote clients. Under idealized assumptions, the schedules derived are optimal in the rate of producing eligible tasks and are either exactly or approximately optimal in memory requirements.