Succinct representations of graphs
Information and Control
A note on succinct representations of graphs
Information and Control
Towards an architecture-independent analysis of parallel algorithms
SIAM Journal on Computing
Compile-Time Scheduling and Assignment of Data-Flow Program Graphs with Data-Dependent Iteration
IEEE Transactions on Computers
Journal of Computer and System Sciences
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Static scheduling of conditional branches in parallel programs
Journal of Parallel and Distributed Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Complexity of Problems on Graphs Represented as OBDDs (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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A fundamental problem in programming multiprocessors is scheduling elementary tasks on the available hardware efficiently. Traditionally, one represents tasks and precedence constraints by a data-flow graph. This representation requires that the set of tasks is known beforehand. Such an approach is not appropriate in situations where the set of tasks is not known exactly in advance, for example, when different options how to continue a program are possible. In this paper dynamic process graph (DPG) will be used to represent the set of all possible executions of a given program. An important feature of this model is that graphs are encoded in a very succinct way. The encoded executions are directed acyclic graphs with a "regular" structure that is typical for parallel programs. With respect to such a graph representation we investigate the computational complexity of some basic graph-theoretic problems like e.g. what is the minimum depth of a graph represented by a DPG? or what is the size of a subgraph induced by a given node v? In this paper the complexities of these problems are determined precisely. As a consequence approximations of the computational complexity of some variants of scheduling problems are obtained.