On the relationship between parallel computation and graph embedding

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5827011

Gupta, A K

The problem of efficiently simulating an algorithm designed for an n-processor parallel machine G on an m-processor parallel machine H with n > m arises when parallel algorithms designed for an ideal size machine are simulated on existing machines which are of a fixed size. The author studies this problem when every processor of H takes over the function of a number of processors in G, and he phrases the simulation problem as a graph embedding problem. New embeddings presented address relevant issues arising from the parallel computation environment. The main focus centers around embedding complete binary trees into smaller-sized binary trees, butterflies, and hypercubes. He also considers simultaneous embeddings of r source machines into a single hypercube. Constant factors play a crucial role in his embeddings since they are not only important in practice but also lead to interesting theoretical problems. All of his embeddings minimize dilation and load, which are the conventional cost measures in graph embeddings and determine the maximum amount of time required to simulate one step of G on H. His embeddings also optimize a new cost measure called ({alpha},{beta})-utilization which characterizes how evenly the processors of H are used by the processors of G. Ideally, the utilization should be balanced (i.e., every processor of H simulates at most (n/m) processors of G) and the ({alpha},{beta})-utilization measures how far off from a balanced utilization the embedding is. He presents embeddings for the situation when some processors of G have different capabilities (e.g. memory or I/O) than others and the processors with different capabilities are to be distributed uniformly among the processors of H. Placing such conditions on an embedding results in an increase in some of the cost measures.

• Research Organization: Purdue Univ., Lafayette, IN (USA)
• OSTI ID: 5827011
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
BENCH-SCALE EXPERIMENTS
COMPUTERIZED SIMULATION
DATA PROCESSING
DECISION TREE ANALYSIS
DESIGN
DISTRIBUTED DATA PROCESSING
GRAPHS
MATHEMATICAL LOGIC
OPTIMIZATION
PARALLEL PROCESSING
PERFORMANCE TESTING
PROCESSING
PROGRAMMING
SIMULATION
TECHNOLOGY UTILIZATION
TESTING