Performance analysis for parallel solutions to generic search problems

A b s t r a c t The performance analysis of parallel algor i thms for search problems is discussed in this paper. Using the Traveling Salesman Problem (TSP) as the prototype of the search problems, we propose the use of a performance analysis methodolosy for such parallel computat ions b a s e d o n probabilistlc theory. Dtvideand-conquer s trategy is widely used in solving search problems in pa ra l l e l by parti t ioning and allocating a number of given tasks to available computing resources. When the tasks exhibit nondeterministic behaviors during execution and share a universal distribution function in their execution times, analysis of parallel execution time can be performed with the assistance of probabilistic and stat ist ical models given in this paper. Correlation (dependence) in execution times among tasks has posed a significant factor in influencin G the analysis accuracy which is unmanageable by any Known analysis methodologies. We establish a relation between a task's o r / and a processor's execution time and the parallel execution time, in terms of expected value as well as variance when each task's execution time can be closely modeled by a normal distribution, for either uncorrelated or correlated tasks. The method proposed has a wider application scope and gives more accurate analysis results titan previously known approaches. Experimental results in analyzing two parallel algorithms for solving TSP show very accurate analysis with the proposed method.