The assignment problem in distributed computing
This dissertation focuses on the problem of assigning the modules of a program to the processors in a distributed system with the goal of minimizing the overall cost of running the program. The cost depends on the execution times of the modules on the processors and on the cost of communication between modules. This module allocation problem arises in a variety of situations where one is interested in making optimum use of available computer resources. The general module allocation problem is intractable; however it becomes polynomially-solvable when the communication graph is restricted. In this dissertation, we restrict our attention to k-trees;As the first problem, we study parametric module allocation on partial k-trees. We allow the costs, both execution and communication, to vary linearly as functions of a real parameter t. We show that if the number of processors is fixed, the sequence of optimum assignments that are obtained, as t varies from zero to infinity, can be constructed in polynomial time. As an auxiliary result, we develop a linear-time algorithm to find a separator in a k-tree. We discuss the implications of our results for parametric versions of the weighted vertex cover, independent set, and 0-1 quadratic programming problems on partial k-trees;Next, we consider two variants of the assignment problem. The first problem is to find a minimum-cost assignment when one of the processors has a limited memory. The second is to find an assignment that minimizes the maximum processor load. We present exact dynamic programming algorithms for both problems, which lead to approximation schemes for the case where the communication graph is a partial k-tree. Faster algorithms are presented for trees with uniform costs. In contrast to these results, we show that, for arbitrary graphs, no fully polynomial time approximation schemes exist unless P = NP. Both dynamic programming algorithms have been implemented. The implementation details and our experimental results are presented.