Parallel approximate algorithms for combinatorially hard problems
Thesis/Dissertation
·
OSTI ID:5180559
Several combinatorial optimization problems have been shown to be NP-complete. Consequently, fast parallel algorithms for finding optimal solutions to such problems using a polynomial number of processors are unlikely. An important practical approach to solving such problems on sequential machines has been to seek algorithms that find approximate solutions. This thesis explores a similar approach to solving NP-complete optimization problems on parallel machines. The model of computation is a parallel random access machine (PRAM) in which a common memory is used to communicate between processors. It is first proved that the first-fit algorithm for bin packing is inherently sequential in a certain formal sense and argue that many other existing approximate algorithms are hard to parallelize. Then, a general technique is presented for finding approximate solutions on the PRAM for a class of NP-complete optimization problems. This class includes the knapsack problem, the sum of subsets problem, the job-scheduling problem with deadlines, and scheduling independent tasks on multiprocessors to minimize finish times. A divide-and-conquer algorithm that finds an optimal solution by generating sets of partial solutions and merging them is first designed. The tree-partitioning problem is next investigated, parallel algorithms are presented that exhibit linear speedups over the existing sequential approximate algorithms for a limited number of processors.
- Research Organization:
- Maryland Univ., College Park (USA)
- OSTI ID:
- 5180559
- Country of Publication:
- United States
- Language:
- English
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