EFFICIENT GRAPH ALGORITHMS FOR SEQUENTIAL AND PARALLEL COMPUTERS

• Authors: A. V. Goldberg
• Venue: EFFICIENT GRAPH ALGORITHMS FOR SEQUENTIAL AND PARALLEL COMPUTERS
• Year: 1987

In this thesis we study graph algorithms, both in sequential and parallel contexts. In the following outline of the thesis, algorithms complexities are stated in terms of the number of vertices n, the number of edges m, the largest absolute value of capacities U, and the largest value of costs C. In Chapter 1 we introduce a new approach to the maximum flow problem that leads to better algorithms for the problem. These algorithms include an O(nmlog(n /m)) time sequential algorithm, an O(n logn) time parallel algorithm that uses O(n) processors and O(m) memory, and both synchronous and asynchronous distributed algorithms. Chapter 2 is devoted to the minimum cost flow problem, which is a generalization of the maximum flow problem. We introduce a frame work that allows the generalization of the maximum flow techniques to the minimum-cost flow problem. We exhibit O(nmlog(n)log(nC)), O(n m log(nC)), and O(nnnlog(nC)) time sequential algorithms as well as parallel and distributed algorithms. In Chapter 3 we address implementation of parallel algorithms through a case-study implementation of a parallel maximum flow algorithm. Parallel prefix operations play an important role in our implementation. We present experimental results achieved by the implementation. Parallel symmetry-breaking techniques are the main topic of Chapter 4. We give an O(lg*n) algorithm for 3-coloring a rooted tree. This algorithm is used to improve several parallel algorithms, including algorithms for +1-coloring and finding maximal independent set in constant-degree graphs, 5-coloring planar graphs, and finding a maximal matching in planar graphs. We also prove lower bounds on the parallel complexity of the maximal independent set problem and the problem of 2-coloring a rooted tree.