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Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for design ..."
Abstract

Cited by 234 (7 self)
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Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems, as well as in scheduling and locational problems.
TWO EFFICIENT ALGORITHMS FOR THE GENERALIZED MAXIMUM BALANCED FLOW PROBLEM Akira Nakayama
, 2000
"... Abstract Minoux considered the manmum balanced /low problem, i.e. the problem of finding a maximum flow in a twoterminal network Af = (V, A) with source s and sink t satisfying the constraint that any arcflow of Af is bounded by a fixed proportion of the total flow value from s to t, where V is ve ..."
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Abstract Minoux considered the manmum balanced /low problem, i.e. the problem of finding a maximum flow in a twoterminal network Af = (V, A) with source s and sink t satisfying the constraint that any arcflow of Af is bounded by a fixed proportion of the total flow value from s to t, where V is vertex set and A is arc set. Several efficient algorithms, so far, have been proposed for this problem. As a natural generalization of this problem we focus on the problem of maximizing the total flow value of a generalized flow in a network Af = (V, A) with gains?(a)> 0 (a E A) satisfying any arcflow of Af is bounded by a fixed proportion of the total flow value from s to t, where?(a) f (a) units arrive at the vertex w for each arcflow f (a) (a ' = (v, w) E A) entering vertex v in a generalized flow in At. We call it the generalized maximum balanced flow problem and if?(a) = 1 for any a E A then it is a maximum balanced flow problem. The authors believe that no algorithms have been shown for this generalized version. Our main results are to propose two polynomial algorithms for solving the generalized maximum balanced flow problem. The first algorithm runs in O(mM(n, m, B') log B) time, where B is the maximum absolute value among integral values used by an instance of the problem, and M(n, m, Bf) denotes the complexity of solving a generalized maximum flow problem in a network with n vertices, and m arcs, and a rational instance expressed with integers between 1 and B'. In the second algorithm we combine a parameterized technique of Megiddo with one of algorithms for the generalized maximum flow problem, and show that it runs in O({M(n, ~X,B')}~) time. 1.