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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 ..."
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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.
An Algorithm for Fractional Assignment Problems
 Discrete Applied Mathematics
, 1995
"... . In this paper, we propose a polynomial time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G = (I; J; E) be a bipartite graph where I and J are vertex sets and E ` I 2 J is an edge set. We call an edge subset X(` E) an assignment if ..."
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Cited by 2 (0 self)
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. In this paper, we propose a polynomial time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G = (I; J; E) be a bipartite graph where I and J are vertex sets and E ` I 2 J is an edge set. We call an edge subset X(` E) an assignment if every vertex is incident to exactly one edge from X: Given an integer weight c ij and a positive integer weight d ij for every edge (i; j) 2 E; the fractional assignment problem finds an assignment X(` E) such that the ratio ( P (i;j)2X c ij )=( P (i;j)2X d ij ) is minimized. There developed some algorithms for the fractional assignment problem. Recently, T. Radzik showed that an algorithm which is based on the parametric approach and Newton's method is the fastest one among them. Actually, it solves the fractional assignment problem in O( p nm log(nCD) log(nCD) 1+log log(nCD)0log log(nD) ) time where jIj = jJ j = n; jEj = m; C = maxf1; maxfjc ij j : (i; j) 2 Egg and D = maxfd ij :...