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New scaling algorithms for the assignment and minimum mean cycle problems
, 1992
"... In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing th ..."
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Cited by 50 (4 self)
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In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing the optimality conditions, and the amount of relaxation is successively reduced to zero. On a network with 2n nodes, m arcs, and integer arc costs bounded by C, the algorithm runs in O(,/n m log(nC)) time and uses very simple data structures. This time bound is comparable to the time taken by Gabow and Tarjan's scaling algorithm, and is better than all other time bounds under the similarity assumption, i.e., C = O(n k) for some k. We next consider the minimum mean cycle problem. The mean cost of a cycle is defined as the cost of the cycle divided by the number of arcs it contains. The minimum mean cycle problem is to identify a cycle whose mean cost is minimum. We show that by using ideas of the assignment algorithm in an approximate binary search procedure, the minimum mean cycle problem can also be solved in O(~/n m log nC) time. Under the similarity assumption, this is the best available time bound to solve the minimum mean cycle problem.
A Fast and Simple Algorithm for the Maximum Flow Problem
 OPERATIONS RESEARCH
, 1989
"... We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best b ..."
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Cited by 34 (5 self)
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We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best bound of O(nm log(n 2 /m)), obtained by Goldberg and Taran, by a factor of log n for networks that are both nonsparse and nondense without using any complex data structures. We also describe a parallel implementation of the algorithm that runs in O(n'log U log p) time in the PRAM model with EREW and uses only p processors where p = [m/n
SublinearTime Parallel Algorithms for Matching and Related Problems
, 1988
"... This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial struc ..."
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Cited by 33 (6 self)
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This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial structure of the above problems, which leads to new algorithmic techniques. In particular, we show how to use maximal matching to extend, in parallel, a current set of nodedisjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are "active" during an execution of a pushrelabel network flow algorithm. We also show how to apply our techniques to design parallel algorithms for the weighted versions of the above problems. In particular, we present sublineartime deterministic parallel algorithms for finding a minimumweight bipartite matching and for finding a minimumcost flow in a network with zeroone capacities, if the weights are polynomially ...
Finding MinimumCost Flows by Double Scaling
 MATHEMATICAL PROGRAMMING
, 1992
"... Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and ..."
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Cited by 25 (4 self)
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Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and maximum arc cost magnitude C. The major techniques used are the capacityscaling approach of Edmonds and Karp, the excessscaling approach of Ahuja and Orlin, the costscaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Taijan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (uncapacitated) transportation problem. In addition, we discuss a capacitybounding approach to the
unknown title
, 1988
"... New scaling algorithms for the assignment and minimum mean cycle problems ·r I · · · r · · · ·IP · · 1 ·I ..."
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New scaling algorithms for the assignment and minimum mean cycle problems ·r I · · · r · · · ·IP · · 1 ·I