J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the Association for Computing Machinery, 19:248--264, 1972.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....what is perhaps the generic algorithm of the class, the e relaxation method [7] Section 4 develops some basic serial complexity analysis tools for this algorithm [28, 29, 8] also addressing the special case of maximum flow problems. Section 5 combines this analysis with the notion of scaling [30 32, 19, 24, 41, 5], yielding a polynomial (O(N 3 log NC) serial algorithm for the minimum cost flow problem (N is the number of nodes, and C the largest absolute value of the arc cost coefficients) In Section 6, we introduce the auction algorithm [9] for the assignment problems, and show how it may be regarded ....

.... motivation for this algorithm seems to have been quite different from the theory we emphasize in this paper; it appears to have been originally conceived of as a distributed, approximate computa tion of the layered representation of the residual network that is common in maximum flow algorithms [24]. However, it turns out that the first phase of this two phase algorithm, in its simpler implementations, is virtually identical to erelaxation as applied to a specific formulation of the maximum flow problem. This connection will become apparent later. Basically, the distance estimates of the ....

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J. Edmonds and R.M. Karp, "Theoretical improvements in algorithmic efficiency for network flow problems," Journal of the ACM 19 (1972) pp. 248-264.

....k clustering solution. Similarly, any solution to the k clustering problem is corresponding to a solution to the flow problem on the constructed graph and these two solutions have the same cost. The min cost flow problem, can be optimally solved using existing techniques in O( V ) time [16,11] where V is the total number of vertices in the graph. Constructing G and the corresponding k clustering solution can be done in O(n.k) time. Hence, the k clustering problem can be optimally solved in O( n k) time. 4. 2 Clustering to Minimize the Maximum Diameter Some sensor network ....

Edmonds, J.; Karp, R. M. Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems, Journal of the Association for Computation Machine 1972, 19, 248-261.

....the node that has highest weight. To find the matching, for each one of the nodes we need to search all N links of the bipartite graph. Since there are 2N nodes, the complexity of LPF turns out to be O(N ) Basically this algorithm is a modification of the Edmonds Karp max flow algorithm [4] and its complexity is the same as that. The only introduced matching algorithm with O(N complexity is Hopcroft and Karp algorithm [6] which is a maximum size matching algorithm. In this algorithm the nodes are introduced into the matching simultaneously; this is not possible in LPF ....

J. Edmonds, R.M. Karp, "Theoretical improvements in the algorithmic efficiency for network flow problems", Journal of the ACM,v.19, 248-264, 1972

....minimum cost. As we show later, we model flow as time units, and cost as energy dissipation. We intend to maximize the flow, i.e. time, but at the same time we want a minimum cost solution. Such problems come under the category of min cost flow problems. These are discussed extensively in [For62] [Edm72]. 4 Combinatorial Optimization for Energy Minimization In this paper, we are trying to schedule nodes in K time slots such that in each time slot there exists at least one connected path from S to T. It can be seen that this amounts to finding K units of flow from S to T such that the node ....

....Coverage with Minimum Power Consumption In the previous sections we explained the construction of a network with from a spatial distribution of sensor nodes. Each node (except S and T) has an associated Ei and Pi. We will try to solve this problem using the theory of mincost flows [For62] [Edm72]. The first requirement of any network problem is to have a network with edge capacities. The Mincost flow problem also needs non negative cost per unit flow for each edge. The network also needs to be directed. Our abstraction of the sensor nodes generates an undirected graph having a set of ....

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J. Edmonds, R.M. Karp, "Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems". In Procs Journal of the Association for Computation Machine, Vol 19, No 2, April 1972, pp. 248-264

....on cycle canceling [22] and achieves a running time of O(n4h min log(nC) n 2 log n ) See [15] for a recent survey of submodular flow algorithms. The dual approach to scaling costs is to instead scale the capacities. The prototype capacity scaling min cost flow algorithm is the Edmonds Karp [5] algorithm that scales and then rounds the capacities. Generalizing this to submodular flow is difficult because rounding a scaled submodular function does not preserve submodularity. To obviate this difficulty, the algorithm in [19] adds a small multiple of the strictly submodular function b ....

....flow problems. We assume throughout this section that l, u and f are integer valued. 5.1 Algorithm Overview To obtain a polynomial time algorithm, we embed a variant of the successive shortest path algorithm within a capacity scaling framework. For the minimum cost flow problem, Edmonds and Karp [5] propose a capacity scaling algorithm that maintains reduced cost optimality condi tions while rounding the arc capacities. We modify the Edmonds Karp algorithm by attaching a complete directed graph on the node set, which effectively relaxes the submodular constraints. Without loss of ....

J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM, 19 (1972), 248-264,. 18

....for any set A , the fraction of edges leading to a set X U increases or decreases by an additive amount of at most O(e) We now go into more detail in describing and analyzing Step 5. To remove the appropriate edges, we solve a max flow problem using the Edmonds Karp polynomial time algorithm [12]. We begin with graph G4 and form a directed graph from it. From the construction all the nodes of O have degree dt, t(O) 1 4e)d(Oh) and all the nodes of have degree either dt, t( J or [dt, t( where dt, t( lull dt, t(U) At the end of Step 5 the graph will have nodes U s with degrees ....

J. Edmonds and R. Karp. Theoretical improvements in the algorithmic efficiency for network flow problems. Journal of the ACM, 19:248 264, 1972.

....is quite trivial: we have cost(a) 1 if a is an overnight arc, and cost(a) 0 for all other arcs. Having this model, we can apply standard min cost circulation algorithms, based on mincost augmenting paths and cycles ( Jewell [1958] Iri [1960] Busacker and Gowen [1960] Edmonds and Karp [1972]) or on out of kilter (Fulkerson [1961] Minty [1960] Implementation gives solutions of the problem (for the above data) in about 0.05 CPUseconds on an SGI R4400. See also the classical standard reference Ford and Fulkerson [1962] and the recent encyclopedic treatment Ahuja, Magnanti, and ....

J. Edmonds, R.M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, Journal of the Association for Computing Machinery 19 (1972) 248--264.

....vector x i 1 x i in each iteration, in order to result in a polynomial number of overall iterations. We give two examples. In augmenting path algorithms for the max flow problem, a shortest augmenting path or one with largest residual capacity helps to obtain a polynomial time algorithm [4]. In cycle canceling algorithms for the min cost flow problem, in each iteration flow is to be augmented along a negative cycle with, e.g. minimum (mean) cost [5] Main Result. We present two primal algorithms for solving the integer programming problem (1) Both algorithms assume that at any ....

J. Edmonds and R. M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, Journal of the Association for Computing Machinery 19 (1972), 248 -- 264.

....are integer, there exists an integer valued maximum flow. If we choose always a shortest r Gamma s path in D f as our flow augmenting path P (that is, with a minimum number of arcs) then the number of iterations is at most jV j Delta jAj. This was shown by Dinits [5] and Edmonds and Karp [6]. Exercise 3. Determine with the maximum flow algorithm an r Gamma s flow of maximum value and an r Gamma s cut of minimum capacity in the following graphs (where the numbers at the arcs give the capacities) i) 1 11 5 2 5 1 2 4 2 7 4 10 1 2 2 2 r s 2 (ii) 12 7 3 4 1 1 3 1 9 1 11 2 1 3 2 3 ....

J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, Journal of the Association for Computing Machinery 19 (1972) 248--264.

....If we have a sustainable static injection process, then there must be some fixed set of flow paths that can be used to send the injected flow to the destination. This set of paths can be easily obtained by solving the single commodity flow problem using, for instance, the Edmonds Karp method [10]. Given these paths, an optimal solution to send the injected flow is simply to send it along these paths without waiting. In this case, the amount of flow in the system (and therefore the amount of active flow) is bounded by the sum of the lengths of the paths. This sum is always bounded by the ....

J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM, 19(2):248--264, 1972.

....In order to find a maxsize match that is also a maxweight LPF match, the maxsize algorithm must give appropriate preference to requests when searching for a match. The problem, however, is that existing maxsize algorithms generally do not take preference into consideration when finding a match [13][18][23] 67] Nonetheless, it is possible to modify an existing maxsize algorithms to find an LPF match. Specifically, the search algo N 2 N N ON 2 N log ( ON N log ( CHAPTER 3 The LPF Algorithm 51 rithms may be changed so as to favor a request based on input and output occupancies. As an ....

....algorithms to find an LPF match. Specifically, the search algo N 2 N N ON 2 N log ( ON N log ( CHAPTER 3 The LPF Algorithm 51 rithms may be changed so as to favor a request based on input and output occupancies. As an example, we choose to modify the well known Edmonds Karp algorithm [13][18]. We later prove that the modified algorithm finds a maxsize match which is also a maxweight LPF match. Moreover, we show that the modification does not increase the complexity either of the running time or of the arithmetic. The analysis of the running time is described later in the section. ....

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Edmonds, J.; Karp, R.M.; "Theoretical improvements in algorithmic efficiency for network flow problems," Journal of the Association for Computing Machinery, April 1972. vol.19, no.2, pp. 248-264.

....a n b ) log n ng) worst case time. Here n a is the number of affected nodes, and n b is the number of nodes considered by the algorithm and maintaining both the distance and the parent in the shortest paths tree. The common idea behind these algorithms is to use a technique of Edmonds and Karp [6], which allows it to transform the weight of each arc in a digraph into a non negative real without changing the shortest paths, and to apply an adaptation of Dijkstra s algorithm to the modified graph. Differently from the case where all arc weights are non negative (for which no efficient ....

....fully dynamic algorithms: 1) the algorithm in [10] referred as FMN; 2) the algorithm in [16] referred as RR; 3) a simple variant of FMN, denoted as DFMN; 4) a new simple algorithm we suggest, denoted as DF. The common idea behind all these algorithms is to use a technique of Edmonds and Karp [6], which allows it to transform the weight of each arc in a digraph into a non negative real without changing the shortest paths. This is done as follows: after an input update, for each (z; v) 2 A, replace w z;v with the reduced weight r z;v = d(z) w z;v Gamma d(v) and apply an adaptation of ....

J. Edmonds, R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM, 19:248--264, 1972.

....and iteratively increases the value of the flow until it reaches the maximum. Every increase in the flow is due to an augmenting path from s to t. The contribution of an augmenting path p in increasing the value of the flow is r f (p) min (u;v)2p r(u; v) Based on this method, Edmonds and Karp [15] develop the shortest augmenting path algorithm whose running time is O(jV j Theta jEj 2 ) where jV j is the number of vertices and jEj the number of edges. Improvements have followed. Galil and Naamad [18] obtain an O(jV j Theta jEj Theta log 2 jV j) time algorithm, which is the first ....

J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. In R. K. Guy, H. Hanani, N. Sauer, and J. Schonheim, editors, Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications, pages 93--96. Gordon and Breach, New York, London, Paris, 1970.

....the machinery which allows us to design polynomial time combinatorial algorithms for the generalized circulation problem. We present two algorithms, one based on the repeated application of a minimum cost flow subroutine, and another based on the idea of augmenting along a biggest improvement path [4] and the idea of canceling negative cycles [14, 21] We assume that the capacities are integers represented in binary, each gain is given as a ratio of two integers, and denote the value of the biggest integer used to represent the gains and capacities by B. Under these assumptions, the first ....

....We have presented two polynomial time combinatorial algorithms for the generalized circulation problem. The first algorithm is based on the repeated application of a minimum cost flow subroutine; the second algorithm is based on the idea of augmenting along the biggest improvement path [4] and the idea of canceling negative cycles [14, 21] Previous polynomial time algorithms for the problem were based on general purpose linear programming techniques, and the combinatorial structure of the problem was used solely for improving the efficiency of computing the required matrix ....

J. Edmonds and R. M. Karp. Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems. J. Assoc. Comput. Mach., 19:248--264, 1972.

....lower bound PCPS for the maximum flow problem. The above protocol uses a proof of size O(jf j) For larger flows, it may be desirable to find a protocol that uses a proof whose size is polynomial in n, even at the cost of requiring a slightly less efficient verifier. We use the result of [EK72] which shows that any flow can be decomposed into at most m (where m is the number of edges in the graph) path flows. The weighted version of the constraint enforcement protocol can be used to give a protocol with runtime O( n=ffl) lg n) Corollary 18 There is an ( n=ffl) lg n) approximate lower ....

J. Edmonds and R. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. J. of the ACM, 19(2):248--264, 1972.

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J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the Association for Computing Machinery, 19:248--264, 1972.

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J. Edmonds and R. M. Karp, "Theoretical improvements in algorithmic efficiency for network flow problems," Journal of ACM, vol. 19, No. 2, 1990.

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Edmonds, J. and Karp, R.M., "Theoretical improvements in algorithmic efficiency for network flow problems," J. ACM 19 pp. 248-264 (1972). As cited in reference [45].

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Edmonds, J. and Karp, R.M., "Theoretical improvements in algorithmic efficiency for network flow problems," J. ACM 19 pp. 248-264 (1972).

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J. Edmonds, R.M. Karp, "Theoretical improvements in algorithmic efficiency for network flow problems," Journal of the ACM, 19(1972), pp. 248--264.

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J. Edmonds and R. M. Karp. Theoretical improvements in the algorithmic efficiency for network flow problems. Journal of the ACM, 19:248--264, 1972.

No context found.

Edmonds, J. and Karp, R.M., "Theoretical improvements in algorithmic efficiency for network flow problems," J. ACM 19 pp. 248-264 (1972).

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J. Edmonds and R. M. Karp, "Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems," J Assoc. Comput. Mach., vol. 19, pp. 248--264, 1972.

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Edmonds, J., and Karp, R. M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems. J. Assoc. Comput. Math., Vol 19, 1972.

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J. Edmonds and R.M. Karp. Theoretical improvements in the algorithmic efficiency for network flow problems. Journal of the ACM, 19:248--264, 1972. 52

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