Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach

Cheung, Tsang

doi:10.1145/355900.355910

Cited by 7 publications

(8 citation statements)

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“…We should also note that the time used to set up the networks in our method is no greater (and generally smaller because fewer flow computations are done) than that used in the previous methods [16], [2], [23]. So our method reduces dramatically the time needed for the flow computations while not increasing the bookkeeping time.…”

Section: ~I4)[w(ij) X D(ij)] Where D(ij) Is the Distance Between mentioning

confidence: 88%

“…Below we outline a solution, due to Picard and Ratliff [16], for the one-dimensional layout problem. A similar solution was developed by Cheung [2] and by Trubin [23]. For a one-dimensional problem, Picard and Ratliff [16] show that the distance between each fixed point can be assumed to be one, and also that there is an optimal solution where each new point is placed on top of a fixed point.…”

Section: ~I4)[w(ij) X D(ij)] Where D(ij) Is the Distance Between mentioning

confidence: 96%

“…Define the function F(2) to be the value of the maximum flow in G (2). If the capacity functions out of s and into t are affine functions of 4, then it is easy to see that F(2) is a piecewise linear function with at most n breakpoints [20], [7].…”

Section: G(2k) Can Be Computed On-line In Total Time O(nm Log(n2/mentioning

confidence: 99%

“…Flow fz satisfies the properties of flow f in condition (1), and flow fmax satisfies the properties of fR in condition (2). Thus the next 41 value which falls in the range 4x < 4i < 4m.x can have its flow computed by ,continuing the flow from fl, since 4mi~, 41, 4i form an increasing sequence; also, 2i can have its flow computed from 4ma x since 41 is the next value in the decreasing sequence 2m.x; 4i, and no flow computation has yet been charged to 4max.…”

Section: Complexity Analysismentioning

confidence: 99%

“…Thus with this structure it is easy, given a 2 value, to find a minimum cut for G (2). We note that this problem is solved in GGT only when the edge capacities are monotone afline* functions of 2.…”

Section: A Sequence Of K Minimum Cuts In a Monotone Parametric Flow Nmentioning

confidence: 99%

See 4 more Smart Citations

A fast algorithm for the generalized parametric minimum cut problem and applications

Gusfield

Martel

1992

Algorithmica

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Abstract. Many combinatorial optimization problems are solved by a sequence of network flow computations on a network whose edge capacities are given as a function of a parameter 2. Recently Gallo et al. I-7] made a major advance in solving such parametric flow problems. They showed that for an important class of networks, called monotone parametric flow networks, a sequence of O(n) flow computations could be solved in the same worst-case time bound as a single flow. However, these results require one of two special assumptions: either that the 2 values are presented in increasing or decreasing order; or that the edge capacity functions are affine functions of 2. In this paper we show how to remove both of these assumptions while obtaining the same running times as in [7]. This observation generalizes and unifies the two major results of 1-7], and allows its ideas to be applied to many new combinatorial problems. Of greatest importance, it allows the efficient application of binary search and successive binary search to a sequence of network flow problems.

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Section: ~I4)[w(ij) X D(ij)] Where D(ij) Is the Distance Between mentioning

confidence: 88%