Minimum Feedback Arc Sets for a Directed Graph

Younger, D. H.

doi:10.1109/tct.1963.1082116

Cited by 93 publications

(47 citation statements)

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“…A directed graph contains a cycle if there exists a backward edge during a DFS (Depth First Search). This means that removing all backward edges ensures that the VCG contain no cycles [12]. To remove a cycle, a net on the cycle is split into multiple nets and a vertical dogleg is inserted [3].…”

Section: Contact Cycle Removal: Dogleggingmentioning

confidence: 99%

QCA channel routing with wire crossing minimization

Smith

Lim

2005

Proceedings of the 15th ACM Great Lakes Symposium on VLSI

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Quantum-dot Cellular Automata (QCA) is a novel computing mechanism that can represent binary information based on spatial distribution of electron charge configuration in chemical molecules. QCA layout is currently restricted to a single layer with very limited number of wire crossing permitted. Thus, wire crossing minimization is crucial in improving the manufacturability of QCA circuits. In this article, we present the first QCA channel routing algorithm for wire crossing minimization. Our channel routing algorithm is able to reduce crossings, where Left-Edge First, Yoshimura and Kuh, and topologically-based algorithms fail to do so.

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Section: Contact Cycle Removal: Dogleggingmentioning

confidence: 99%

QCA channel routing with wire crossing minimization

Smith

Lim

2005

Proceedings of the 15th ACM Great Lakes Symposium on VLSI

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“…With asymmetric data, the most popular seriation objective function has been to find the ordering of the stimuli maximizing the sum of the elements within one triangle (say, the lower triangle) which simultaneously minimizes the (Baker & Hubert, 1977), dynamic programming (Hubert & Arabie, 1986;Hubert & Golledge, 1981), and simulated annealing (De Soete et al, 1988) The seriation algorithm presented here is a slight adaptation of a nonmetric counting rule suggested by Hubert and Golledge (1981) and has relationships to early procedures proposed by Kendall (1955) and Flueck and Korsh (1974). From (Younger, 1963) (Hubert, 1976, pp. 35, 44 Rodgers, 1988 Table 5.…”

Section: Models Of Asymmetric Relationshipsmentioning

confidence: 99%

Seriation and Multidimensional Scaling: A Data Analysis Approach to Scaling Asymmetric Proximity Matrices

Rodgers

Thompson

1992

Applied Psychological Measurement

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“…For instance, using Younger's conditions (Younger, 1963), it may be possible to strengthen considerably the heuristic search through a rather minimal increase in computational time. In particular, suppose some sequencing of the n objects in 8 is given:…”

Section: A Two-stage Heuristicmentioning

confidence: 99%

Applications of combinatorial programming to data analysis: Seriation using asymmetric proximity measures

Baker¹,

Hubert²

1977

Brit J Math & Statis

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Based on a given Bsymmetric proximity function, a two-stage computetional heuristic for sequencing a set of objmts along a continuum is presented and illustrated with the type of example common in the paired-comparison literature. The first stage, defined by the pairwise interchange of objects, is intended to generate reasonably good orderinga from randomly chosen initial starts; the second stage c m be considered to be a refinement phase and depends on a general condition for m optimal solution suggested by Younger involving the interchange of consecutively placed groups of objects. An extension of the heuristic is also described that allows the selection and sequencing of a subset of all the possible objects.

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Minimum Feedback Arc Sets for a Directed Graph

Cited by 93 publications

References 0 publications

QCA channel routing with wire crossing minimization

QCA channel routing with wire crossing minimization

Seriation and Multidimensional Scaling: A Data Analysis Approach to Scaling Asymmetric Proximity Matrices

Applications of combinatorial programming to data analysis: Seriation using asymmetric proximity measures

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