Citations: Finding a minimum feedback arc set in reducible flow graphs

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V. Ramachandran (1988), Finding a minimum feedback arc set in reducible flow graphs, in 'Journal of Algorithms', Vol. 9, pp. 299--313

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Placing Forced Checkpoints in Distributed Real-Time Embedded.. - Chiu, Chiu (2002) (1 citation) (Correct)

....is only one checkpoint vertex in Vh, we can find the optimal solution using max flow min cut algorithm. Moreover, many MSCCs can be characterized as reducible flow graphs [25] Optimal solutions for reducible flow graphs may also be obtained in polynomial time by using Ramachandran s algorithm [20]. For example, in Figure 5, the MSCC H contains only one checkpoint vertex C,2 and MSCC H2 is a reducible flow graph. The solutions for the MSCCs H, H2 and Hs of Fig. 5 are x , x4 and x7, x9 , respectively. All three solutions are optimal in this case. Figure 5. The MSCCs for the ZC digraph of ....

V. Ramachandran "Finding a minimum feedback arc set in re-ducible flow graphs"Journal of algorithms, pp. 299-313, 1988

Feedback Set Problems - Festa, Pardalos, Resende (1999) (7 citations) (Correct)

....time to be performed. 4.3. State of the art of feedback arc set problems. In the literature of feedback set problems most of the proposed algorithms are designed to solve the problem in vertex weighted graphs. One of the pioneering papers on feedback arc set problems is due to to Ramachandran [73], where it is proved that finding a minimum feedback arc set in an arc weighted reducible flow graph is as difficult as finding a minimum cut in a flow network. The proposed algorithm has complexity O m n 2 log n 2 m , where m T E G and n T V G . The algorithm was ....

V. Ramachandran, Finding a minimum feedback arc set in reducible flow graphs, Journal of Algorithms Vol.9 (1988) pp. 299-313.

The Parallel Complexity of Approximation Algorithms for the.. - Greenlaw (1990) (Correct)

....algorithms with the parallelizable ones. The differences are small. The maximum acyclic subgraph problem is to find a subgraph H of a directed graph G with the properties that H is acyclic and has cardinality as large as possible. This problem and variations of it have been studied before [12, 18, 5, 2]. An equivalent formulation of the problem called the feedback arc set problem was proved NP complete by Karp [12] A similar problem involving vertices instead of arcs called the feedback vertex set problem was also proved NP complete [12] There are weighted versions of both of these problems as ....

....these reductions rely on the edges vertices being weighted with arbitrary values. When the weights are restricted to unary values, there are RNC algorithms for both problems [17] The restrictions to reducible flow graphs are important here because the problems are known to be in P in these cases [19, 18]. Other versions of the feedback arc set problem and the feedback vertex set problem are in P when restricted to completely contractible graphs [14] The reductions presented in this paper do not rely on weights, although it follows from our results that weighted versions of the decision ....

V. Ramachandran. Finding a minimum feedback arc set in reducible flow graphs. Journal of Algorithms, 9(3):299--313, 1988.

Approximations For The Maximum Acyclic Subgraph Problem - Hassin, Rubinstein (1994) (10 citations) (Correct)

.... these algorithms is O(n 3 ) Ga1] and O(n 5=2 log(nW ) where W is the largest magnitude of an arc weight (and the weights are assumed to be integral) Ga2] The problem is also polynomially solvable for the more general class of K 3;3 free graphs [PN] and the classes of reducible flow graphs [Ram] and weakly acyclic graphs [GJR] A variation of the problem in which the objective is to minimize the greatest outdegree of a vertex in the subgraph (V; A 00 ) can be solved in linear time [LS] The problem has a variety of applications such as ordering alternatives by group voting, determining ....

.... (V; A 00 ) can be solved in linear time [LS] The problem has a variety of applications such as ordering alternatives by group voting, determining of a hierarchy of the sectors of an economy, determining ancestry relationships, analysis of systems with feedback, and certain scheduling problems [Fl, J, Ram]. Flood [Fl] used the relation of the problem to quadratic assignment for developing an efficient branch and bound algorithm. Junger [J] studied the acyclic subgraph polytope. The maximum acyclic subgraph and minimum feedback arc set problems are equivalent with respect to their optimal solution. ....

V. Ramachandran, "Finding a minimum feedback arc set in reducible flow graphs", J. of Algorithms 9 299-313, 1988.

A Contraction Algorithm for finding Minimal Feedback Sets - Koehler (2005) (Correct)