An efficient method for finding a minimal feedback arc set in directed graphs

  title={An efficient method for finding a minimal feedback arc set in directed graphs},
  author={S. Park and Sheldon B. Akers},
  journal={[Proceedings] 1992 IEEE International Symposium on Circuits and Systems},
  pages={1863-1866 vol.4}
  • S. Park, S. Akers
  • Published 3 May 1992
  • Mathematics
  • [Proceedings] 1992 IEEE International Symposium on Circuits and Systems
Finding a minimum cardinality set of arcs that breaks all cycles in a directed graph is important in the study of large-scale systems with feedback. This problem is viewed as finding an ordering for the vertices in a graph such that the set of arcs from higher to lower numbered vertices becomes minimum. After partitioning the graph into strongly and bi-connected components, depth-first search traversing is performed on each component. Reordering is done so that only backward arcs become… 

An Exact Method for the Minimum Feedback Arc Set Problem

An exact method is proposed for sparse graphs that enumerates simple cycles in a lazy fashion and iteratively extends an incomplete cycle matrix and the practical limits of the new method are evaluated on a test set containing computationally challenging sparse graphs, relevant for industrial applications.

Quasi-source heuristic for the production line formation of a manufacturing system

  • J. ZhouM. BarthR. De Guio
  • Computer Science
    1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929)
  • 1996
In this work, the production line formation problem (PLF-problem) is stated as a classical feedback arc set problem with additional order constraints. The constraint consistency checking, which in

Timing analysis of embedded real-time systems

This work addresses the problem of timing constraint derivation and validation for reactive and real-time embedded systems and makes the codesign methodology timing-driven in that it makes it possible to maintain a handle on the system''s timing correctness from very early stages in the system’s design flow.



Minimum Feedback Arc Sets for a Directed Graph

This paper establishes a relationship between these feedback arcs and order; in particular, such a minimum set of arcs is shown to be determined by a sequential ordering of the nodes which minimizes the number of arcs.

A Linear Time Algorithm for Finding Minimum Cutsets in Reducible Graphs

  • A. Shamir
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1979
It is shown that in reducible graphs (and thus in almost all the “practical” flowcharts of programs), minimum cutsets can be found in linear time and that the linear algorithm can check its own applicability to a given graph, thus eliminating the need of prechecking whether it is reducible or not.

Depth-First Search and Linear Graph Algorithms

The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components

Finding a Minimum Feedback Arc Set in Reducible Flow Graphs

Approximation alogorithms for the maximum acyclic subgraph problem

It is found that all graphs without two-cycles contain large acyclic subgraphs, a fact which was not previously known.

The Design and Analysis of Computer Algorithms

This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.

BALLAST: a methodology for partial scan design

In the proposed partial scan methodology, the scan path is constructed so that the rest of the circuit belongs to a class of circuits called balanced sequential structures. Test patterns for this

Combinational profiles of sequential benchmark circuits

A set of 31 digital sequential circuits described at the gate level is presented. These circuits extend the size and complexity of the ISCAS'85 set of combinational circuits and can serve as