## Abstract

The placement problem that minimizes the channel density in the standard cell (polycell) layout is considered. This problem is formalized as a min-cut arrangement problem for a given bipartite graph G equals (A, B, E), where the vertices of A and B are placed on two different rows. It is shown that this problem is NP-hard even when the positions of the vertices in A are fixed. In this restricted version, an O(nlog n) optimal algorithm is given for three-regular bipartite graphs. Also given are a three-approximation algorithm for regular bipartite graphs, i. e. , an algorithm whose answer is guaranteed not to be more than a factor of three of the optimal solution, and a (d plus 1)-approximation algorithm for bipartite graphs with degree at most d.

Original language | English (US) |
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Title of host publication | Unknown Host Publication Title |

Publisher | IEEE |

Pages | 466-469 |

Number of pages | 4 |

ISBN (Print) | 0818608145 |

State | Published - Dec 1 1987 |

## All Science Journal Classification (ASJC) codes

- Engineering(all)