### Abstract

In this paper, we present an ()(l) time algorithm to solve the minimum coloring problem defined on a set of intervals, which is also called the channel assignment problem. This problem has not been solved in O(1) time before, even on the idealistic CRCW PRAM model. For large-sized problems, it is desirable to have fast hardware solutions. Our algorithm is based on the processor arrays with a reconfigurable bus system (abbreviated to PARBS) that consists of a processor array and a reconfigurable bus system. In order to solve this problem with constant time complexity, we first transform the “left-edge” channel assignment algorithm to the parenthesis-matching problem. Based on this novel scheme, we are able to explore constant-time parallel algorithms to solve the minimum coloring problem for n intervals, which is also called the channel assignment problem, on a PARBS with ()(n2) processors.

Original language | English |
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Pages (from-to) | 884-890 |

Number of pages | 7 |

Journal | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |

Volume | 13 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1994 Jul |

### Keywords

- Complexity
- channel assignment problem
- computation model
- minimum-coloring problem
- parallel processing
- processor array
- reconfigurable bus system

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering