### Abstract

Delay constrained path selection is concerned with finding a source-to-destination path so that the delay of the path is within a given delay bound. When the network is modeled by a directed graph where the delay of a link is a random variable with a known mean and a known variance, the problem becomes that of computing a most probable delay constrained path. In this paper, we present a comprehensive theoretical study of this problem. First, we prove that the problem is NP-hard. Next, for the case where there exists a source-to-destination path with a delay mean no more than the given delay bound, we present a fully polynomial time approximation scheme. In other words, for any given constant ε such that 0 < ε < 1, our algorithm computes a path whose probability of satisfying the delay constraint is at least (1-\epsilon ) times the probability that the optimal path satisfies the delay constraint, with a time complexity bounded by a polynomial in the number of network nodes and 1/ε. Finally, for the case where any source-to- destination path has a delay mean larger than the given delay bound, we present a simple approximation algorithm with an approximation ratio bounded by the square root of the hop count of the optimal path.

Original language | English (US) |
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Article number | 5740849 |

Pages (from-to) | 738-744 |

Number of pages | 7 |

Journal | IEEE Transactions on Computers |

Volume | 61 |

Issue number | 5 |

DOIs | |

State | Published - Apr 18 2012 |

### Keywords

- Delay constrained path selection
- approximation schemes
- computational complexity

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

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## Cite this

*IEEE Transactions on Computers*,

*61*(5), 738-744. [5740849]. https://doi.org/10.1109/TC.2011.61