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STOC

2007

ACM

2007

ACM

Given as input a directed graph on N vertices and a set of source-destination pairs, we study the problem of routing the maximum possible number of source-destination pairs on paths, such that at most c(N) paths go through any edge. We show that the problem is hard to approximate within an N(1/c(N)) factor even when we compare to the optimal solution that routes pairs on edge-disjoint paths, assuming NP doesn't have NO(log log N) -time randomized algorithms. Here the congestion c(N) can be any function in the range 1 c(N) log N/ log log N for some absolute constant > 0. The hardness result is in the right ballpark since a factor NO(1/c(N)) approximation algorithm is known for this problem, via rounding a natural multicommodity-flow relaxation. We also give a simple integrality gap construction that shows that the multicommodity-flow relaxation has an integrality gap of N(1/c) for c ranging from 1 to ( log n log log n ). A solution to the routing problem involves selecting whi...

Related Content

Added |
03 Dec 2009 |

Updated |
03 Dec 2009 |

Type |
Conference |

Year |
2007 |

Where |
STOC |

Authors |
Julia Chuzhoy, Venkatesan Guruswami, Sanjeev Khanna, Kunal Talwar |

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