12-12-2013, 01:06 PM
We introduce the Upgrading Shortest Paths Problem, a new
combinatorial problem for improving network connectivity with a wide
range of applications from multicast communication to wildlife habitat
conservation. We define the problem in terms of a network with node
delays and a set of node upgrade actions, each associated with a cost and
an upgraded (reduced) node delay. The goal is to choose a set of upgrade
actions to minimize the shortest delay paths between demand pairs of
terminals in the network, subject to a budget constraint. We show that
this problem is NP-hard. We describe and test two greedy algorithms
against an exact algorithm on synthetic data and on a real-world instance
from wildlife habitat conservation. While the greedy algorithms can do
arbitrarily poorly in the worst case, they perform fairly well in practice.
For most of the instances, taking the better of the two greedy solutions
accomplishes within 5% of optimal on our benchmarks.
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combinatorial problem for improving network connectivity with a wide
range of applications from multicast communication to wildlife habitat
conservation. We define the problem in terms of a network with node
delays and a set of node upgrade actions, each associated with a cost and
an upgraded (reduced) node delay. The goal is to choose a set of upgrade
actions to minimize the shortest delay paths between demand pairs of
terminals in the network, subject to a budget constraint. We show that
this problem is NP-hard. We describe and test two greedy algorithms
against an exact algorithm on synthetic data and on a real-world instance
from wildlife habitat conservation. While the greedy algorithms can do
arbitrarily poorly in the worst case, they perform fairly well in practice.
For most of the instances, taking the better of the two greedy solutions
accomplishes within 5% of optimal on our benchmarks.
[ATTACHMENT NOT FOUND]