Journal
PHYSICAL REVIEW LETTERS
Volume 102, Issue 23, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.102.238703
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Funding
- Swiss National Research Foundation [200020-116286]
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Navigability of networks, that is, the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small world networks provided that a special recipe was used to establish long range connections, and that a greedy algorithm, that ensures that the destination will be reached, is used. Here we provide an exact solution for the asymptotic behavior of such a greedy algorithm as a function of the system's parameters. Our solution enables us to show that the original claim that only a very special construction is optimal can be relaxed depending on further constraints, such as, for example, cost minimization, that must be satisfied.
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