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Issue No.07 - July (2000 vol.11)

pp: 749-759

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.877833

ABSTRACT

<p><b>Abstract</b>—Ad hoc networks are self-organizing entities that are deployed on demand in support of various events including collaborative computing, multimedia classroom, disaster-relief, search-and-rescue, interactive mission planning, and law enforcement operations. One of the fundamental tasks that have to be addressed when setting up an ad hoc network (AHN, for short) is <it>initialization</it>. This involves assigning each of the <tmath>$n$</tmath> stations in the AHN a distinct ID number (e.g., a local IP address) in the range from <tmath>$1$</tmath> to <tmath>$n$</tmath>. Our main contribution is to propose efficient randomized initialization protocols for AHNs. We begin by showing that if the number <tmath>$n$</tmath> of stations is known beforehand, an <tmath>$n$</tmath>-station, single-channel AHN can be initialized with probability exceeding <tmath>$1-{1\over n}$</tmath>, in <tmath>$en + O( \sqrt {n \log n})$</tmath> time slots, regardless of whether the AHN has collision detection capability. We then go on to show that even if <tmath>$n$</tmath> is not known in advance, an <tmath>$n$</tmath>-station, single-channel AHN with collision detection can be initialized with probability exceeding <tmath>$1-{1\over n}$</tmath>, in <tmath>${\frac{10n}{3}} + O(\sqrt { n \ln n})$</tmath> time slots. Using this protocol as a stepping stone, we then present an initialization protocol for the <tmath>$n$</tmath>-station, <tmath>$k$</tmath>-channel AHN with collision detection that terminates with probability exceeding <tmath>$1-{1\over n}$</tmath>, in <tmath>${\frac{10n}{3k}} + O \left( \sqrt { {\frac{n \ln n}{k}}}\right )$</tmath> time slots. Finally, we look at the case where the collision detection capability is not present. Our first result in this direction is to show that the task of electing a leader in an <tmath>$n$</tmath>-station, single-channel AHN can be completed with probability exceeding <tmath>$1-{1\over n}$</tmath>, in fewer than <tmath>$11.37(\log n)^2 + 2.39 \log n$</tmath> time slots. This leader election protocol allows us to design an initialization protocol for the <tmath>$n$</tmath>-station, single-channel AHN with no collision detection that terminates with probability exceeding <tmath>$1-{1\over n}$</tmath>, in fewer than <tmath>$5.67n + O(\sqrt {n \ln n})$</tmath> time slots, even if <tmath>$n$</tmath> is not known beforehand. We then discuss an initialization protocol for the <tmath>$n$</tmath>-station, <tmath>$k$</tmath>-channel AHN with no collision detection that terminates with probability exceeding <tmath>$1-{1\over n}$</tmath>, in fewer than <tmath>$5.67{\frac{n}{k}} + O \left (\sqrt {\frac{n \ln n}{k}} \right )$</tmath> time slots, whenever <tmath>$k \leq {\frac{n}{(\log n)^3}}$</tmath>.</p>

INDEX TERMS

Ad hoc networks, hierarchical networks, clustering, leader election, collaborative computing, initialization.

CITATION

Koji Nakano, Stephan Olariu, "Randomized Initialization Protocols for Ad Hoc Networks",

*IEEE Transactions on Parallel & Distributed Systems*, vol.11, no. 7, pp. 749-759, July 2000, doi:10.1109/71.877833