Analysis Of The Golomb Ruler And The Sidon Set Problems And Determination Of Large Near-Optimal Golomb Rulers (2002) [3 citations — 0 self]
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author = {Apostolos Dimitromanolakis},
title = {Analysis Of The Golomb Ruler And The Sidon Set Problems And Determination Of Large Near-Optimal Golomb Rulers},
institution = {},
year = {2002}
}
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Abstract:
Golomb rulers have extensive uses in communications, from optimal spectrum allocation, to antenna design. This work presents efficient algorithms for the creation of near optimal rulers with a high number of marks. Furthermore, this work computationally extends the search for sub-quadratic rulers from the previously known figure of 150 marks up to 65,000 marks. The first part of this thesis presents in detail the equivalence of the optimal bounding functions related to Golomb rulers vs. Sidon sets. The theorems provided in this paper allow for easy restatement of present and future results between the two problems and are used to prove a near-quadratic lower bound for the length of Golomb rulers. The second part describes two new constructions and all the previously known ones which produce Sidon sets, so that they can be applied to Golomb rulers. Based on the Ruzsa and the Bose-Chowla constructions, two efficient algorithms are developed and applied in computational search for near-optimal Golomb rulers. This search extends the verification of a conjecture on both Sidon sets (by Erd\H os) and Golomb rulers (by Atkinson et. al.), which states that rulers of sub-quadratic size exist for any number of marks.
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