Abstract
A Golomb Ruler (GR) is a set of integer marks along an imaginary ruler such that all the distances of the marks are different. Computing a GR of minimum length is associated to many applications (from astronomy to information theory). Although not yet demonstrated to be NP-hard, the problem is computationally very challenging. This brief note proposes a new continuous optimization model for the problem and, based on a given theoretical result and some computational experiments, we conjecture that an optimal solution of this model is also a solution to an associated GR of minimum length.
Highlights
Given a positive integer n, the Golomb Ruler Problem (GRP) asks for locating n integer marks along an imaginary ruler such that all distances between pairs of marks are distinct and the length of the ruler is minimum [3,6]
We say that we have a Golomb Ruler (GR), given n marks, when the associated distances are all different, and an Optimal Golomb Ruler (OGR), when a GR has the smallest length
We present a new model to the GRP based on a continuous optimization formulation (Sect. 2.1)
Summary
Given a positive integer n, the Golomb Ruler Problem (GRP) asks for locating n integer marks along an imaginary ruler such that all distances between pairs of marks are distinct and the length of the ruler is minimum [3,6]. We say that we have a Golomb Ruler (GR), given n marks, when the associated distances are all different, and an Optimal Golomb Ruler (OGR), when a GR has the smallest length. Federal University of Sao Paulo, Science and Technology Institute, Sao Jose dos Campos, Brazil.
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