A Constraint-Based Approach to the Golomb Ruler Problem

A Golomb ruler with m marks can be defined as a set of m distinct integers such that the differences between them are all distinct. An optimal Golomb ruler minimizes the value of the largest mark. The Golomb ruler problem is highly combinatorial and difficult to solve efficiently even for small sizes. Golomb rulers and related problems play an important role in, e.g., radio communication, VLSI architectures, convolutional selforthogonal codes and radio-astronomy. We propose a combination of constraint programming and improved lower bounds in order to solve it. In particular, we introduce a new lower bound based on minimum weight matchings and multi-decompositions. Experimental results are given.

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